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Abstract

For the scalar conservation law
$$ u_t + cu_x = 0, $$
first-order upwind is written as
$$ u_j^{n + 1} = u_j^n - c_ + \frac{{\Delta t}} {{\Delta x}}\left( {u_j^n - u_{j - 1}^n } \right) - c_ - \frac{{\Delta t}} {{\Delta x}}\left( {u_{j + 1}^n - u_{j - 1}^n } \right), $$
where
$$ c_ + = max(c,0), c\_ = min(c,0). $$
.

Keywords

Scalar Equation Riemann Problem Upwind Scheme Entropy Inequality Piecewise Constant Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag 2009

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