Calculation of Flows of Gas-Liquid Mixtures by a Modified Nodal Method of Characteristics

Abstract

To calculate flows of a gas-liquid mixture, a modified inverse method of characteristics is proposed. An additional fractional time step is introduced in its algorithm, which makes it possible to carry out calculations with a large time step without loss of accuracy and stability. A formulation of boundary conditions on curvilinear walls is discussed in relation to a multidimensional nodal method of characteristics which is based on splitting along the coordinate directions of the original system of equations into a number of one-dimensional subsystems. For the boundary points located on curvilinear impenetrable surfaces, a calculation method based on a method of fictitious nodes is proposed. When testing the modified method, a supersonic interaction of a homogeneous dispersed flow with a barrier is calculated for a flow regime with an attached shock wave. Problems of steady mixture flows near an external obtuse angle, as well as near a cone, which are analogues of Prandtl–Meyer and Busemann flows in gas dynamics, are solved. The calculation results are compared with available self-similar solutions, and a satisfactory agreement is reached.