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.

GPU ACCELERATED SIMULATIONS OF RAREFIED GASESMICROFLOWS

FREZZOTTI, ALDO;GHIROLDI, GIAN PIETRO;GIBELLI, LIVIO
2010

Abstract

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.
Proceedings of the 2nd European Conference on Microfluidics
9782906831858
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/575763
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact