Computational Study of Partial Differential Equations with Compressible Two–phase Flow Application

The one–dimensional differential equations for the conservation mixture mass and mixture momentum coupled by a relative velocity conservation equation have been solved for an isentropic mixture of gas and liquid two–phase flow. Under certain restrictions the resulting system of partial differential equations is hyperbolic and allow discontinuous solutions. These equations have been solved by the TVD SLIC scheme with good accuracy in a simple way. To illustrate the character of the solution of the model, results are presented for an isentropic gas–liquid mixture two–phase flow Riemann problem. The solution is validated against existing exact results in conjunction with the SLIC scheme.