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Wave propagation

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== Compact scheme ==
== Compact scheme ==
-
== Runga Kutta ==
+
== Runga Kutta ==  
Consider  
Consider  
:<math> \frac {\partial U}{\partial t}=H </math>
:<math> \frac {\partial U}{\partial t}=H </math>
 +
The low storage scheme is implemented as follows
 +
:<math> U^{M+1}=U^M+b^{M+1}dtH^M </math>
 +
== Sample result ==  
== Sample result ==  
[[Image:wp_result.jpg]]
[[Image:wp_result.jpg]]

Revision as of 15:47, 19 September 2005

Contents

Introduction

The 1-D wave propagation problem is used as a test case for studying the dissipation and dispersion errors in a given finite difference scheme.There are a number of schemes which can be used to solve the problem. The usage of a higher order compact stencil with a low storage 4th order Runga Kutta scheme to solve the current problem is discussed.

Compact scheme

Runga Kutta

Consider

 \frac {\partial U}{\partial t}=H

The low storage scheme is implemented as follows

 U^{M+1}=U^M+b^{M+1}dtH^M

Sample result

Wp result.jpg

Reference

Williamson, Williamson (1980), "Low Storage Runge-Kutta Schemes", Journal of Computational Physics, Vol.35, pp.48–56.


Lele, Lele, S. K. (1992), "Compact Finite Difference Schemes with Spectral-like Resolution,” Journal of Computational Physics", Journal of Computational Physics, Vol. 103, pp 16–42.

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