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Steady, Laminar Flow Between Parallel Plates01:17

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Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
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Fluid dynamics is the study of fluids in motion. Velocity vectors are often used to illustrate fluid motion in applications like meteorology. For example, wind—the fluid motion of air in the atmosphere—can be represented by vectors indicating the speed and direction of the wind at any given point on a map. Another method for representing fluid motion is a streamline. A streamline represents the path of a small volume of fluid as it flows. When the flow pattern changes with time, the...
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Laminar Flow: Problem Solving01:24

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Laminar flow occurs when a fluid moves smoothly in parallel layers with minimal mixing and turbulence. In fluid mechanics, ensuring laminar flow within a pipe is essential for precise control of flow characteristics, especially in engineering applications. The key factor in determining whether flow remains laminar is the Reynolds number, a dimensionless quantity that depends on the fluid's velocity, density, viscosity, and the pipe's diameter. A Reynolds number of 2100 or lower...
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Bernoulli's Equation for Flow Along a Streamline01:30

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Couette Flow01:22

Couette Flow

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Couette flow represents the flow of fluid between two parallel plates, with one plate fixed and the other moving with a constant velocity. This configuration allows for a simplified analysis using the Navier-Stokes equations, which govern fluid motion under conditions of viscosity and incompressibility. For Couette flow, the assumptions include a steady, laminar, incompressible flow with a zero-pressure gradient in the flow direction. This flow type is beneficial for understanding shear-driven...
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Maxwell-Boltzmann Distribution: Problem Solving01:20

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Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
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Updated: Dec 11, 2025

Author Spotlight: Optimization of Airflow Velocities in Battery Cooling Systems for Enhanced Thermal Performance and Reduced Energy Consumption
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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.