1. Euler equations of Gas Dynamics Hailiang Liu Math517@ISU October 15, 2004

2. Simulated Gas Flow Where u has components of density, momentum and energy. Nonlinear Conservation Laws: of great practical importance since they govern a variety of physical phenomena that appear in fluid mechanics, astrophysics, groundwater flow, meterology, semiconductors, and reactive flows Euler equation: Modeling inviscid non-heat conducting ( ideal polytropic) gases

3. Eigen-structure Here c^2=\gamma p/\rho=dh/dp, and c is called the sound speed.

4. Numerical Test by Sod Riemann problem proposed by Sod (1978)

5. Numerical Test by Lax Riemann problem proposed by Lax (1974)

6. Woodward-Collela’s test Woodward-Collela proposed this test in 1984

7. The shock Interaction A model of the interaction of a sinusoidal disturbance and a shock wave due to the initial conditions A density wave will emerge behind the shock discontinuity, its fine structure makes the current problem a suitable test case for high order methods.

8. Test I--required The first order central non-staggered LxF scheme (1954) The staggered NT scheme (4.2), (4.4a), (4.5). The non-staggered NT second order accurate central scheme, (2.18), (4.4a), (4.5). Ref: Paper by Nessyahu and Tadmor(1990).

9. Test II--optional The first order accurate Godunov-type scheme of Roe (1983) The ENO second order accurate scheme (1988)