To the calculation of flows of gas-liquid mixtures by a modified nodal characteristics

To calculate flows of a gas-liquid mixture, a modified inverse method of characteristics is proposed, in whose algorithm an additional fractional time step is introduced, 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 the 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 the method of fictitious nodes is proposed. When testing the modified method, the 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 the 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.