Numerical Solution of the Boltzmann Equation by Time Relaxed Monte Carlo (trmc) Methods
نویسندگان
چکیده
A new family of Monte Carlo schemes has been recently introduced for the numerical solution of the Boltzmann equation of rarefied gas dynamics[14]. After a splitting of the equation the time discretization of the collision step is obtained from the Wild sum expansion of the solution by replacing high order terms in the expansion with the equilibrium Maxwellian distribution. The corresponding time relaxed Monte Carlo (TRMC) schemes allow the use of time steps larger than those required by direct simulation Monte Carlo (DSMC) and guarantee consistency in the fluid-limit with the compressible Euler equations. Conservation of mass, momentum, and energy are also preserved by the schemes. Applications to a two-dimensional gas dynamic flow around an obstacle are presented which show the improvement in terms of computational efficiency of TRMC schemes over standard DSMC for regimes close to the fluid-limit.
منابع مشابه
Comparison between Time Relaxed Monte Carlo Method and Majorant Frequency Scheme methods for the space homogeneous Boltzmann equation
Recently a new class of schemes, called Time Relaxed Monte Carlo (TRMC) has been introduced for the numerical solution of the Boltzmann equation of gas dynamics. The motivation is to propose a systematic framework to derive Monte Carlo methods effective near the fluid dynamic regime. Before the methods can be accepted as alternative tools to other methods, they have to show that they are able t...
متن کاملDevelopment of a novel method in TRMC for a Binary Gas Flow Inside a Rotating Cylinder
A new approach to calculate the axially symmetric binary gas flow is proposed Dalton’s law for partial pressures contributed by each species of a binary gas mixture (argon and helium) is incorporated into numerical simulation of rarefied axially symmetric flow inside a rotating cylinder using the time relaxed Monte-Carlo (TRMC) scheme and the direct simulation Monte-Carlo (DSMC) method. The res...
متن کاملAdaptive and Recursive Time Relaxed Monte Carlo Methods for Rarefied Gas Dynamics
Recently a new class of Monte Carlo methods, called Time Relaxed Monte Carlo (TRMC), designed for the simulation of the Boltzmann equation close to fluid regimes have been introduced [16]. A generalized Wild sum expansion of the solution is at the basis of the simulation schemes. After a splitting of the equation the time discretization of the collision step is obtained from the Wild sum expans...
متن کاملA Relaxation Scheme for Solving the Boltzmann Equation Based on the Chapman-Enskog Expansion
In [16] a visco-elastic relaxation system, called the relaxed Burnett system, was proposed by Jin and Slemrod as a moment approximation to the Boltzmann equation. The relaxed Burnett system is weakly parabolic, has a linearly hyperbolic convection part, and is endowed with a generalized entropy inequality. It agrees with the solution of the Boltzmann equation up to the Burnett order via the Cha...
متن کاملPlane Couette Flow Computations by TRMC and MFS Methods
Abstract. A new class of schemes of the DSMC type for computing near-continuum flows has been recently suggested: the time-relaxed Monte Carlo (TRMC) methods. An important step preceding the wide use of these schemes is their validation by classical homogeneous and one-dimensional problems of gas dynamics. For this purpose, a plane Couette flow is considered in the present paper. A comparison o...
متن کامل