scholarly journals On numerical solution of nonlinear parabolic multicomponent convection-diffusion problems

2021 ◽  
Author(s):  
Gheorghe Sarbu ◽  
Constantin Popa
Keyword(s):  
Numerical Solution ◽  
Convection Diffusion ◽  
Nonlinear Parabolic ◽  
Multicomponent Convection ◽  
Diffusion Problems

An Adaptive Grid Method for Singularly Perturbed Time-Dependent Convection-Diffusion Problems

2016 ◽  
Vol 20 (5) ◽  
pp. 1340-1358 ◽  
Author(s):  
Yanping Chen ◽  
Li-Bin Liu
Keyword(s):  
Numerical Solution ◽  
Time Derivative ◽  
Adaptive Grid ◽  
Singularly Perturbed ◽  
Time Dependent ◽  
Uniform Mesh ◽  
Convection Diffusion ◽  
Monitor Function ◽  
Backward Euler ◽  
Diffusion Problems

AbstractIn this paper, we study the numerical solution of singularly perturbed time-dependent convection-diffusion problems. To solve these problems, the backward Euler method is first applied to discretize the time derivative on a uniform mesh, and the classical upwind finite difference scheme is used to approximate the spatial derivative on an arbitrary nonuniform grid. Then, in order to obtain an adaptive grid for all temporal levels, we construct a positive monitor function, which is similar to the arc-length monitor function. Furthermore, the ε-uniform convergence of the fully discrete scheme is derived for the numerical solution. Finally, some numerical results are given to support our theoretical results.

An Efficient Algorithm Based on Extrapolation for the Solution of Nonlinear Parabolic Equations

2019 ◽  
Vol 20 (5) ◽  
pp. 527-541
Author(s):  
M. Ghasemi
Keyword(s):  
Parabolic Equations ◽  
Nonlinear Parabolic Equations ◽  
Spatial Direction ◽  
One Dimensional ◽  
Convection Diffusion ◽  
Nonlinear Parabolic ◽  
End Conditions ◽  
Finite Difference Discretization ◽  
Difference Discretization ◽  
Diffusion Problems

AbstractTwo numerical procedures are developed to approximate the solution of one-dimensional parabolic equations using extrapolated collocation method. By defining two different end conditions and forcing cubic spline to satisfy the interpolation conditions along with one of the end conditions, we obtain fourth- (CBS4) and sixth-order (CBS6) approximations to the solution in spatial direction. Also in time direction, a weighted finite difference discretization is used to approximate the solution at each time level. The convergence analysis is discussed in detail and some error bounds are obtained theoretically. Finally, some different examples of Burgers’ equation with applications in fluid mechanics as well as convection–diffusion problems with applications in transport are solved to show the applicability and good performance of the procedures.

Numerical solution of convection-diffusion problems in irregular domains mapped onto a circle

10.2514/3.233 ◽  
1991 ◽  
Vol 5 (1) ◽  
pp. 103-109 ◽  
Author(s):  
Makoto Asaba ◽  
Yutaka Asako ◽  
Hiroshi Nakamura ◽  
Mohammad Faghri
Keyword(s):  
Numerical Solution ◽  
Irregular Domains ◽  
Convection Diffusion ◽  
Diffusion Problems

An Efficient Algorithm Based on Extrapolation for the Solution of Nonlinear Parabolic Equations

2018 ◽  
Vol 19 (1) ◽  
pp. 37-51 ◽  
Author(s):  
M. Ghasemi
Keyword(s):  
Parabolic Equations ◽  
Nonlinear Parabolic Equations ◽  
Spatial Direction ◽  
Convection Diffusion ◽  
Nonlinear Parabolic ◽  
End Conditions ◽  
Finite Difference Discretization ◽  
Transport Problems ◽  
Difference Discretization ◽  
Diffusion Problems

AbstractTwo numerical procedures are developed to approximate the solution of one-dimensional parabolic equations using extrapolated collocation method. By defining two different end conditions and forcing cubic spline to satisfy the interpolation conditions along with one of the end conditions, we obtain fourth- (CBS4) and sixth-order (CBS6) approximations to the solution in spatial direction. Also in time direction, a weighted finite-difference discretization is used to approximate the solution at each time level. The convergence analysis of the methods is discussed in detail and some error bounds are obtained theoretically. Finally, some different examples of Burgers’ equations with applications in fluid mechanics as well as convection–diffusion problems with applications in transport problems are solved to show the applicability and good performance of the procedures.

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