Assessment of schemes for coupling Monte Carlo and Navier-Stokes solution methods

Hash, David; Hassan, H. A.

doi:10.2514/3.781

Cited by 96 publications

(60 citation statements)

References 4 publications

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“…Some researchers determine the average flux of mass, momentum, and energy carried by DSMC particles as they cross the interface and impose this as the macroscopic flux into the neighboring NS cell. Such "flux-based" coupling was used by Hash and Hassan to couple the DSMC method with a NS solver for simulations of Couette flow 7 and hypersonic flow over a blunted cone. 8 More recently, Wijesinghe et al also used flux-based coupling to embed a DSMC solver in the finest level of an adaptive mesh and algorithmic refinement (AMAR) scheme for the Euler equations.…”

Section: B Coupled Hybrid Methodsmentioning

confidence: 99%

Hybrid Particle-Continuum Simulations of Non-Equilibrium Hypersonic Blunt Body Flow Fields

Schwartzentruber

Scalabrin

Boyd

2006

9th AIAA/ASME Joint Thermophysics and Heat Transfer Conference

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A modular particle-continuum (MPC) numerical method is presented which solves the Navier-Stokes (NS) equations in regions of near-equilibrium and uses the direct simulation Monte Carlo (DSMC) method where the flow is in non-equilibrium. The MPC method is designed specifically for steady-state, hypersonic, nonequilibrium flows and couples existing, state-of-the-art DSMC and NS solvers into a single modular code. The MPC method is tested for 2D flow of N 2 at various Mach numbers over a cylinder where the global Knudsen number is 0.01. For these conditions, NS simulations significantly over-predict the local shear-stress, and also over-predict the peak heating rate by 5-10% when compared with full DSMC simulations. DSMC also predicts faster wake closure and 10-15% higher temperatures in the immediate wake region. The MPC code is able to accurately reproduce DSMC flow field results, local velocity distributions, and surface properties up to 2.8 times faster than full DSMC simulations. The computational time saved by the MPC method is directly proportional to the fraction of the flow field which is in near-equilibrium. It is found that particle simulation of the shock interior is not necessary for accurate prediction of surface properties, however particle simulation of the boundary layer and near-wake region is.

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Section: B Coupled Hybrid Methodsmentioning

confidence: 99%

Hybrid Particle-Continuum Simulations of Non-Equilibrium Hypersonic Blunt Body Flow Fields

Schwartzentruber

Scalabrin

Boyd

2006

9th AIAA/ASME Joint Thermophysics and Heat Transfer Conference

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“…Clearly the details of the schemes are rather problem dependent [1,10,18,20,29,38,42,51,52,62,63,65]. We quote the recent works by Weinan E and Bjorn Engquist for a general approach to heterogeneous multiscale methods in scientific computing [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Hybrid Multiscale Methods for Hyperbolic and Kinetic Problems

Pareschi

2005

ESAIM: Proc.

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Abstract. In these notes we present some recent results on the development of hybrid methods for hyperbolic and kinetic equations with multiple scales. The main ingredients in the schemes are a suitable merging of particle methods in non stiff regimes with high resolution shock capturing techniques in stiff ones. The key aspect in the development of the algorithms is the choice of a suitable hybrid representation of the solution.First, after a brief review on sampling methods and Monte Carlo techniques, we introduce the hybrid schemes for hyperbolic systems with relaxation and present numerical applications to the simple JinXin relaxation model both in one and two space dimensions. Next, we show how to extend the above methodology to the case of kinetic models of BGK type and discuss the challenging case of the full Boltzmann equation. Some numerical results are also presented.Résumé. Nous présentons dans ces notes quelques résultats récents concernant le développement de méthodes hybrides pour leséquations hyperboliques et cinétiques. L'ingrédient principal de ces schémas réside dans un mélange pertinent de méthodes particulaires dans les régimes réguliers et de techniques haute résolution de capture de choc dans les zones raides. La clef du développement de ces algorithmes est donnée par le choix d'une bonne représentation hybride de la solution.Après une brève revue des méthodes d'échantillonnage et des techniques Monte-Carlo, nous introduisons des schémas hybrides pour des systèmes hyperboliques avec relaxation et présentons des applications numériques pour le modèle de Jin-Xin, en dimension un et deux. Ensuite, nous montrons comment cette méthodologie s'étendà des modèles cinétiques de type BGK et discutons le cas délicat de l'équation de Boltzmann. Des résultats numériques sont aussi présentés pour ces situations.

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“…Previous techniques for acceleration of DSMC close to uid regimes, such as [16][17][18][19], have divided the spatial region into two subregions: a uid region in which the Euler or Navier-Stokes equations are solved and an RGD region in which DSMC is used. The focus of these methods has been to determine how best to choose the two domains and on design of boundary conditions to couple the uid and RGD regions.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of the Boltzmann equation by time relaxed Monte Carlo (TRMC) methods

Pareschi

Trazzi

2005

Numerical Methods in Fluids

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A new family of Monte Carlo schemes has been recently introduced\ud for the numerical solution of the Boltzmann equation of rarefied gas\ud dynamics[14]. After a splitting of the equation the time discretization of the\ud collision step is obtained from the Wild sum expansion of the solution by replacing\ud high order terms in the expansion with the equilibrium Maxwellian\ud distribution. The corresponding time relaxed Monte Carlo (TRMC) schemes\ud allow the use of time steps larger than those required by direct simulation\ud Monte Carlo (DSMC) and guarantee consistency in the fluid-limit with the\ud compressible Euler equations. Conservation of mass, momentum, and energy\ud are also preserved by the schemes. Applications to a two-dimensional gas dynamic\ud flow around an obstacle are presented which show the improvement in\ud terms of computational efficiency of TRMC schemes over standard DSMC for\ud regimes close to the fluid-limit

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Assessment of schemes for coupling Monte Carlo and Navier-Stokes solution methods

Cited by 96 publications

References 4 publications

Hybrid Particle-Continuum Simulations of Non-Equilibrium Hypersonic Blunt Body Flow Fields

Hybrid Particle-Continuum Simulations of Non-Equilibrium Hypersonic Blunt Body Flow Fields

Hybrid Multiscale Methods for Hyperbolic and Kinetic Problems

Numerical solution of the Boltzmann equation by time relaxed Monte Carlo (TRMC) methods

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