A High Order Compact Difference Scheme and Multigrid Method for Solving the 3D Convection Diffusion Equation on Non-uniform Grids

2012 ◽  
Author(s):  
Yongbin Ge ◽  
Fujun Cao
Keyword(s):  
Diffusion Equation ◽  
Difference Scheme ◽  
Multigrid Method ◽  
High Order ◽  
Compact Difference Scheme ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Compact Difference ◽  
Uniform Grids

scholarly journals High-Order Compact Difference Scheme and Multigrid Method for Solving the 2D Elliptic Problems

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Yan Wang ◽  
Yongbin Ge
Keyword(s):  
Difference Scheme ◽  
Multigrid Method ◽  
Elliptic Problems ◽  
High Order ◽  
Compact Difference Scheme ◽  
Central Difference ◽  
Present Scheme ◽  
Compact Difference ◽  
Compact Approximations ◽  
Error Terms

A high-order compact difference scheme for solving the two-dimensional (2D) elliptic problems is proposed by including compact approximations to the leading truncation error terms of the central difference scheme. A multigrid method is employed to overcome the difficulties caused by conventional iterative methods when they are used to solve the linear algebraic system arising from the high-order compact scheme. Numerical experiments are conducted to test the accuracy and efficiency of the present method. The computed results indicate that the present scheme achieves the fourth-order accuracy and the effect of the multigrid method for accelerating the convergence speed is significant.

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