Numerical Simulation of Supersonic Plane Gas Dynamics Problems on a Triangular Grid

This study focuses on modification of the Davydov’s method (large particles) in case of the triangular grid. Numerical approach to the solution of two-dimensional equations of non-viscous perfect gas flow (flat case) using triangular grids is developed. The only class of triangular cells is used in this method, instead of the two classes of cells of differential grid (fractional cell directly beside the body and regular cells in other cases) that are used in classical method of large particles, which simplifies the logic of computations. Vector notation is used to write equations of the method instead of matrix notation in the case of a regular grid. Due to the usage of triangular mesh formulas of all three stages of the method are considerably changed, while the ideology of the method remains the same: splitting of the initial equations on physical factors. Triangular mesh, except for the undoubted advantages associated with the construction of a body of complex shape, introduces additional complexity in the numerical calculations: the generation of grid itself (triangulation); neighboring triangles are not necessarily have adjacent indexes; calculation time increases for the movable body due to rebuild of the grid; additional memory for storing the geometry of the computational domain. Also in this paper the comparison of numerical solutions of the perfect nonviscous gas flows on an irregular grid using different methods is carried out. The comparison of numerical results obtained by the method of large particles in the case of a triangular mesh and for the case of a regular grid is carried out. The comparison of numerical results with the approximate analytic ones is carried out.

Davydov’s method, compressible gas, irregular triangular grid, Euler equations, three stages of computation on each step of time, loop integrals, isolines on a triangular grid, mass operations with normal and tangent components of a velocity vector, formula for the initial conditions of boundary value problems