DIFFERENCE SCHEME WITH WELL CONTROLLED DISSIPATION FOR SOLUTION OF KAPILA MODEL

The work is devoted to the derivation and numerical studies of a difference scheme with well-controlled dissipation for solution of equations of the Kapila model. Kapila model is widely used for analysis of two-phase compressible flows. It has a form of first order non-conservative hyperbolic system. As any other 1st order non-conservative hyperbolic system it requires definition of the regularizing dissipative operator to define discontinuous solutions and Rankin–Hugoniot conditions. The choice of dissipative operator influence wave structure observed in the solutions. Schemes with well-controlled are constructed in such a way that the dissipative operator which is determined by the form of their equivalent equation coincides with the one used to define correct setting of the original problem to be solved. As a result, it is expected that numerical solution converges to the solution of the system under consideration. Numerical experiments presented in the work demonstrate the effectiveness of this approach. As exact solutions numerical solutions of the traveling wave type obtained by other methods were used.