On two approaches to modelling the inflow boundary

Two approaches to modeling inflow boundary through solving one-dimensional equations of gas dynamics by means of boundary conditions and right-hand sides in the equations involving the Dirac delta function are discussed. Comparisons of numerical solutions of one-dimensional stationary equations of gas dynamics with the exact ones, as well as between numerical solutions of unsteady gas dynamics equations are performed for two approaches. Three kinds of boundary conditions are considered, namely, a constant inflow, pressure-dependent inflow, and inflow varying in time. It is shown that the numerical solutions obtained based on the finite-difference scheme of first order accuracy by the two considered approaches converge to each other with the mesh refinement. The numerical solution for the steady state problem coincides with the analytical one if the pressure at the boundary cell face is set equal to the pressure in the center of the boundary cell.