# 2-D linearised Euler equation

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== Problem Definition == | == Problem Definition == | ||

:<math> \frac{\partial u}{\partial t}+M \frac{\partial u}{\partial x}+\frac{\partial p}{\partial x}=0 </math> | :<math> \frac{\partial u}{\partial t}+M \frac{\partial u}{\partial x}+\frac{\partial p}{\partial x}=0 </math> | ||

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== Reference == | == Reference == | ||

- | *{{reference-paper|author=Williamson, Williamson|year=1980|title=Low Storage Runge-Kutta Schemes|rest=Journal of Computational Physics, Vol.35, pp. | + | *{{reference-paper|author=Williamson, Williamson|year=1980|title=Low Storage Runge-Kutta Schemes|rest=Journal of Computational Physics, Vol.35, pp.48–56}} |

- | *{{reference-paper|author=Lele, Lele, S. K.|year=1992|title=Compact Finite Difference Schemes with Spectral-like Resolution, | + | *{{reference-paper|author=Lele, Lele, S. K.|year=1992|title=Compact Finite Difference Schemes with Spectral-like Resolution,” Journal of Computational Physics|rest=Journal of Computational Physics, Vol. 103, pp 16–42}} |

## Latest revision as of 12:31, 19 December 2008

## Contents |

## Problem Definition

where M is the mach number , speed of sound is assumed to be 1, all the variabled refer to acoustic perturbations over the mean flow.

## Domain

[-50,50]*[-50,50]

## Initial Condition

## Boundary Condition

Characteristic Boundary Condition

## Numerical Method

4th Order Compact scheme in space 4th order low storage RK in time

## Results

Pressure

- No mean flow

- Mean Flow to left at U=0.5 (c assumed to be 1 m/s)

## 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.