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Non linear wave propagation

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Contents

1 Problem definition
2 Domain
3 Initial Condition
4 Boundary condition
5 Exact solution
6 Numerical method
7 Results
8 Reference

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

Reference

Retrieved from "https://openfoam.cfd-online.com/Wiki/Non_linear_wave_propagation"

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