In this paper,we developed a class of the fourth order accurate finite volume Hermite weighted essentially non-oscillatory(HWENO)schemes based on the work(Computers&Fluids,34:642-663(2005))by Qiu and Shu,with Tota...In this paper,we developed a class of the fourth order accurate finite volume Hermite weighted essentially non-oscillatory(HWENO)schemes based on the work(Computers&Fluids,34:642-663(2005))by Qiu and Shu,with Total Variation Diminishing Runge-Kutta time discretization method for the two-dimensional hyperbolic conservation laws.The key idea of HWENO is to evolve both with the solution and its derivative,which allows for using Hermite interpolation in the reconstruction phase,resulting in a more compact stencil at the expense of the additional work.The main difference between this work and the formal one is the procedure to reconstruct the derivative terms.Comparing with the original HWENO schemes of Qiu and Shu,one major advantage of new HWENOschemes is its robust in computation of problem with strong shocks.Extensive numerical experiments are performed to illustrate the capability of the method.展开更多
There is increasing concern about the safety of homologous blood transfusion during cardiac surgery,and a restrictive transfusion practice is associated with improved outcome.Transfusion-free pediatric cardiac surgery...There is increasing concern about the safety of homologous blood transfusion during cardiac surgery,and a restrictive transfusion practice is associated with improved outcome.Transfusion-free pediatric cardiac surgery is unrealistic for the vast majority of procedures in neonates or small infants;however,considerable progress has been made by using techniques that decrease the need for homologous blood products or even allow bloodless surgery in older infants and children.These techniques involve a decrease in prime volume by downsizing the bypass circuit with the help of vacuumassisted venous drainage,microplegia,autologous blood predonation with or without infusion of recombinant(erythropoietin),cell salvaging,ultrafiltration and retrograde autologous priming.The three major techniques which are simple,safe,efficient,and cost-effective are:a prime volume as small as possible,cardioplegia with negligible hydric balance and circuit residual blood salvaged without any alteration.Furthermore,these three techniques can be used for all the patients,including emergencies and small babies.In every pediatric surgical unit,a strategy to decrease or avoid blood bank transfusion must be implemented.A strategy to minimize transfusion requirement requires a combined effort involving the entire surgical team with pre-,peri-,and postoperative planning and management.展开更多
In this paper,we propose a finite volume Hermite weighted essentially non-oscillatory(HWENO)method based on the dimension by dimension framework to solve hyperbolic conservation laws.It can maintain the high accuracy ...In this paper,we propose a finite volume Hermite weighted essentially non-oscillatory(HWENO)method based on the dimension by dimension framework to solve hyperbolic conservation laws.It can maintain the high accuracy in the smooth region and obtain the high resolution solution when the discontinuity appears,and it is compact which will be good for giving the numerical boundary conditions.Furthermore,it avoids complicated least square procedure when we implement the genuine two dimensional(2D)finite volume HWENO reconstruction,and it can be regarded as a generalization of the one dimensional(1D)HWENO method.Extensive numerical tests are performed to verify the high resolution and high accuracy of the scheme.展开更多
This paper presents the development and validation of a fully coupled computational fluid dynamics—discrete element method—volume of fluid(CFD-DEM-VOF)model to simulate the complex behavior of particle-laden flows w...This paper presents the development and validation of a fully coupled computational fluid dynamics—discrete element method—volume of fluid(CFD-DEM-VOF)model to simulate the complex behavior of particle-laden flows with free surfaces.The coupling between the fluid and particle phases is established through the implemented continuity,momentum,and alpha transport equation.The coupled particle forces such as drag,pressure gradient,dense virtual mass,viscous,and interface forces are also integrated,with drag and dense virtual mass forces being dependent on local porosity.The integrated conservative alpha transport equation ensures phase volume conservation during interactions between particles and water.Additionally,we have implemented a trilinear interpolation method designed to operate on unstructured hexahedral meshes.This method has been tested for its ability to properly resolve the coupling effects in the numerical simulations,particularly in cases with a relatively low cell-size ratio.The model is validated through three distinct test cases:single particle water entry,dam break with particles,and water entry of a group of particles case.The experimental setup is built to study the dynamics of the water entry of a group of particles,where three key flow features are analyzed:the evolution of average particle velocity,cavity shape,and particle dispersion cloud profiles in water.The tests involve four different scenarios,including two different water levels(16.1 and 20.1 cm)and two different particle densities(2650 and 4000 kg/m3).High-speed videometry and particle tracking velocimetry(using ImageJ/TrackMate)methods are employed for experimental data acquisition.It is demonstrated that numerical results are in excellent agreement with theoretical predictions and experimental data.The study highlights the significance of vortices in cavity shaping and particle dispersion.The validated CFD-DEM-VOF model constitutes a robust tool for simulating particle-laden flows,contributing valuable insights into the complex 展开更多
In this paper, a reactive dynamic user equilibrium model is extended to simulate two groups of pedestrians traveling on crossing paths in a continuous walking facility. Each group makes path choices to minimize the tr...In this paper, a reactive dynamic user equilibrium model is extended to simulate two groups of pedestrians traveling on crossing paths in a continuous walking facility. Each group makes path choices to minimize the travel cost to its destination in a reactive manner based on instantaneous information. The model consists of a conservation law equation coupled with an Eikonal-type equation for each group. The velocity-density relationship of pedestrian movement is obtained via an experimental method. The model is solved using a finite volume method for the conservation law equation and a fast-marching method for the Eikonal-type equation on unstructured grids. The numerical results verify the rationality of the model and the validity of the numerical method. Based on this continuum model, a number of results, e.g., the formation of strips or moving clusters composed of pedestrians walking to the same destination, are also observed.展开更多
In this paper the authors discuss a numerical simulation problem of three-dimensional compressible contamination treatment from nuclear waste. The mathematical model, a nonlinear convection-diffusion system of four PD...In this paper the authors discuss a numerical simulation problem of three-dimensional compressible contamination treatment from nuclear waste. The mathematical model, a nonlinear convection-diffusion system of four PDEs, determines four major physical unknowns: the pressure, the concentrations of brine and radionuclide, and the temperature. The pressure is solved by a conservative mixed finite volume element method, and the computational accuracy is improved for Darcy velocity. Other unknowns are computed by a composite scheme of upwind approximation and mixed finite volume element. Numerical dispersion and nonphysical oscillation are eliminated, and the convection-dominated diffusion problems are solved well with high order computational accuracy. The mixed finite volume element is conservative locally, and get the objective functions and their adjoint vector functions simultaneously. The conservation nature is an important character in numerical simulation of underground fluid. Fractional step difference is introduced to solve the concentrations of radionuclide factors, and the computational work is shortened significantly by decomposing a three-dimensional problem into three successive one-dimensional problems. By the theory and technique of a priori estimates of differential equations, we derive an optimal order estimates in L2norm. Finally, numerical examples show the effectiveness and practicability for some actual problems.展开更多
We have developed approximate Riemann solvers for ideal MHD equations based on a relaxation approach in [4], [5]. These lead to entropy consistent solutions with good properties like guaranteed positive density. We de...We have developed approximate Riemann solvers for ideal MHD equations based on a relaxation approach in [4], [5]. These lead to entropy consistent solutions with good properties like guaranteed positive density. We describe the extension to higher order and multiple space dimensions. Finally we show our implementation of all this into the astrophysics code FLASH.展开更多
A volume-amending method is developed both to keep the level set function as an algebraic distance function and to preserve the bubble mass in a level set approach for incompressible two-phase flows with the significa...A volume-amending method is developed both to keep the level set function as an algebraic distance function and to preserve the bubble mass in a level set approach for incompressible two-phase flows with the significantly deformed free interface. After the traditional reinitialization procedure, a vol-ume-amending method is added for correcting the position of the interface according to mass loss/gain error until the mass error falls in the allowable range designated in advance. The level set approach with this volume-amending method incorporated has been validated by three test cases: the motion of a single axisymmetrical bubble or drop in liquid, the motion of a two-dimensional water drop falling through the air into a water pool, and the interactional motion of two buoyancy-driven three- dimensional deformable bubbles. The computational results with this volume-amending method in-corporated are in good agreement with the reported experimental data and the mass is well preserved in all cases.展开更多
Re-initialization procedure in level-set interface capturing method were investigated. The algorithm accomplishes the re-initialization step through locking the interface positions. Better accuracy was obtained both o...Re-initialization procedure in level-set interface capturing method were investigated. The algorithm accomplishes the re-initialization step through locking the interface positions. Better accuracy was obtained both on the interface positions and the total fluid volume keeping. Though one more step of the interpolations is added in the procedure, there is no significant increase in total machine time spent.展开更多
This paper deals with the Burgers equation which is the most common model used in the nonlinear conservation laws. Here the theoretical aspect of conservation law is discussed by using inviscid Burgers equation. At fi...This paper deals with the Burgers equation which is the most common model used in the nonlinear conservation laws. Here the theoretical aspect of conservation law is discussed by using inviscid Burgers equation. At first, we introduce the general non-linear conservation law as a partial differential equation and its solution procedure by the method of characteristic. Next, we present the weak solution of the problem with entropy condition. Taking into account shock wave and rarefaction wave, the Riemann problem has also been discussed. Finally, the finite volume method is considered to approximate the numerical solution of the inviscid Burgers equation with continuous and discontinuous initial data. An illustration of the problem is provided by some examples. Moreover, the Godunov method provides a good approximation for the problem.展开更多
In this paper the authors discuss the numerical simulation problem of threedimensional compressible contamination treatment from nuclear waste.The mathematical model is defined by an initial-boundary nonlinear convect...In this paper the authors discuss the numerical simulation problem of threedimensional compressible contamination treatment from nuclear waste.The mathematical model is defined by an initial-boundary nonlinear convection-diffusion system of four partial differential equations:a parabolic equation for the pressure,two convection-diffusion equations for the concentrations of brine and radionuclide and a heat conduction equation for the temperature.The pressure appears within the concentration equations and heat conduction equation,and the Darcy velocity controls the concentrations and the temperature.The pressure is solved by the conservative mixed volume element method,and the order of the accuracy is improved by the Darcy velocity.The concentration of brine and temperature are computed by the upwind mixed volume element method on a changing mesh,where the diffusion is discretized by a mixed volume element and the convection is treated by an upwind scheme.The composite method can solve the convection-dominated diffusion problems well because it eliminates numerical dispersion and nonphysical oscillation and has high order computational accuracy.The mixed volume element has the local conservation of mass and energy,and it can obtain the brine and temperature and their adjoint vector functions simultaneously.The conservation nature plays an important role in numerical simulation of underground fluid.The concentrations of radionuclide factors are solved by the method of upwind fractional step difference and the computational work is decreased by decomposing a three-dimensional problem into three successive one-dimensional problems and using the method of speedup.By the theory and technique of a priori estimates of differential equations,we derive an optimal order result in L^(2) norm.Numerical examples are given to show the effectiveness and practicability and the composite method is testified as a powerful tool to solve the well-known actual problem.展开更多
This paper presents a parallel method for simulating real-time 3D deformable objects using the volume preservation mass-spring system method on tetrahedron meshes.In general,the conventional mass-spring system is mani...This paper presents a parallel method for simulating real-time 3D deformable objects using the volume preservation mass-spring system method on tetrahedron meshes.In general,the conventional mass-spring system is manipulated as a force-driven method because it is fast,simple to implement,and the parameters can be controlled.However,the springs in traditional mass-spring system can be excessively elongated which cause severe stability and robustness issues that lead to shape restoring,simulation blow-up,and huge volume loss of the deformable object.In addition,traditional method that uses a serial process of the central processing unit(CPU)to solve the system in every frame cannot handle the complex structure of deformable object in real-time.Therefore,the first order implicit constraint enforcement for a mass-spring model is utilized to achieve accurate visual realism of deformable objects with tough constraint error.In this paper,we applied the distance constraint and volume conservation constraints for each tetrahedron element to improve the stability of deformable object simulation using the mass-spring system and behave the same as its real-world counterparts.To reduce the computational complexity while ensuring stable simulation,we applied a method that utilizes OpenGL compute shader,a part of OpenGL Shading Language(GLSL)that executes on the graphic processing unit(GPU)to solve the numerical problems effectively.We applied the proposed methods to experimental volumetric models,and volume percentages of all objects are compared.The average volume percentages of all models during the simulation using the mass-spring system,distance constraint,and the volume constraint method were 68.21%,89.64%,and 98.70%,respectively.The proposed approaches are successfully applied to improve the stability of mass-spring system and the performance comparison from our experimental tests also shows that the GPU-based method is faster than CPU-based implementation for all cases.展开更多
Hyperbolic balance laws have steady state solutions in which the flux gradients are nonzero but are exactly balanced by the source terms.In our earlier work[31–33],we designed high order well-balanced schemes to a cl...Hyperbolic balance laws have steady state solutions in which the flux gradients are nonzero but are exactly balanced by the source terms.In our earlier work[31–33],we designed high order well-balanced schemes to a class of hyperbolic systems with separable source terms.In this paper,we present a different approach to the same purpose:designing high order well-balanced finite volume weighted essentially non-oscillatory(WENO)schemes and RungeKutta discontinuous Galerkin(RKDG)finite element methods.We make the observation that the traditional RKDG methods are capable of maintaining certain steady states exactly,if a small modification on either the initial condition or the flux is provided.The computational cost to obtain such a well balanced RKDG method is basically the same as the traditional RKDG method.The same idea can be applied to the finite volume WENO schemes.We will first describe the algorithms and prove the well balanced property for the shallow water equations,and then show that the result can be generalized to a class of other balance laws.We perform extensive one and two dimensional simulations to verify the properties of these schemes such as the exact preservation of the balance laws for certain steady state solutions,the non-oscillatory property for general solutions with discontinuities,and the genuine high order accuracy in smooth regions.展开更多
In this paper,we investigate the coupling of the Multi-dimensional Optimal Order Detection(MOOD)method and the Arbitrary high order DERivatives(ADER)approach in order to design a new high order accurate,robust and com...In this paper,we investigate the coupling of the Multi-dimensional Optimal Order Detection(MOOD)method and the Arbitrary high order DERivatives(ADER)approach in order to design a new high order accurate,robust and computationally efficient Finite Volume(FV)scheme dedicated to solve nonlinear systems of hyperbolic conservation laws on unstructured triangular and tetrahedral meshes in two and three space dimensions,respectively.The Multi-dimensional Optimal Order Detection(MOOD)method for 2D and 3D geometries has been introduced in a recent series of papers for mixed unstructured meshes.It is an arbitrary high-order accurate Finite Volume scheme in space,using polynomial reconstructions with a posteriori detection and polynomial degree decrementing processes to deal with shock waves and other discontinuities.In the following work,the time discretization is performed with an elegant and efficient one-step ADER procedure.Doing so,we retain the good properties of the MOOD scheme,that is to say the optimal high-order of accuracy is reached on smooth solutions,while spurious oscillations near singularities are prevented.The ADER technique permits not only to reduce the cost of the overall scheme as shown on a set of numerical tests in 2D and 3D,but it also increases the stability of the overall scheme.A systematic comparison between classical unstructured ADER-WENO schemes and the new ADER-MOOD approach has been carried out for high-order schemes in space and time in terms of cost,robustness,accuracy and efficiency.The main finding of this paper is that the combination of ADER with MOOD generally outperforms the one of ADER and WENO either because at given accuracy MOOD is less expensive(memory and/or CPU time),or because it is more accurate for a given grid resolution.A large suite of classical numerical test problems has been solved on unstructured meshes for three challenging multi-dimensional systems of conservation laws:the Euler equations of compressible gas dynamics,the classical equations of ideal magneto-Hydrod展开更多
To estimate the shape of tapered fibers using tapering machines with movable large-zone furnaces, a new calculation method is proposed based on the discrete deducing method and the principle of the volume conservation...To estimate the shape of tapered fibers using tapering machines with movable large-zone furnaces, a new calculation method is proposed based on the discrete deducing method and the principle of the volume conservation of the fiber materials. This method can estimate the tapering results, i.e., the shape of the tapered fibers, based on arbitrary moving parameters of the large-zone furnace and the fiber holders. The theoretical estimated results agree with the experimental measuring shape of the tapered fibers quite well.展开更多
We propose a numerical solution to incorporate in the simulation of a system of conservation laws boundary conditions that come from a microscopic modeling in the small mean free path regime.The typical example we dis...We propose a numerical solution to incorporate in the simulation of a system of conservation laws boundary conditions that come from a microscopic modeling in the small mean free path regime.The typical example we discuss is the derivation of the Euler system from the BGK equation.The boundary condition relies on the analysis of boundary layers formation that accounts from the fact that the incoming kinetic flux might be far from the thermodynamic equilibrium.展开更多
基金the National Natural Science Foundation of China(Grant No.10671097)the European project ADIGMA on the development of innovative solution algorithms for aerodynamic simu-lations+1 种基金Scientific Research Foundation for the Returned Overseas Chinese ScholarsState Education Ministry and the Natural Science Foundation of Jiangsu Province(Grant No.BK2006511)
文摘In this paper,we developed a class of the fourth order accurate finite volume Hermite weighted essentially non-oscillatory(HWENO)schemes based on the work(Computers&Fluids,34:642-663(2005))by Qiu and Shu,with Total Variation Diminishing Runge-Kutta time discretization method for the two-dimensional hyperbolic conservation laws.The key idea of HWENO is to evolve both with the solution and its derivative,which allows for using Hermite interpolation in the reconstruction phase,resulting in a more compact stencil at the expense of the additional work.The main difference between this work and the formal one is the procedure to reconstruct the derivative terms.Comparing with the original HWENO schemes of Qiu and Shu,one major advantage of new HWENOschemes is its robust in computation of problem with strong shocks.Extensive numerical experiments are performed to illustrate the capability of the method.
文摘There is increasing concern about the safety of homologous blood transfusion during cardiac surgery,and a restrictive transfusion practice is associated with improved outcome.Transfusion-free pediatric cardiac surgery is unrealistic for the vast majority of procedures in neonates or small infants;however,considerable progress has been made by using techniques that decrease the need for homologous blood products or even allow bloodless surgery in older infants and children.These techniques involve a decrease in prime volume by downsizing the bypass circuit with the help of vacuumassisted venous drainage,microplegia,autologous blood predonation with or without infusion of recombinant(erythropoietin),cell salvaging,ultrafiltration and retrograde autologous priming.The three major techniques which are simple,safe,efficient,and cost-effective are:a prime volume as small as possible,cardioplegia with negligible hydric balance and circuit residual blood salvaged without any alteration.Furthermore,these three techniques can be used for all the patients,including emergencies and small babies.In every pediatric surgical unit,a strategy to decrease or avoid blood bank transfusion must be implemented.A strategy to minimize transfusion requirement requires a combined effort involving the entire surgical team with pre-,peri-,and postoperative planning and management.
基金supported by the NSFC grant 12101128supported by the NSFC grant 12071392.
文摘In this paper,we propose a finite volume Hermite weighted essentially non-oscillatory(HWENO)method based on the dimension by dimension framework to solve hyperbolic conservation laws.It can maintain the high accuracy in the smooth region and obtain the high resolution solution when the discontinuity appears,and it is compact which will be good for giving the numerical boundary conditions.Furthermore,it avoids complicated least square procedure when we implement the genuine two dimensional(2D)finite volume HWENO reconstruction,and it can be regarded as a generalization of the one dimensional(1D)HWENO method.Extensive numerical tests are performed to verify the high resolution and high accuracy of the scheme.
基金Sepro Mineral Systems through the Mitacs Accelerate project No:IT12396.We would also like to express our appreciation to Compute Canada and UBC ARC for supporting PIME Lab by granting us access to their high-performance computing platforms.The simulations presented in this work were conducted using the Compute Canada Beluga and UBC ARC Sockeye clusters,both of which contributed equally to the computational resources utilized.
文摘This paper presents the development and validation of a fully coupled computational fluid dynamics—discrete element method—volume of fluid(CFD-DEM-VOF)model to simulate the complex behavior of particle-laden flows with free surfaces.The coupling between the fluid and particle phases is established through the implemented continuity,momentum,and alpha transport equation.The coupled particle forces such as drag,pressure gradient,dense virtual mass,viscous,and interface forces are also integrated,with drag and dense virtual mass forces being dependent on local porosity.The integrated conservative alpha transport equation ensures phase volume conservation during interactions between particles and water.Additionally,we have implemented a trilinear interpolation method designed to operate on unstructured hexahedral meshes.This method has been tested for its ability to properly resolve the coupling effects in the numerical simulations,particularly in cases with a relatively low cell-size ratio.The model is validated through three distinct test cases:single particle water entry,dam break with particles,and water entry of a group of particles case.The experimental setup is built to study the dynamics of the water entry of a group of particles,where three key flow features are analyzed:the evolution of average particle velocity,cavity shape,and particle dispersion cloud profiles in water.The tests involve four different scenarios,including two different water levels(16.1 and 20.1 cm)and two different particle densities(2650 and 4000 kg/m3).High-speed videometry and particle tracking velocimetry(using ImageJ/TrackMate)methods are employed for experimental data acquisition.It is demonstrated that numerical results are in excellent agreement with theoretical predictions and experimental data.The study highlights the significance of vortices in cavity shaping and particle dispersion.The validated CFD-DEM-VOF model constitutes a robust tool for simulating particle-laden flows,contributing valuable insights into the complex
基金supported by grants from the Research Grants Council of the Hong Kong Special Administrative Region, China (HKU 7183/06E)the University of Hong Kong (10207394)the National Natural Science Foundation of China (70629001 and 10771134)
文摘In this paper, a reactive dynamic user equilibrium model is extended to simulate two groups of pedestrians traveling on crossing paths in a continuous walking facility. Each group makes path choices to minimize the travel cost to its destination in a reactive manner based on instantaneous information. The model consists of a conservation law equation coupled with an Eikonal-type equation for each group. The velocity-density relationship of pedestrian movement is obtained via an experimental method. The model is solved using a finite volume method for the conservation law equation and a fast-marching method for the Eikonal-type equation on unstructured grids. The numerical results verify the rationality of the model and the validity of the numerical method. Based on this continuum model, a number of results, e.g., the formation of strips or moving clusters composed of pedestrians walking to the same destination, are also observed.
基金supported by the Natural Science Foundation of Shangdong Province (Grant No.ZR2021MA019)Natural Science Foundation of Hunan Province (Grant No.2018JJ2028)。
文摘In this paper the authors discuss a numerical simulation problem of three-dimensional compressible contamination treatment from nuclear waste. The mathematical model, a nonlinear convection-diffusion system of four PDEs, determines four major physical unknowns: the pressure, the concentrations of brine and radionuclide, and the temperature. The pressure is solved by a conservative mixed finite volume element method, and the computational accuracy is improved for Darcy velocity. Other unknowns are computed by a composite scheme of upwind approximation and mixed finite volume element. Numerical dispersion and nonphysical oscillation are eliminated, and the convection-dominated diffusion problems are solved well with high order computational accuracy. The mixed finite volume element is conservative locally, and get the objective functions and their adjoint vector functions simultaneously. The conservation nature is an important character in numerical simulation of underground fluid. Fractional step difference is introduced to solve the concentrations of radionuclide factors, and the computational work is shortened significantly by decomposing a three-dimensional problem into three successive one-dimensional problems. By the theory and technique of a priori estimates of differential equations, we derive an optimal order estimates in L2norm. Finally, numerical examples show the effectiveness and practicability for some actual problems.
文摘We have developed approximate Riemann solvers for ideal MHD equations based on a relaxation approach in [4], [5]. These lead to entropy consistent solutions with good properties like guaranteed positive density. We describe the extension to higher order and multiple space dimensions. Finally we show our implementation of all this into the astrophysics code FLASH.
基金the National Natural Science Foundation of China (Grant Nos. 20490206, 50404009, 20576133 & 20676134)PetroChina,and the National Basic Research Priorities Program (Grant Nos. 2004CB217604, 2007CB613507)
文摘A volume-amending method is developed both to keep the level set function as an algebraic distance function and to preserve the bubble mass in a level set approach for incompressible two-phase flows with the significantly deformed free interface. After the traditional reinitialization procedure, a vol-ume-amending method is added for correcting the position of the interface according to mass loss/gain error until the mass error falls in the allowable range designated in advance. The level set approach with this volume-amending method incorporated has been validated by three test cases: the motion of a single axisymmetrical bubble or drop in liquid, the motion of a two-dimensional water drop falling through the air into a water pool, and the interactional motion of two buoyancy-driven three- dimensional deformable bubbles. The computational results with this volume-amending method in-corporated are in good agreement with the reported experimental data and the mass is well preserved in all cases.
文摘Re-initialization procedure in level-set interface capturing method were investigated. The algorithm accomplishes the re-initialization step through locking the interface positions. Better accuracy was obtained both on the interface positions and the total fluid volume keeping. Though one more step of the interpolations is added in the procedure, there is no significant increase in total machine time spent.
文摘This paper deals with the Burgers equation which is the most common model used in the nonlinear conservation laws. Here the theoretical aspect of conservation law is discussed by using inviscid Burgers equation. At first, we introduce the general non-linear conservation law as a partial differential equation and its solution procedure by the method of characteristic. Next, we present the weak solution of the problem with entropy condition. Taking into account shock wave and rarefaction wave, the Riemann problem has also been discussed. Finally, the finite volume method is considered to approximate the numerical solution of the inviscid Burgers equation with continuous and discontinuous initial data. An illustration of the problem is provided by some examples. Moreover, the Godunov method provides a good approximation for the problem.
基金The authors express their deep appreciation to Prof.J.Douglas Jr,Prof.R.E.Ewing,and Prof.L.S.Jiang for their many helpful suggestions in the series research on numerical simulation of energy sciences.Also,the project is supported by NSAF(Grant No.U1430101)Natural Science Foundation of Shandong Province(Grant No.ZR2016AM08)National Tackling Key Problems Program(Grant Nos.2011ZX05052,2011ZX05011-004,20050200069).
文摘In this paper the authors discuss the numerical simulation problem of threedimensional compressible contamination treatment from nuclear waste.The mathematical model is defined by an initial-boundary nonlinear convection-diffusion system of four partial differential equations:a parabolic equation for the pressure,two convection-diffusion equations for the concentrations of brine and radionuclide and a heat conduction equation for the temperature.The pressure appears within the concentration equations and heat conduction equation,and the Darcy velocity controls the concentrations and the temperature.The pressure is solved by the conservative mixed volume element method,and the order of the accuracy is improved by the Darcy velocity.The concentration of brine and temperature are computed by the upwind mixed volume element method on a changing mesh,where the diffusion is discretized by a mixed volume element and the convection is treated by an upwind scheme.The composite method can solve the convection-dominated diffusion problems well because it eliminates numerical dispersion and nonphysical oscillation and has high order computational accuracy.The mixed volume element has the local conservation of mass and energy,and it can obtain the brine and temperature and their adjoint vector functions simultaneously.The conservation nature plays an important role in numerical simulation of underground fluid.The concentrations of radionuclide factors are solved by the method of upwind fractional step difference and the computational work is decreased by decomposing a three-dimensional problem into three successive one-dimensional problems and using the method of speedup.By the theory and technique of a priori estimates of differential equations,we derive an optimal order result in L^(2) norm.Numerical examples are given to show the effectiveness and practicability and the composite method is testified as a powerful tool to solve the well-known actual problem.
基金This work was supported by the Basic Science Research Program through the National Research Foundation of Korea(NRF-2019R1F1A1062752)funded by the Ministry of Education+1 种基金was funded by BK21 FOUR(Fostering Outstanding Universities for Research)(No.:5199990914048)and was also supported by the Soonchunhyang University Research Fund.
文摘This paper presents a parallel method for simulating real-time 3D deformable objects using the volume preservation mass-spring system method on tetrahedron meshes.In general,the conventional mass-spring system is manipulated as a force-driven method because it is fast,simple to implement,and the parameters can be controlled.However,the springs in traditional mass-spring system can be excessively elongated which cause severe stability and robustness issues that lead to shape restoring,simulation blow-up,and huge volume loss of the deformable object.In addition,traditional method that uses a serial process of the central processing unit(CPU)to solve the system in every frame cannot handle the complex structure of deformable object in real-time.Therefore,the first order implicit constraint enforcement for a mass-spring model is utilized to achieve accurate visual realism of deformable objects with tough constraint error.In this paper,we applied the distance constraint and volume conservation constraints for each tetrahedron element to improve the stability of deformable object simulation using the mass-spring system and behave the same as its real-world counterparts.To reduce the computational complexity while ensuring stable simulation,we applied a method that utilizes OpenGL compute shader,a part of OpenGL Shading Language(GLSL)that executes on the graphic processing unit(GPU)to solve the numerical problems effectively.We applied the proposed methods to experimental volumetric models,and volume percentages of all objects are compared.The average volume percentages of all models during the simulation using the mass-spring system,distance constraint,and the volume constraint method were 68.21%,89.64%,and 98.70%,respectively.The proposed approaches are successfully applied to improve the stability of mass-spring system and the performance comparison from our experimental tests also shows that the GPU-based method is faster than CPU-based implementation for all cases.
基金supported by ARO grant W911NF-04-1-0291,NSF grant DMS-0510345 and AFOSR grant FA9550-05-1-0123.
文摘Hyperbolic balance laws have steady state solutions in which the flux gradients are nonzero but are exactly balanced by the source terms.In our earlier work[31–33],we designed high order well-balanced schemes to a class of hyperbolic systems with separable source terms.In this paper,we present a different approach to the same purpose:designing high order well-balanced finite volume weighted essentially non-oscillatory(WENO)schemes and RungeKutta discontinuous Galerkin(RKDG)finite element methods.We make the observation that the traditional RKDG methods are capable of maintaining certain steady states exactly,if a small modification on either the initial condition or the flux is provided.The computational cost to obtain such a well balanced RKDG method is basically the same as the traditional RKDG method.The same idea can be applied to the finite volume WENO schemes.We will first describe the algorithms and prove the well balanced property for the shallow water equations,and then show that the result can be generalized to a class of other balance laws.We perform extensive one and two dimensional simulations to verify the properties of these schemes such as the exact preservation of the balance laws for certain steady state solutions,the non-oscillatory property for general solutions with discontinuities,and the genuine high order accuracy in smooth regions.
基金the European Research Council(ERC)under the European Union’s Seventh Framework Programme(FP7/2007-2013)the research project STiMulUs,ERC Grant agreement no.278267+1 种基金.R.L.has been partially funded by the ANR under the JCJC project“ALE INC(ubator)3D”the reference LA-UR-13-28795.The authors would like to acknowledge PRACE for awarding access to the SuperMUC supercomputer based in Munich,Germany at the Leibniz Rechenzentrum(LRZ)。
文摘In this paper,we investigate the coupling of the Multi-dimensional Optimal Order Detection(MOOD)method and the Arbitrary high order DERivatives(ADER)approach in order to design a new high order accurate,robust and computationally efficient Finite Volume(FV)scheme dedicated to solve nonlinear systems of hyperbolic conservation laws on unstructured triangular and tetrahedral meshes in two and three space dimensions,respectively.The Multi-dimensional Optimal Order Detection(MOOD)method for 2D and 3D geometries has been introduced in a recent series of papers for mixed unstructured meshes.It is an arbitrary high-order accurate Finite Volume scheme in space,using polynomial reconstructions with a posteriori detection and polynomial degree decrementing processes to deal with shock waves and other discontinuities.In the following work,the time discretization is performed with an elegant and efficient one-step ADER procedure.Doing so,we retain the good properties of the MOOD scheme,that is to say the optimal high-order of accuracy is reached on smooth solutions,while spurious oscillations near singularities are prevented.The ADER technique permits not only to reduce the cost of the overall scheme as shown on a set of numerical tests in 2D and 3D,but it also increases the stability of the overall scheme.A systematic comparison between classical unstructured ADER-WENO schemes and the new ADER-MOOD approach has been carried out for high-order schemes in space and time in terms of cost,robustness,accuracy and efficiency.The main finding of this paper is that the combination of ADER with MOOD generally outperforms the one of ADER and WENO either because at given accuracy MOOD is less expensive(memory and/or CPU time),or because it is more accurate for a given grid resolution.A large suite of classical numerical test problems has been solved on unstructured meshes for three challenging multi-dimensional systems of conservation laws:the Euler equations of compressible gas dynamics,the classical equations of ideal magneto-Hydrod
基金supported by the National Natural Science Foundation of China (No.11078009)the Natural Science Foundation of Heilongjiang Province (No.A200914)
文摘To estimate the shape of tapered fibers using tapering machines with movable large-zone furnaces, a new calculation method is proposed based on the discrete deducing method and the principle of the volume conservation of the fiber materials. This method can estimate the tapering results, i.e., the shape of the tapered fibers, based on arbitrary moving parameters of the large-zone furnace and the fiber holders. The theoretical estimated results agree with the experimental measuring shape of the tapered fibers quite well.
基金This work is supported by Thales Alenia Space.We are gratefully indebted to J.-F.Coulombel,F.GolseK.Aoki for many useful advices concerning this work and for their kind encouragements。
文摘We propose a numerical solution to incorporate in the simulation of a system of conservation laws boundary conditions that come from a microscopic modeling in the small mean free path regime.The typical example we discuss is the derivation of the Euler system from the BGK equation.The boundary condition relies on the analysis of boundary layers formation that accounts from the fact that the incoming kinetic flux might be far from the thermodynamic equilibrium.
