scholarly journals Compact Difference Schemes Combined with Runge-Kutta Methods for Solving Unsteady Convection-Diffusion Problems

2021 ◽  
Vol 1 (1) ◽  
pp. 1-10
Author(s):  
Zhenwei Zhu ◽  
Junjie Chen
Keyword(s):  
Difference Schemes ◽  
Convection Diffusion ◽  
Compact Difference Schemes ◽  
Compact Difference ◽  
Runge Kutta ◽  
Diffusion Problems

scholarly journals Numerical Solution to Unsteady One-Dimensional Convection-Diffusion Problems Using Compact Difference Schemes Combined with Runge-Kutta Methods

2021 ◽  
pp. 399-408
Author(s):  
Zhenwei Zhu ◽  
Junjie Chen
Keyword(s):  
Diffusion Equation ◽  
Difference Schemes ◽  
Combination Method ◽  
Time And Space ◽  
One Dimensional ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Compact Difference Schemes ◽  
Compact Difference ◽  
Diffusion Problems

The convection-diffusion equation is of primary importance in understanding transport phenomena within a physical system. However, the currently available methods for solving unsteady convection-diffusion problems are generally not able to offer excellent accuracy in both time and space variables. A procedure was given in detail to solve the unsteady one-dimensional convection-diffusion equation through a combination of Runge-Kutta methods and compact difference schemes. The combination method has fourth-order accuracy in both time and space variables. Numerical experiments were conducted and the results were compared with those obtained by the Crank-Nicolson method in order to check the accuracy of the combination method. The analysis results indicated that the combination method is numerically stable at low wave numbers and small CFL numbers. The combination method has higher accuracy than the Crank-Nicolson method.

Simulating waves in flows by Runge-Kutta and compact difference schemes

AIAA Journal ◽  
1995 ◽  
Vol 33 (3) ◽  
pp. 421-429 ◽  
Author(s):  
Sheng-Tao Yu ◽  
Kwang-Chung Hsieh ◽  
Y.-L. Peter Tsai
Keyword(s):  
Difference Schemes ◽  
Compact Difference Schemes ◽  
Compact Difference ◽  
Runge Kutta

scholarly journals Compact difference schemes for convection-diffusion equations

2021 ◽  
Vol 57 (3) ◽  
pp. 311-318
Author(s):  
B. D. Utebaev
Keyword(s):  
Difference Schemes ◽  
Numerical Calculations ◽  
Diffusion Equations ◽  
Stability And Convergence ◽  
Convection Diffusion ◽  
Compact Difference Schemes ◽  
Compact Difference

This work is devoted to the construction of compact difference schemes for convection-diffusion equations with divergent and nondivergent convective terms. Stability and convergence in the discrete norms are proved. The obtained results are generalized to multidimensional convection-diffusion equations. The test numerical calculations presented in the work are consistent with the theoretical conclusions.

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