The system of multiphase flow equations in the equilibrium barotropic approximation: a numerical scheme

In the paper, an economical integration scheme of a differential equation system has been proposed for the model of multiphase medium with a common pressure in liquids. The algorithm allows someone to consider various cases of multiphase medium flows with formation of any structure by the number of liquids under study and admits an asymptotic transition to a single-fluid model. The algebraic balance relation of the fluid volume fraction was stated through the form of a differential equation in pressure. The correctness of the Cauchy problem for an equation system was remade using repeated derivatives of the sought-for functions with respect to a spatial coordinate.The Riemann problem in the varying-area channel at various values of liquid pressure and its volume fraction on the different sides of a diaphragm in the three-fluid version was solved.