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Non linear wave propagation

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(fixed up some formulas)
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== Reference ==
== Reference ==
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{{reference-paper|author=Mihaela Popescu, Wei Shyy , Marc Garbey|year=2005|title=Finite volume treatment of dispersion-relation-preserving and optimized prefactored compact schemes for wave propagation|rest=Journal of Computational Physics, Vol. 210, pp. 705-729}}
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{{reference-paper|author=Tam and Webb|year=1993|title=Dispersion-relation-preserving finite difference schemes for computational acoustics|rest=Journal of Computational Physics, Vol. 107, pp. 262-281}}
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{{reference-paper|author=SK Lele|year=1992|title=Compact finite difference schemes with spectrum-like resolution|rest=Journal of Computational Physics, Vol.103, pp.16-42}}
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{{reference-paper|author=Williamson|year=1980|title=Low Storage Runge-Kutta Schemes|rest=Journal of Computational Physics, Vol.35, pp.48–56}}

Revision as of 21:56, 14 January 2006

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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