Simulation of Shock Wave Diffraction over 90° Sharp Corner in Gases of Arbitrary Statistics

The unsteady shock wave diffraction over a 90° sharp corner in gases of arbitrary particle statistics is simulated using an accurate and direct algorithm for solving the semiclassical Boltzmann equation with relaxation time approximation in phase space. The numerical method is based on the usage of discrete ordinate method for discretizing the velocity space of the distribution function; whereas a second order accurate TVD scheme (Harten in J. Comput. Phys. 49(3):357–393, 1983) with Van Leer’s limiter (J. Comput. Phys. 32(1):101–136, 1979) is used for evolving the solution in physical space and time. The specular reflection surface boundary condition is assumed. The complete diffraction patterns are recorded using various flow property contours. Different range of relaxation times approximately corresponding to continuum, slip and transitional regimes are considered and the equilibrium Euler limit solution is also computed for comparison. The effects of gas particles that obey the Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics are examined and depicted.