The staggered finite-difference method

Maple
  2023-06-25 13:52:40 2023-06-25 13:52:40 Created   2023-11-09 21:29:10 2023-11-09 21:29:10 Updated    121 Words  1 Mins  

One-dimension Problem

∂u∂t–∂v∂x=0,∂v∂t–∂u∂x=0.\frac{\partial u}{\partial t} – \frac{\partial v}{\partial x} =0, \quad \frac{\partial v}{\partial t} – \frac{\partial u}{\partial x} =0.

Let us start with a 1d model problem for acoustic problem. (Please See Ref. 1)

Two-dimension Problem

Similarly, We have:

∂u∂t−(∂v∂x+∂v∂y)=0\frac{\partial u}{\partial t}-(\frac{\partial v}{\partial x}+\frac{\partial v}{\partial y})=0

Reference

  1. The staggered finite-difference method (交错网格有限差分方法) - 数值分析大巴 (numanal.com)
  • Title: The staggered finite-difference method
  • Author: Maple
  • Created at : 2023-06-25 13:52:40
  • Updated at : 2023-11-09 21:29:10
  • Link: https://www.maple367.eu.org/Numerical-Analysis/the-staggered-finite-difference-method/
  • License: This work is licensed under CC BY-NC-SA 4.0.
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The staggered finite-difference method
  1. One-dimension Problem
  2. Two-dimension Problem
  3. Reference