A nonlinear flow of Jeffrey liquid with Cattaneo-Christov heat flux is investigated in the presence of nanoparticles. The features of thermophoretic and Brownian movement are retained. The effects of nonlinear radiati...A nonlinear flow of Jeffrey liquid with Cattaneo-Christov heat flux is investigated in the presence of nanoparticles. The features of thermophoretic and Brownian movement are retained. The effects of nonlinear radiation, magnetohydrodynamic(MHD), and convective conditions are accounted. The conversion of governing equations into ordinary differential equations is prepared via stretching transformations. The consequent equations are solved using the Runge-Kutta-Fehlberg(RKF) method. Impacts of physical constraints on the liquid velocity, the temperature, and the nanoparticle volume fraction are analyzed through graphical illustrations. It is established that the velocity of the liquid and its associated boundary layer width increase with the mixed convection parameter and the Deborah number.展开更多
The solution of the real Ginzburg-Landau (GL) equation with a time-periodic coefficient is obtained in the form of a series, with assured convergence, using the computer-assisted ‘Homotopy Analysis Method’ (HAM) pro...The solution of the real Ginzburg-Landau (GL) equation with a time-periodic coefficient is obtained in the form of a series, with assured convergence, using the computer-assisted ‘Homotopy Analysis Method’ (HAM) propounded by Liao [1]. The formulation has been kept quite general to keep open the possibility of obtaining the solution of the GL equation for different continua as limiting cases of the present study. New ideas have been added and clear explanations are provided in the paper to the existing concepts in HAM. The method can easily be extended to solve complex GL equation, system of GL equations or even the GL equations with a diffusion term, each having a time-periodic coefficient. The necessary code in Mathematica that implements the HAM for the current problem is appended to the paper for use by the readers.展开更多
In this paper, a predictor-corrector finite difference-streamline diffusion finite element scheme is constructed for time-dependent quasilinear convection-diffusion problem. For the scheme considered, the solvility is...In this paper, a predictor-corrector finite difference-streamline diffusion finite element scheme is constructed for time-dependent quasilinear convection-diffusion problem. For the scheme considered, the solvility is proved, and the error estimate in L(L2)-norm is established. It has 2-order accuracy in time direction and quasi-optimal order accuracy in space variables.展开更多
For the three-dimensional convection-dominated problem of dynamics of fluids in porous media, the second order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward. Fract...For the three-dimensional convection-dominated problem of dynamics of fluids in porous media, the second order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward. Fractional steps techniques are needed to convert a multi-dimensional problem into a series of successive one-dimensional problems. Some techniques, such as calculus of variations, energy method, multiplicative commutation rule of difference operators, decomposition of high order difference operators, and the theory of prior estimates are adopted. Optimal order estimates are derived to determine the error in the second order approximate solution. These methods have already been applied to the numerical simulation of migration-accumulation of oil resources and predicting the consequences of seawater intrusion and protection projects.展开更多
The Asselin-Robert time As an attractive alternative filter used in the leaptYog scheme does degrade the accuracy of calculations. to leapfrog time differencing, the second-order Adams-Bashforth method is not subject ...The Asselin-Robert time As an attractive alternative filter used in the leaptYog scheme does degrade the accuracy of calculations. to leapfrog time differencing, the second-order Adams-Bashforth method is not subject to time splitting instability and keeps excellent calculation accuracy. A second-order Adams- Bashforth model has been developed, which represents better stability, excellent convergence and improved simulation of prognostic variables. Based on these results, the higher-order Adams-Bashforth methods are developed on the basis of NCAR （National Center for Atmospheric Research） CAM 3.1 （Community Atmosphere Model 3.1） and the characteristics of dynamical cores are analyzed in this paper. By using Lorenz nonlinear convective equations, the filtered leapfrog scheme shows an excellent pattern for eliminating 2At wave solutions after 20 steps but represents less computational solution accuracy. The fourth-order Adams- Bashforth method is closely converged to the exact solution and provides a reference against which other methods may be compared. Thus, the Adams-Bashforth methods produce more accurate and convergent solution with differencing order increasing. The Held-Suarez idealized test is carried out to demonstrate that all methods have similar climate states to the results of many other global models for long-term integration. Besides, higher-order methods perform better in mass conservation and exhibit improvement in simulating tropospheric westerly jets, which is likely equivalent to the advantages of increasing horizontal resolutions. Based on the idealized baroclinic wave test, a better capability of the higher-order method in maintaining simulation stability is convinced. Furthermore, after the baroclinic wave is triggered through overlaying the steady-state initial conditions with the zonal perturbation, the higher-order method has a better ability in the simulation of baroclinic wave perturbation.展开更多
A singlestep characteristic finite difference method is given based on the linear and quadratic interpolations for solving two-dimensional nonlinear convection-diffusionproblems. The convergence of approximate solutio...A singlestep characteristic finite difference method is given based on the linear and quadratic interpolations for solving two-dimensional nonlinear convection-diffusionproblems. The convergence of approximate solutions is obtained in L2 under milder restrictions in the temporal stepsize and spatial stepsize than those required in [1].展开更多
A multistep characteristic finite difference method is given on the basis ofthe linear and quadratic interpolations for solving two-dimensional nonlinear convection-diffusion problems. The convergence of approximate s...A multistep characteristic finite difference method is given on the basis ofthe linear and quadratic interpolations for solving two-dimensional nonlinear convection-diffusion problems. The convergence of approximate solutions is obtained in L2.展开更多
基金University Grant Commission (UGC),New Delhi,for their financial support under National Fellowship for Higher Education (NFHE) of ST students to pursue M.Phil/PhD Degree (F117.1/201516/NFST201517STKAR2228/ (SAIII/Website) Dated:06-April-2016)the Management of Christ University,Bengaluru,India,for the support through Major Research Project to accomplish this research work
文摘A nonlinear flow of Jeffrey liquid with Cattaneo-Christov heat flux is investigated in the presence of nanoparticles. The features of thermophoretic and Brownian movement are retained. The effects of nonlinear radiation, magnetohydrodynamic(MHD), and convective conditions are accounted. The conversion of governing equations into ordinary differential equations is prepared via stretching transformations. The consequent equations are solved using the Runge-Kutta-Fehlberg(RKF) method. Impacts of physical constraints on the liquid velocity, the temperature, and the nanoparticle volume fraction are analyzed through graphical illustrations. It is established that the velocity of the liquid and its associated boundary layer width increase with the mixed convection parameter and the Deborah number.
文摘The solution of the real Ginzburg-Landau (GL) equation with a time-periodic coefficient is obtained in the form of a series, with assured convergence, using the computer-assisted ‘Homotopy Analysis Method’ (HAM) propounded by Liao [1]. The formulation has been kept quite general to keep open the possibility of obtaining the solution of the GL equation for different continua as limiting cases of the present study. New ideas have been added and clear explanations are provided in the paper to the existing concepts in HAM. The method can easily be extended to solve complex GL equation, system of GL equations or even the GL equations with a diffusion term, each having a time-periodic coefficient. The necessary code in Mathematica that implements the HAM for the current problem is appended to the paper for use by the readers.
文摘In this paper, a predictor-corrector finite difference-streamline diffusion finite element scheme is constructed for time-dependent quasilinear convection-diffusion problem. For the scheme considered, the solvility is proved, and the error estimate in L(L2)-norm is established. It has 2-order accuracy in time direction and quasi-optimal order accuracy in space variables.
基金Project supported by the Major State Basic Research Program of China (No.G1999032803)the National Tackling Key Problems Program (No.20050200069)the National Natural Science Foundation of China (Nos.10372052, 10271066)the Doctoral Foundation of Ministry of Education of China (No.20030422047).
文摘For the three-dimensional convection-dominated problem of dynamics of fluids in porous media, the second order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward. Fractional steps techniques are needed to convert a multi-dimensional problem into a series of successive one-dimensional problems. Some techniques, such as calculus of variations, energy method, multiplicative commutation rule of difference operators, decomposition of high order difference operators, and the theory of prior estimates are adopted. Optimal order estimates are derived to determine the error in the second order approximate solution. These methods have already been applied to the numerical simulation of migration-accumulation of oil resources and predicting the consequences of seawater intrusion and protection projects.
基金Supported by the China Meteorological Administration Special Fund for Numerical Prediction of GRAPES(2200504)
文摘The Asselin-Robert time As an attractive alternative filter used in the leaptYog scheme does degrade the accuracy of calculations. to leapfrog time differencing, the second-order Adams-Bashforth method is not subject to time splitting instability and keeps excellent calculation accuracy. A second-order Adams- Bashforth model has been developed, which represents better stability, excellent convergence and improved simulation of prognostic variables. Based on these results, the higher-order Adams-Bashforth methods are developed on the basis of NCAR （National Center for Atmospheric Research） CAM 3.1 （Community Atmosphere Model 3.1） and the characteristics of dynamical cores are analyzed in this paper. By using Lorenz nonlinear convective equations, the filtered leapfrog scheme shows an excellent pattern for eliminating 2At wave solutions after 20 steps but represents less computational solution accuracy. The fourth-order Adams- Bashforth method is closely converged to the exact solution and provides a reference against which other methods may be compared. Thus, the Adams-Bashforth methods produce more accurate and convergent solution with differencing order increasing. The Held-Suarez idealized test is carried out to demonstrate that all methods have similar climate states to the results of many other global models for long-term integration. Besides, higher-order methods perform better in mass conservation and exhibit improvement in simulating tropospheric westerly jets, which is likely equivalent to the advantages of increasing horizontal resolutions. Based on the idealized baroclinic wave test, a better capability of the higher-order method in maintaining simulation stability is convinced. Furthermore, after the baroclinic wave is triggered through overlaying the steady-state initial conditions with the zonal perturbation, the higher-order method has a better ability in the simulation of baroclinic wave perturbation.
文摘A singlestep characteristic finite difference method is given based on the linear and quadratic interpolations for solving two-dimensional nonlinear convection-diffusionproblems. The convergence of approximate solutions is obtained in L2 under milder restrictions in the temporal stepsize and spatial stepsize than those required in [1].
文摘A multistep characteristic finite difference method is given on the basis ofthe linear and quadratic interpolations for solving two-dimensional nonlinear convection-diffusion problems. The convergence of approximate solutions is obtained in L2.
