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8.1.1 Explicit Eulerian Methods



EXAMPLE: 1D Euler / Lax
$\displaystyle \rho_{j}^{n+1}$ $\textstyle =$ $\displaystyle \frac{1}{2}\left(\rho_{j+1}^{n}+\rho_{j-1}^{n} \right)
-\frac{\De...
...{2 \Delta x}
\left(\rho_{j+1}^{n} v_{j+1}^{n}-\rho_{j-1}^{n}v_{j-1}^{n} \right)$ (8.14)
$\displaystyle \rho_{j}^{n+1}v_{j}^{n+1}$ $\textstyle =$ $\displaystyle \frac{1}{2}
\left(\rho_{j+1}^{n}v_{j+1}^{n}+\rho_{j-1}^{n}v_{j-1}...
...{j+1}^{n})^{2}+p_{j+1}^{n}
-\rho_{j-1}^{n}(v_{j-1}^{n})^{2}-p_{j-1}^{n} \right]$ (8.15)
       
$\displaystyle e_{j}^{n+1}$ $\textstyle =$ $\displaystyle \frac{1}{2}\left(e_{j+1}^{n}-e_{j-1}^{n} \right)
-\frac{\Delta t}...
...^{n}\right)v_{j+1}^{n}
-\left(e_{j-1}^{n}+p_{j-1}^{n}\right)v_{j-1}^{n}
\right]$ (8.16)




Franz J. Vesely Oct 2005
See also:
"Computational Physics - An Introduction," Kluwer-Plenum 2001