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Efficient supersonic flow simulations using lattice Boltzmann methods based on numerical equilibria.

Jonas Latt1,2, Christophe Coreixas1, Joël Beny1

  • 1Department of Computer Science, University of Geneva, 1204 Geneva, Switzerland.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|August 25, 2020
PubMed
Summary
This summary is machine-generated.

A new double-distribution-function lattice Boltzmann method (DDF-LBM) efficiently simulates supersonic gas flows. This enhanced model accurately captures complex fluid dynamics, offering a powerful tool for high-speed flow research.

Keywords:
CFDCPUGPUcompressiblelattice Boltzmann methodsupersonic

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Area of Science:

  • Computational Fluid Dynamics
  • Fluid Dynamics
  • Aerodynamics

Background:

  • The Lattice Boltzmann Method (LBM) is a powerful numerical technique for simulating fluid flows.
  • Existing LBM models face challenges in accurately simulating polyatomic gases in supersonic regimes.
  • The Maxwell-Boltzmann distribution is fundamental to kinetic gas theory.

Purpose of the Study:

  • To develop an advanced double-distribution-function based lattice Boltzmann method (DDF-LBM) for simulating polyatomic gases in supersonic flow.
  • To extend existing discrete velocity methods to accurately reproduce higher moments of the Maxwell-Boltzmann distribution.
  • To enhance the efficiency and applicability of LBM for high-Reynolds-number, supersonic flow simulations.

Main Methods:

  • Implementation of a numerical equilibrium capable of reproducing arbitrary moments of the Maxwell-Boltzmann distribution.
  • Extension of the standard 5-constraint (mass, momentum, energy) approach to a 39-velocity model in 3D.
  • Analytical computation of Knudsen-number-dependent relaxation times to ensure stability.
  • Validation through simulation of the 1D Riemann problem, supersonic flow past a NACA0012 airfoil, and 3D flow past a sphere.

Main Results:

  • The proposed 39-velocity DDF-LBM accurately simulates thermal, compressible flows, including discontinuities.
  • The model demonstrates excellent behavior in low-viscosity, supersonic regimes for both 2D and 3D cases.
  • Stability is achieved through analytically computed, Knudsen-number-dependent relaxation times.
  • The new DDF-LBM shows significant efficiency improvements over previous models on both CPU and GPU architectures.

Conclusions:

  • The developed DDF-LBM provides an efficient and accurate method for simulating supersonic flows of polyatomic gases.
  • This approach overcomes limitations of previous LBM models in handling complex flow regimes.
  • The method opens new possibilities for tackling a wider range of compressible flow problems using LBM.