Two approaches for simulating the burning surface in gas dynamics by means boundary conditions and right sides in the equations involving Dirac delta function are discussed. A comparison of numerical steady-state solutions and the exact ones in one-dimensional approximation is performed for two approaches. It is shown that the numerical solutions obtained with the finite-difference scheme of first order accuracy on the base of two considered approaches converge to each other when the mesh refinement is applied. 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.

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The axisymmetric solid rocket motor (SRM) with an “umbrella” shape is considered in this paper. The numerical algorithm based on the inverse Lax-Wendroff procedure for a gas dynamic equation and on the level-set method for tracking the burning surface is overviewed for internal ballistics problems. Assuming that the propellant combustion proceeds in a quasi-stationary regime and a mass flow from the burning surface depends on the pressure raised to the power of parameter ν, the numerical computations of intra-chamber combustion product flows during the main-firing phase are carried out using the numerical algorithm developed for “umbrella”-shaped SRM at different parameter values. The approximation convergence of flow parameters in a case of the stationary propellant surface and average intra-chamber pressure for all the time of motor operation is examined. The numerical simulation results are obtained and analyzed for different “umbrella” inclination angles. Though the developed algorithm has been applied to the motors with a specific shape, it can also be used for propellant grains of different shapes and is easily extended to 3D models.