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Related Experiment Videos

Three-dimensional lattice Boltzmann model for compressible flows.

Chenghai Sun1, Andrew T Hsu

  • 1Department of Mechanical Engineering, Indiana University-Purdue University, Indianapolis, Indiana 46202-5132, USA. csun@hms.harvard.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 26, 2003
PubMed
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A new 3D compressible lattice Boltzmann model efficiently handles wide Mach number flows and shock waves. This model simplifies calculations and improves accuracy for viscous and inviscid compressible fluid dynamics.

Area of Science:

  • Computational Fluid Dynamics (CFD)
  • Fluid Mechanics
  • Numerical Analysis

Background:

  • Standard lattice Boltzmann models face challenges with high Mach numbers and shock wave capturing.
  • Existing models often require complex treatments for fourth-order velocity tensors, increasing computational cost.
  • Accurate simulation of compressible flows, both viscous and inviscid, remains a significant computational challenge.

Purpose of the Study:

  • To develop a novel three-dimensional compressible lattice Boltzmann model.
  • To enhance the model's capability to handle a wide range of Mach numbers and capture shock waves efficiently.
  • To simplify the formulation and boundary condition implementation for compressible flow simulations.

Main Methods:

  • Formulation of a 3D compressible lattice Boltzmann model on a cubic lattice with a large particle-velocity set.

Related Experiment Videos

  • Incorporation of a simplified equilibrium distribution function with a six-direction support set.
  • Recovery of Navier-Stokes equations using the Chapman-Enskog method from the Bhatnagar-Gross-Krook (BGK) lattice Boltzmann equation.
  • Elimination of second-order discretization error via a modified collision invariant.

    • Main Results:

    • The model efficiently handles flows across a wide range of Mach numbers and captures shock waves.
    • Elimination of fourth-order velocity tensors simplifies the formulation and avoids special treatments.
    • Accurate simulation of inviscid flows, including 3D shock-wave propagation and Mach 10 normal shock.
    • Successful application to viscous flows: flat plate boundary layer, flow over a cylinder, and transonic flow over an airfoil cascade.

    Conclusions:

    • The developed lattice Boltzmann model is suitable for both viscous and inviscid compressible flows, with or without shocks.
    • The simplified equilibrium distribution allows for easy implementation of boundary conditions on curved walls.
    • The model offers an efficient and accurate approach for complex compressible flow simulations.