Kinetic methods for solving the internal structure of shock waves

The objective of the study is to assess the accuracy of kinetic schemes in resolving the internal structure of the shock waves. Two kinetic schemes were used, a gas kinetic BGK scheme and the direct integration of the Boltzmann equation. The argon hard sphere collision model was considered for freestream Mach numbers ranging from 1.2 to 10. The results from the calculations of the direct integration of Boltzmann equations of Ohwada were used as benchmark for Mach 1.2, 2, and 3 shock waves. The results from the direct integration solvers matched reasonably well. Agreement from gas kinetic BGK scheme at the low Mach number was good, but at higher Mach number the starting jump location was missed. A study of the velocity grid requirements for a numerical solution of the Boltzmann equation was conducted by the method developed by Tcheremissine.1 The requirements are modest but are most stringent at the shock front location. Both the solution of the kinetic equation and the numerical evaluation of the macroscopic parameters determine the grid requirement