IMPLICIT ECONOMICAL ALGORITHM FOR NUMERICAL INTEGRATION OF A SYSTEM OF EQUATIONS FOR DESCRIBING THE STATE OF A MULTIPHASE FLOW WITH COMMON PRESSURE IN THE BAROTROPIC APPROXIMATION

Abstract

An economical scheme for numerical integration of a system of differential equations is proposed for the model of a multiphase medium with a common pressure in liquids. The algorithm allows us to consider an arbitrary number of liquids and allows for the possibility of degeneration of this parameter to one liquid in the calculation process. The equation of state for liquids has no restriction related to the finite compressibility of the medium, i.e. the liquid can be incompressible. An implicit method for generating a solution is used. Cost-effectiveness is provided by the fact that the algorithm for constructing the inverse matrix is based on the splitting scheme for physical processes and the solvability of equations within scalar runs. As an example, the flow variant for three liquids is considered.

Keywords

• multi-fluid model
• barotropic approximation
• implicit algorithm
• numerical simulation
• cauchy problem