A solution algorithm for the fluid dynamic equations based on a stochastic model for molecular motion

DOI10.1016/j.jcp.2009.10.008zbMath1285.76031OpenAlexW2075504980MaRDI QIDQ846539

Manuel Torrilhon, Stefan Heinz, Patrick Jenny

Publication date: 9 February 2010

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2009.10.008

zbMATH Keywords

Fokker-Planck equationstochastic differential equationsMonte-Carlo methodPDF methodskinetic gas theoryBoltzman equation

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Particle methods and lattice-gas methods (76M28) Fokker-Planck equations (35Q84)

Related Items (46)

A Fokker-Planck model of the Boltzmann equation with correct Prandtl number ⋮ Cubic Fokker-Planck method for rarefied monatomic gas flow through a slit and an orifice ⋮ A hybrid particle approach based on the unified stochastic particle Bhatnagar-Gross-Krook and DSMC methods ⋮ Master equation approach for modeling diatomic gas flows with a kinetic Fokker-Planck algorithm ⋮ Entropic Fokker-Planck kinetic model ⋮ An accurate treatment of diffuse reflection boundary conditions for a stochastic particle Fokker-Planck algorithm with large time steps ⋮ Steady-state heat conduction in a gas undergoing rigid-body rotation. Comparison of Navier-Stokes-Fourier and bivelocity paradigms ⋮ Fokker–Planck model for computational studies of monatomic rarefied gas flows ⋮ Probability density function approach for modelling multi-phase flow with ganglia in porous media ⋮ Coupling kinetic and continuum using data-driven maximum entropy distribution ⋮ Transported Probability and Mass Density Function (PDF/MDF) Methods for Uncertainty Assessment and Multi-Scale Problems ⋮ Nonparametric inference for diffusion processes in systems with smooth evolution ⋮ Assessment of the cubic Fokker-Planck-DSMC hybrid method for hypersonic rarefied flows past a cylinder ⋮ Automatic mesh refinement and parallel load balancing for Fokker-Planck-DSMC algorithm ⋮ A diffusive information preservation method for small Knudsen number flows ⋮ An efficient particle Fokker-Planck algorithm for rarefied gas flows ⋮ Variance reduction for Fokker-Planck based particle Monte Carlo schemes ⋮ Capturing the influence of intermolecular potential in rarefied gas flows by a kinetic model with velocity-dependent collision frequency ⋮ A Fokker-Planck model of the Boltzmann equation with correct Prandtl number for polyatomic gases ⋮ Global existence and long time behavior of the ellipsoidal-statistical-Fokker-Planck model for diatomic gases ⋮ Importance sampling variance reduction for the Fokker-Planck rarefied gas particle method ⋮ Adaptive particle-cell algorithm for Fokker-Planck based rarefied gas flow simulations ⋮ Data-driven stochastic particle scheme for collisional plasma simulations ⋮ Variance reduced particle solution of the Fokker-Planck equation with application to rarefied gas and plasma dynamics ⋮ SPARTACUS: an open-source unified stochastic particle solver for the simulation of multiscale nonequilibrium gas flows ⋮ A comprehensive review on micro- and nano-scale gas flow effects: slip-jump phenomena, Knudsen paradox, thermally-driven flows, and Knudsen pumps ⋮ A high-order unified stochastic particle method based on the Bhatnagar-Gross-Krook model for multi-scale gas flows ⋮ Verification of a stochastic diffusion gas model ⋮ An efficient jump-diffusion approximation of the Boltzmann equation ⋮ A time-relaxed Monte Carlo method preserving the Navier-Stokes asymptotics ⋮ Parallel Fokker-Planck-DSMC algorithm for rarefied gas flow simulation in complex domains at all Knudsen numbers ⋮ Global existence and long time behavior of the ellipsoidal-Fokker–Planck equation ⋮ Comment on ``A solution algorithm for the fluid dynamic equations based on a stochastic model for molecular motion ⋮ Accurate particle time integration for solving Vlasov-Fokker-Planck equations with specified electromagnetic fields ⋮ A unified stochastic particle Bhatnagar-Gross-Krook method for multiscale gas flows ⋮ Unified gas-kinetic wave-particle methods. I: Continuum and rarefied gas flow ⋮ A Particle Fokker-Planck Algorithm with Multiscale Temporal Discretization for Rarefied and Continuum Gas Flows ⋮ Analysis of transport properties determined by Langevin dynamics using Green-Kubo formulae ⋮ Comment on analysis of transport properties determined by Langevin dynamics using Green-Kubo formulae ⋮ Particle simulation of nonequilibrium gas flows based on ellipsoidal statistical Fokker-Planck model ⋮ Fokker-Planck-DSMC algorithm for simulations of rarefied gas flows ⋮ An ES-BGK model for polyatomic gases in rotational and vibrational nonequilibrium ⋮ Treatment of long-range interactions arising in the Enskog-Vlasov description of dense fluids ⋮ A unified stochastic particle method based on the Bhatnagar-Gross-Krook model for polyatomic gases and its combination with DSMC ⋮ Fokker-Planck-Poisson kinetics: multi-phase flow beyond equilibrium ⋮ A variance-reduced direct Monte Carlo simulation method for solving the Boltzmann equation over a wide range of rarefaction

Cites Work

• Unnamed Item
• Unnamed Item
• A multiblock joint PDF finite-volume hybrid algorithm for the computation of turbulent flows in complex geometries
• Macroscopic transport equations for rarefied gas flows. Approximation methods in kinetic theory.
• Unified turbulence models for LES and RANS, FDF and PDF simulations
• The Boltzmann equation and its applications
• Discrete-velocity models and numerical schemes for the Boltzmann-BGK equation in plane and axisymmetric geometries
• Lattice-gas cellular automata and lattice Boltzmann models. An introduction
• Consistent inflow and outflow boundary conditions for transported probability density function methods
• Boundary conditions for regularized 13-moment-equations for micro-channel-flows
• From stochastic processes to the hydrodynamic equations
• Hybrid Navier-Stokes/DSMC Simulations of Gas Flows with Rarefied-Continuum Transitions
• Numerical analysis of the Poiseuille and thermal transpiration flows between two parallel plates on the basis of the Boltzmann equation for hard-sphere molecules
• Direct simulation of gas flows at the molecular level
• Regularization of Grad’s 13 moment equations: Derivation and linear analysis
• Nonequilibrium Distribution Functions in a Fluid
• Application of PDF methods to compressible turbulent flows
• A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems
• A hybrid algorithm for the joint PDF equation of turbulent reactive flows
• PDF simulations of a bluff-body stabilized flow

This page was built for publication: A solution algorithm for the fluid dynamic equations based on a stochastic model for molecular motion