Solving the Boltzmann Equation on GPU

We show how to accelerate the direct solution of the Boltzmann equation using Graphics Processing Units (GPUs). In order to fully exploit the computational power of the GPU, we choose a method of solution which combines a finite difference discretization of the free-streaming term with a Monte Carlo evaluation of the collision integral. The efficiency of the code is demonstrated by solving the two-dimensional driven cavity flow. Computational results show that it is possible to cut down the computing time of the sequential code of two order of magnitudes. This makes the proposed method of solution a viable alternative to particle simulations for studying unsteady low Mach number flows.Comment: 18 pages, 3 pseudo-codes, 6 figures, 1 tabl

GPU ACCELERATED SIMULATIONS OF RAREFIED GASESMICROFLOWS

Kinetic equations represent the natural theoretical and computational tool for the investigation of rarefaction effects in gaseous flows. Their complex mathematical structure leads to numerical schemes of various complexity whose common feature is the considerable demand of computing resources. In the case of a dilute gas, the most complex term, i.e. the collision term, has a spatially local structure. Hence, its time consuming numerical evaluation or simulation can be concurrently performed on multi-processor hardware platforms. Recent developments of hardware and software tools have made the massively parallel architecture of graphic processing units (GPUs) available for low cost scientific computing. The paper aims at showing that a particular class of numerical schemes, based on finite difference discretization of the distribution function combined with Monte Carlo evaluation of the collision integral, is very well adapted to the single instruction multiple data (SIMD) structure of GPUs, allowing a two orders of magnitude reduction of the computing time required by the single threaded version of the same code. The numerical scheme implementation is discussed and its application is illustrated by solving the full nonlinear unsteady Boltzmann equation in two dimensional planar geometry and by solving a system of coupled Boltzmann equations to investigate the sound propagation in a binary mixture. The strategies to correct the scheme main drawbacks and further improvements of its performances are discussed

Solving model kinetic equations on GPUs

We present an algorithm specifically tailored for solving model kinetic equations onto Graphics Processing Units (GPUs). The efficiency of the algorithm is demonstrated by solving the one-dimensional shock wave structure problem and the two-dimensional low Mach number driven cavity flow. Computational results show that it is possible to cut down the computing time of the sequential codes of two orders of magnitude. The algorithm can be easily extended to more general collision models

Effect of vibrational degrees of freedom on the heat transfer in polyatomic gases confined between parallel plates

Conductive stationary heat transfer through rarefied nonpolar polyatomic gases, confined between parallel plates maintained at different temperatures, is investigated. It is assumed that gas molecules possess both rotational and vibrational degrees of freedom, described by the classical rigid rotator and quantum harmonic oscillator models, respectively. The flow structure is computed by the Holway kinetic model and the Direct Simulation Monte Carlo method. In both approaches the total collision frequency is computed according to the Inverse Power Law intermolecular potential. Inelastic collisions in DSMC simulations are based on the quantum version of the Borgnakke-Larsen collision model. Results are presented for N2, O2, CO2, CH4 and SF6 representing diatomic as well as linear and nonlinear polyatomic molecules with 1 up to 15 vibrational modes. The translational, rotational, vibrational and total temperatures and heat fluxes are computed in a wide range of the rarefaction parameter and for various ratios of the hot over the cold plate temperatures. Very good agreement, between the Holway and DSMC results is observed as well as with experiments. The effect of the vibrational degrees of freedom is demonstrated. In diatomic gases the vibrational heat flux varies from 5% up to 25% of the total one. Corresponding results in polyatomic gases with a higher number of vibrational modes show that even at low reference temperatures the contribution of the vibrational heat flux may be considerably higher. For example in the case of SF6 at 300 K and 500 K the vibrational heat flux is about 67% and 76% respectively of the total heat flux. Furthermore, it is numerically proved that the computed solutions are in agreement with the Chapman-Enskog approximation in a central strip of the computational domain even at moderately large values of the rarefaction parameter, as found in previous investigations. This property has been used to compute the gas thermal conductivity predicted by the adopted models. © 2016 Elsevier Ltd. All rights reserved

On the application of the Boltzmann equation to the simulation of fluid structure interaction in MEMS

A three-dimensional quasi-static Stokes model, with a correction based on the kinetic theory of rarefied gas, is used to evaluate the damping forces exerted by gas flows on the moving surfaces of micromechanical structures in a wide range of pressures. Numerical results are compared with the experimental data collected on a silicon biaxial accelerometer in the continuum and transitional flow regimes. Furthermore, rarefied gas flows in ultra-thin film slider bearings are studied through a generalized Reynolds equation based on the linearized Boltzmann equation which holds for arbitrary Knudsen numbers. Since the generalized Reynolds equation is a flow rate-based model and is obtained by calculating the fundamental flows in the lubrication film (i.e., the Poiseuille and Couette flows), the plane Poiseuille-Couette flow problem between parallel plates has been preliminarly investigated. General boundary conditions of Maxwell's type have been considered by allowing for bounding surfaces with different physical properties