scholarly journals Development and L2-Analysis of a Single-Step Characteristics Finite Difference Scheme of Second Order in Time for Convection-Diffusion Problems

2013 ◽  
Vol 7 (3) ◽  
pp. 343-380 ◽  
Author(s):  
Hirofumi Notsu ◽  
Hongxing Rui ◽  
Masahisa Tabata
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Single Step ◽  
Second Order ◽  
Convection Diffusion ◽  
Second Order In Time ◽  
Diffusion Problems

A High-Accuracy Finite Difference Scheme for Solving Reaction-Convection-Diffusion Problems with a Small Diffusivity

2014 ◽  
Vol 6 (5) ◽  
pp. 637-662 ◽  
Author(s):  
Po-Wen Hsieh ◽  
Suh-Yuh Yang ◽  
Cheng-Shu You
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Stokes Equations ◽  
High Accuracy ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Convection Diffusion ◽  
Alternating Direction ◽  
Diffusion Problems

AbstractThis paper is devoted to a new high-accuracy finite difference scheme for solving reaction-convection-diffusion problems with a small diffusivity ε. With a novel treatment for the reaction term, we first derive a difference scheme of accuracy O(εh2+εh2+h3) for the 1-D case. Using the alternating direction technique, we then extend the scheme to the 2-D case on a nine-point stencil. We apply the high-accuracy finite difference scheme to solve the 2-D steady incompressible Navier-Stokes equations in the stream function-vorticity formulation. Numerical examples are given to illustrate the effectiveness of the proposed difference scheme. Comparisons made with some high-order compact difference schemes show that the newly proposed scheme can achieve good accuracy with a better stability.

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