American Institute of Mathematical Sciences

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October  1998, 4(4): 609-634. doi: 10.3934/dcds.1998.4.609

On two-dimensional Riemann problem for pressure-gradient equations of the Euler system

Peng Zhang 1, , Jiequan Li 2, and  Tong Zhang 3,

1. 

Beijing Information and Technology Institute, Beijing, 100101, China
2. 

Institute of Applied Mathematics, Academia Sinica, Beijing, 100080, China
3. 

Institute of Mathematics, Academia Sinica, Beijing, 100080

Received  December 1997 Published  July 1998

We consider the two-dimensional Riemann problem for the pressure-gradient equations with four pieces of initial data, so restricted that only one elementary wave appears at each interface. This model comes from the flux-splitting of the compressible Euler system. Lack of the velocity in the eigenvalues, the slip lines have little influence on the structures of solutions. The flow exhibits the simpler patterns than in the Euler system, which makes it possible to clarify the interaction of waves in two dimensions. The present paper is devoted to analyzing the structures of solutions and presenting numerical results to the two-dimensional Riemann problem. Especially, we give the criterion of transition from the regular reflection to the Mach reflection in the interaction of shocks.
Keywords: two-dimensional Riemann problem, regular reflection, Mach reflection, Pressure-gradient equations, rarefaction wave, slip line, MmB scheme., shock.
Mathematics Subject Classification: 35L65, 58F40, 65M06, 76N1.
Citation: Peng Zhang, Jiequan Li, Tong Zhang. On two-dimensional Riemann problem for pressure-gradient equations of the Euler system. Discrete & Continuous Dynamical Systems - A, 1998, 4 (4) : 609-634. doi: 10.3934/dcds.1998.4.609
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