Cost-effective multilevel techniques for homogeneous hyperbolic conservation laws are very successful in reducing the computational cost associated to high resolution shock capturing numerical schemes.Because they do ...Cost-effective multilevel techniques for homogeneous hyperbolic conservation laws are very successful in reducing the computational cost associated to high resolution shock capturing numerical schemes.Because they do not involve any special data structure,and do not induce savings in memory requirements,they are easily implemented on existing codes and are recommended for 1D and 2D simulations when intensive testing is required.The multilevel technique can also be applied to balance laws,but in this case,numerical errors may be induced by the technique.We present a series of numerical tests that point out that the use of monotonicity-preserving interpolatory techniques eliminates the numerical errors observed when using the usual 4-point centered Lagrange interpolation,and leads to a more robust multilevel code for balance laws,while maintaining the efficiency rates observed forhyperbolic conservation laws.展开更多
In order to use the second-order 5-point difference scheme mentioned to compute the solution of one dimension unsteady equations of the direct reflection of the strong plane detonation wave meeting a solid wall barrie...In order to use the second-order 5-point difference scheme mentioned to compute the solution of one dimension unsteady equations of the direct reflection of the strong plane detonation wave meeting a solid wall barrier,in this paper,we technically construct the difference schemes of the boundary and sub-boundary of the problem,and deduce the auto-analogue analytic solutions of the initial value problem,and at the same time,we present a method for the singular property of the initial value problem,from which we can get a satisfactory computation result of this difficult problem.The difference scheme used in this paper to deal with the discontinuity problems of the shock wave are valuable and worth generalization.展开更多
The purpose of this study is to establish a depth-averaged 2-D hydrodynamic and sediment transport model for the dambreak flows with vegetation effect. The generalized shallow water equations are solved using an expli...The purpose of this study is to establish a depth-averaged 2-D hydrodynamic and sediment transport model for the dambreak flows with vegetation effect. The generalized shallow water equations are solved using an explicit finite volume method with unstructured quadtree rectangular grid, and in the hydrodynamic model, a Harten-Lax-Van Leer（HLL） approximate Riemann solver is used to calculate the intercell flux for capturing the dry-to-wet moving boundary. The sediment transport and bed variation equations in a coupled fashion are calculated by including the bed variation and the variable flow density in the flow continuity and momentum equations. The drag force of vegetation is modeled as the sink terms in the momentum equations. The developed model is tested against lab experiments of the dam-break flows over a fix bed and a movable bed in vegetated and non-vegetated channels. The results are compared with experimental data, and good agreement is obtained. It is shown that the reduced velocity under vegetated conditions leads to a decrease of the peak discharge and a rise of the water level of rivers and also an enhancement of the sediment deposition.展开更多
A Harten-Lax-van Leer-contact （HLLC） approximate Riemann solver is built with elastic waves （HLLCE） for one-dimensional elastic-plastic flows with a hypo- elastic constitutive model and the von Mises＇ yielding cr...A Harten-Lax-van Leer-contact （HLLC） approximate Riemann solver is built with elastic waves （HLLCE） for one-dimensional elastic-plastic flows with a hypo- elastic constitutive model and the von Mises＇ yielding criterion. Based on the HLLCE, a third-order cell-centered Lagrangian scheme is built for one-dimensional elastic-plastic problems. A number of numerical experiments are carried out. The numerical results show that the proposed third-order scheme achieves the desired order of accuracy. The third-order scheme is used to the numerical solution of the problems with elastic shock waves and elastic rarefaction waves. The numerical results are compared with a reference solution and the results obtained by other authors. The comparison shows that the pre- sented high-order scheme is convergent, stable, and essentially non-oscillatory. Moreover, the HLLCE is more efficient than the two-rarefaction Riemann solver with elastic waves （TRRSE）展开更多
A high-resolution, 1-D numerical model has been developed in the discontinuous Galerkin framework to simulate 1-D flow behavior, sediment transport, and morphological evaluation under unsteady flow conditions. The flo...A high-resolution, 1-D numerical model has been developed in the discontinuous Galerkin framework to simulate 1-D flow behavior, sediment transport, and morphological evaluation under unsteady flow conditions. The flow and sediment concentration variables are computed based on the one-dimensional shallow water flow equations, while empirical equations are used for entrainment and deposition processes. The sediment transport model includes the bed load and suspended load components. New formulations for Harten-Lax-van Leer （HLL） and Harten-Lax-van Contact （HLLC） are presented for shallow water flow equations that include the bed load and suspended load fluxes. The computational results for the flow and morphological changes after two dam break events are compared with the physical model tests. Results show that the modified HLL and HLLC formulations are robust and can accurately predict morphological changes in highly unsteady flows.展开更多
This paper deals with the numerical solution of inviscid compressible flows. The threedimensional Euler equations describing the mentioned problem are presented and solved numerically with the finite volume method. Th...This paper deals with the numerical solution of inviscid compressible flows. The threedimensional Euler equations describing the mentioned problem are presented and solved numerically with the finite volume method. The evaluation of the numerical flux at the interfaces is performed by using the Toro Vazquez-Harten Lax Leer(TV-HLL) scheme. An essential feature of the proposed scheme is to associate two systems of differential equations, called the advection system and the pressure system. It can be implemented with a very simple manner in the standard finite volume Euler and Navier–Stokes codes as extremely simple task. The scheme is applied to some test problems covering a wide spectrum of Mach numbers, including hypersonic, low speed flow and three-dimensional aerodynamics applications.展开更多
为了高效准确地模拟水污染事件中污染物输移过程,该文引入了一套基于GPU加速的水动力及污染物输移的GAST(GPU Accelerated Surface Water Flow and Associated Transport)高分辨率数值模型,并对水污染事件中污染物的输移进行了模拟。模...为了高效准确地模拟水污染事件中污染物输移过程,该文引入了一套基于GPU加速的水动力及污染物输移的GAST(GPU Accelerated Surface Water Flow and Associated Transport)高分辨率数值模型,并对水污染事件中污染物的输移进行了模拟。模型采用Godunov格式的有限体积法求解二维浅水方程和污染物输移方程,利用HLLC(Harten-Lax-van Leer-Contact)近似黎曼求解器计算单元网格界面通量,应用MUSCL限坡线性重构和龙格-库塔时间积分法实现了时空二阶精度,有效地解决了输移方程中对流项产生的数值阻尼过大和剧烈的数值振荡等问题,可准确地模拟复杂地形上干湿界面变化。同时模型引入图形处理器GPU(Graphics Processing Unit)加速计算技术。算例结果表明:模型精度高且稳定性好,能有效抑制数值阻尼和数值振荡,大幅提升了计算效率;模型可用于水污染事故的预警和评估,以期为突发水污染事件的决策提供基础数据和科学支撑。展开更多
基金supported by Grant PID2020-117211GB-I00funded by MCIN/AEI/10.13039/501100011033+4 种基金by Grant CIAICO/2021/227funded by the Generalitat Valencianasupported by the Ministerio de Ciencia e Innovacion of Spain(Grant Ref.PID2021-125709OB-C21)funded by MCIN/AEI/10.13039/501100011033/FEDER,UEby the Generalitat Valenciana(CIAICO/2021/224).
文摘Cost-effective multilevel techniques for homogeneous hyperbolic conservation laws are very successful in reducing the computational cost associated to high resolution shock capturing numerical schemes.Because they do not involve any special data structure,and do not induce savings in memory requirements,they are easily implemented on existing codes and are recommended for 1D and 2D simulations when intensive testing is required.The multilevel technique can also be applied to balance laws,but in this case,numerical errors may be induced by the technique.We present a series of numerical tests that point out that the use of monotonicity-preserving interpolatory techniques eliminates the numerical errors observed when using the usual 4-point centered Lagrange interpolation,and leads to a more robust multilevel code for balance laws,while maintaining the efficiency rates observed forhyperbolic conservation laws.
文摘In order to use the second-order 5-point difference scheme mentioned to compute the solution of one dimension unsteady equations of the direct reflection of the strong plane detonation wave meeting a solid wall barrier,in this paper,we technically construct the difference schemes of the boundary and sub-boundary of the problem,and deduce the auto-analogue analytic solutions of the initial value problem,and at the same time,we present a method for the singular property of the initial value problem,from which we can get a satisfactory computation result of this difficult problem.The difference scheme used in this paper to deal with the discontinuity problems of the shock wave are valuable and worth generalization.
基金supported by the Public Science and Technology Research Funds Projects of Ocean(Grant No.201205023)the Program for Liaoning Province Excellent Talents in University(Grant No.LJQ2013077)+1 种基金the Science and Technology Founda-tion of Dalian City(Grant No.2013J21DW009)the Natu-ral Science Foundation of Liaoning Province(Grant No.2014020148)
文摘The purpose of this study is to establish a depth-averaged 2-D hydrodynamic and sediment transport model for the dambreak flows with vegetation effect. The generalized shallow water equations are solved using an explicit finite volume method with unstructured quadtree rectangular grid, and in the hydrodynamic model, a Harten-Lax-Van Leer（HLL） approximate Riemann solver is used to calculate the intercell flux for capturing the dry-to-wet moving boundary. The sediment transport and bed variation equations in a coupled fashion are calculated by including the bed variation and the variable flow density in the flow continuity and momentum equations. The drag force of vegetation is modeled as the sink terms in the momentum equations. The developed model is tested against lab experiments of the dam-break flows over a fix bed and a movable bed in vegetated and non-vegetated channels. The results are compared with experimental data, and good agreement is obtained. It is shown that the reduced velocity under vegetated conditions leads to a decrease of the peak discharge and a rise of the water level of rivers and also an enhancement of the sediment deposition.
基金Project supported by the National Natural Science Foundation of China(Nos.11172050 and11672047)the Science and Technology Foundation of China Academy of Engineering Physics(No.2013A0202011)
文摘A Harten-Lax-van Leer-contact （HLLC） approximate Riemann solver is built with elastic waves （HLLCE） for one-dimensional elastic-plastic flows with a hypo- elastic constitutive model and the von Mises＇ yielding criterion. Based on the HLLCE, a third-order cell-centered Lagrangian scheme is built for one-dimensional elastic-plastic problems. A number of numerical experiments are carried out. The numerical results show that the proposed third-order scheme achieves the desired order of accuracy. The third-order scheme is used to the numerical solution of the problems with elastic shock waves and elastic rarefaction waves. The numerical results are compared with a reference solution and the results obtained by other authors. The comparison shows that the pre- sented high-order scheme is convergent, stable, and essentially non-oscillatory. Moreover, the HLLCE is more efficient than the two-rarefaction Riemann solver with elastic waves （TRRSE）
文摘A high-resolution, 1-D numerical model has been developed in the discontinuous Galerkin framework to simulate 1-D flow behavior, sediment transport, and morphological evaluation under unsteady flow conditions. The flow and sediment concentration variables are computed based on the one-dimensional shallow water flow equations, while empirical equations are used for entrainment and deposition processes. The sediment transport model includes the bed load and suspended load components. New formulations for Harten-Lax-van Leer （HLL） and Harten-Lax-van Contact （HLLC） are presented for shallow water flow equations that include the bed load and suspended load fluxes. The computational results for the flow and morphological changes after two dam break events are compared with the physical model tests. Results show that the modified HLL and HLLC formulations are robust and can accurately predict morphological changes in highly unsteady flows.
文摘This paper deals with the numerical solution of inviscid compressible flows. The threedimensional Euler equations describing the mentioned problem are presented and solved numerically with the finite volume method. The evaluation of the numerical flux at the interfaces is performed by using the Toro Vazquez-Harten Lax Leer(TV-HLL) scheme. An essential feature of the proposed scheme is to associate two systems of differential equations, called the advection system and the pressure system. It can be implemented with a very simple manner in the standard finite volume Euler and Navier–Stokes codes as extremely simple task. The scheme is applied to some test problems covering a wide spectrum of Mach numbers, including hypersonic, low speed flow and three-dimensional aerodynamics applications.
