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A bottleneck of the numerical solution of the Boltzmann equation from the viewpoint of processor time cost is the computation of the collision integral. An obvious and simple idea of parallelization of these computations on multiprocessor systems is three-dimensional decomposition in the phase space where each process implements a sequential algorithm of the collision integral computation for its node in the physical space. Deeper decomposition that involves the velocity space is more optimal for GPGPU computations. The chosen model of parallelization of data with allowance for specific features of the CUDA architecture made it possible to reach a significant (up to 800 times) speedup of computations by performing them on a GPU cluster. A problem of the shock wave structure was solved as a test computation. [ABSTRACT FROM AUTHOR]

This study is devoted to the analysis of applicability of moment equations to the shock wave structure problem in a wide range of Mach numbers. A modification of original Grad's 13-moment set of equations, so-called regularized Grad's set of equations (R13), is taken as a mathematical model. The numerical method for this set is formulated as a variant of the explicit high-order Godunov scheme with linear reconstruction of flow parameters. The degree of applicability of moment equations is determined by comparisons with Direct Simulation Monte Carlo (DSMC) predictions. Numerical results for hard sphere molecules show that the R13 set of equations describes well the internal structure of the shock wave in a wide range of Mach numbers. Nevertheless, R13 set significantly overpredicts the overall temperature overshoot (about 3 times for M=8), which is apparently related to nonlinearity of the dependence of the product of the transverse temperature component and density on normalized density. [ABSTRACT FROM AUTHOR]

The direct simulation Monte Carlo (DSMC) method is a stochastic approach to solve the Boltzmann equation and is built on various numerical schemes for transport, collision and sampling. This work aims to compare and contrast two popular O(N) DSMC collision schemes - no-time-counter (NTC) and majorant collision frequency (MCF) - with the goal of identifying the fundamental differences. MCF and NTC schemes are used in DSMC simulations of a spatially homogeneous equilibrium gas to study convergence with respect to various collision parameters. While the MCF scheme forces the reproduction of the exponential distribution of time between collisions, the NTC scheme requires larger number of simulators per cell to reproduce this Poisson process. The two collision schemes are also applied to the spatially homogeneous relaxation from an isotropic non-Maxwellian given by the Bobylev exact solution to the Boltzmann equation. While the two schemes produce identical results at large times, the initial relaxation shows some differences during the first few timesteps. [ABSTRACT FROM AUTHOR]

A method of the numerical solution of the Boltzmann equation, which belongs to the family of deterministic particle-in-cell methods, and results of its application are described. Such a method is based on the possibility of presenting the collision integral of the Boltzmann equation in divergent form. [ABSTRACT FROM AUTHOR]

The viscosity effects on strong and weak shock wave reflection are investigated with the Navier-Stokes and DSMC flow solvers. It is shown that the viscosity plays a crucial role in the vicinity of three-shock intersection. Instead of a singular triple point, in viscous flow there is a smooth three shock transition zone, where one-dimensional shock jump relations cannot be applied. At the flow parameters corresponding to the von Neumann reflection, when no inviscid three-shock solution exists, the computations predict an irregular shock-wave configuration similar to that observed previously in experiments. The existence of a viscous zone in the region of shock-wave interaction allows a continuous transition from the parameters behind the Mach stem to the parameters behind the reflected shock, which is impossible in the inviscid three-shock theory. [ABSTRACT FROM AUTHOR]

Entry of a shock wave into a microchannel and its propagation in the channel are studied numerically by the continuum and kinetic approaches. It is shown that the shock wave is amplified immediately after it enters the microchannel. After that, the shock wave in an inviscid computation propagates over the microchannel with a constant velocity. In a viscous computation, the shock wave velocity decreases and the wave attenuates. Qualitative agreement between experimental data and viscous computations is demonstrated. [ABSTRACT FROM AUTHOR]