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Non linear wave propagation

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Revision as of 21:56, 14 January 2006 by Harish gopalan (Talk | contribs)
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Contents

Problem definition

\frac{\partial u}{\partial t}+ u \frac{\partial u}{\partial x}=0

Domain

x \in \left[-5,10\right]

Initial Condition

u(x,0) = \begin{cases} 0 & x \le 0 \\ 1 & x > 0 \end{cases}

Boundary condition

u(0,t)=0

Exact solution

u(x,t) = \begin{cases} 0 & x \le 0 \\ x/t & 0 < x < t \\ 1 & \mbox{otherwise} \end{cases}

Numerical method

Results

Nonlinear 1d.png

Reference

Mihaela Popescu, Wei Shyy , Marc Garbey (2005), "Finite volume treatment of dispersion-relation-preserving and optimized prefactored compact schemes for wave propagation", Journal of Computational Physics, Vol. 210, pp. 705-729.

Tam and Webb (1993), "Dispersion-relation-preserving finite difference schemes for computational acoustics", Journal of Computational Physics, Vol. 107, pp. 262-281.

SK Lele (1992), "Compact finite difference schemes with spectrum-like resolution", Journal of Computational Physics, Vol.103, pp.16-42.

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

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