Application of the "Generalized Riemann Problem" Method to 1D Compressible Flows with Material Interfaces
Abstract
The "Generalized Riemann Problem" (GRP) method is applied to 1D compressible flows with material interfaces and variable cross section. The resulting scheme is secondorder and uses a "mixedtype" grid, where cell boundaries can be either Lagrangian or Eulerian. In fact, using the analytic resolution of discontinuities at cell boundaries, provided by the GRP solution, one can extend the scheme presented here to include any adaptive mesh. Two numerical examples are studied: a planar shocktube and exploding helium sphere. It is shown that discontinuities are sharply resolved while there are no oscillations in the smooth part of the flow. In particular, wave interactions, including formation of new shocks and reflection from the center of symmetry, are automatically taken care of.
 Publication:

Journal of Computational Physics
 Pub Date:
 July 1986
 DOI:
 10.1016/00219991(86)900100
 Bibcode:
 1986JCoPh..65..170B
 Keywords:

 Cauchy Problem;
 Compressible Flow;
 Computational Fluid Dynamics;
 Fluid Boundaries;
 One Dimensional Flow;
 Shock Waves;
 Computational Grids;
 EulerLagrange Equation;
 Gas Explosions;
 Shock Tubes;
 Fluid Mechanics and Heat Transfer