A hybrid method for hydrodynamic-kinetic flow Part I: A particle-grid method for reducing stochastic noise in kinetic regimes

Journal Article · Mon Jun 20 00:00:00 EDT 2011 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2011.03.047· OSTI ID:21499757

Alaia, Alessandro ^[1]; Puppo, Gabriella ^[1]

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1. Department of Mathematics, Politecnico di Torino, c.so Duca Degli Abruzzi 24, 10129 Torino (Italy)

In this work we present a hybrid particle-grid Monte Carlo method for the Boltzmann equation, which is characterized by a significant reduction of the stochastic noise in the kinetic regime. The hybrid method is based on a first order splitting in time to separate the transport from the relaxation step. The transport step is solved by a deterministic scheme, while a hybrid DSMC-based method is used to solve the collision step. Such a hybrid scheme is based on splitting the solution in a collisional and a non-collisional part at the beginning of the collision step, and the DSMC method is used to solve the relaxation step for the collisional part of the solution only. This is accomplished by sampling only the fraction of particles candidate for collisions from the collisional part of the solution, performing collisions as in a standard DSMC method, and then projecting the particles back onto a velocity grid to compute a piecewise constant reconstruction for the collisional part of the solution. The latter is added to a piecewise constant reconstruction of the non-collisional part of the solution, which in fact remains unchanged during the relaxation step. Numerical results show that the stochastic noise is significantly reduced at large Knudsen numbers with respect to the standard DSMC method. Indeed in this algorithm, the particle scheme is applied only on the collisional part of the solution, so only this fraction of the solution is affected by stochastic fluctuations. But since the collisional part of the solution reduces as the Knudsen number increases, stochastic noise reduces as well at large Knudsen numbers.

• OSTI ID: 21499757
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 14 Vol. 230; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
ALGORITHMS
BOLTZMANN EQUATION
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
EQUATIONS
FLUCTUATIONS
FLUID FLOW
GAS FLOW
INTEGRO-DIFFERENTIAL EQUATIONS
KINETIC EQUATIONS
KNUDSEN FLOW
MATHEMATICAL LOGIC
MATHEMATICAL MODELS
MATHEMATICAL SOLUTIONS
MONTE CARLO METHOD
NOISE
PARTIAL DIFFERENTIAL EQUATIONS
STOCHASTIC PROCESSES
TRANSPORT THEORY
VARIATIONS