scholarly journals High Order Compact Difference Scheme and Multigrid Method for 2D Elliptic Problems with Variable Coefficients and Interior/Boundary Layers on Nonuniform Grids

2015 ◽  
Vol 03 (05) ◽  
pp. 509-523
Author(s):  
Bin Lan ◽  
Yongbin Ge ◽  
Yan Wang ◽  
Yong Zhan
Keyword(s):  
Difference Scheme ◽  
Boundary Layers ◽  
Multigrid Method ◽  
Elliptic Problems ◽  
Variable Coefficients ◽  
High Order ◽  
Compact Difference Scheme ◽  
Nonuniform Grids ◽  
Compact Difference ◽  
Interior Boundary

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.

Direct calculation of waves in fluid flows using high-order compact difference scheme

AIAA Journal ◽  
1994 ◽  
Vol 32 (9) ◽  
pp. 1766-1773 ◽  
Author(s):  
Sheng-Tao Yu ◽  
Lennart S. Hultgren ◽  
Nan-Suey Liu
Keyword(s):  
Difference Scheme ◽  
Fluid Flows ◽  
Direct Calculation ◽  
High Order ◽  
Compact Difference Scheme ◽  
Compact Difference
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