One-dimensional inviscid gas dynamics computations are made using a new method to solve the Boltzmann equation. The numerical method is explicit and is based on concepts from the kinetic theory of gases. The gas density, velocity and temperature are computed by integrating numerically the molecular velocity distribution function. This in turn is computed from the Boltzmann equation using an operator splitting approach. The basic algorithm is shown to be efficient and unconditionally stable. The method is tested for a single component diatomic ideal gas on initial-boundary value problems. These include the Riemann shock-tube problem and shock wave reflection from a stationary wall for a range of incident Mach numbers up to M = 10. The results show that the method can offer significant advantages over standard finite difference methods for certain problems. Shock waves are resolved well with minimal oscillations in the solution, and accurate results are obtained with Courant numbers an order of magnitude larger than the usual stability limit. The method performs best in regions of the flow which are close to thermodynamic equilibrium and is first order accurate in regions which are far from equilibrium, as would be predicted from kinetic theory arguments.
Recently several numerical methods have been proposed which use Boltzmann-like equations as the starting point for the computation of inviscid compressible gas dynamics. A velocity distribution function is chosen as the dependent variable and the flow variables (gas temperature, density and velocity) are computed from moments of the distribution function over molecular velocity space.
Kaniel and Falcovitz 121 proposed a transport model for isentropic gas dynamics. In their work an auxiliary thermodynamic distribution function was defined and this was used to yield the macroscopic flow variables via moment relations. This distribution function could be integrated analytically in certain special cases, but its second order moment differs from that of the true molecular velocity distribution function whose evolution is governed by the Boltzmann equation. Pullin [ 1 ] investigated both deterministic and Monte Carlo methods for the solution of gas dynamics problems using the Boltzmann equation. With the Monte Carlo method the velocity distribution function also included the contributions made by an ensemble of individual discrete particles. Their initial distribution corresponded to a Maxwellian 108