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Consistent vortex initialization for the athermal lattice Boltzmann method.

Gauthier Wissocq1,2, Jean-François Boussuge1, Pierre Sagaut3

  • 1CERFACS, 42 Avenue G. Coriolis, 31057 Toulouse cedex, France.

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Summary
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This study introduces a new method for initializing fluid dynamics simulations using an athermal equation of state, reducing errors in barotropic vortex test cases. This approach improves computational accuracy for fluid flow modeling.

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Area of Science:

  • Computational fluid dynamics
  • Fluid dynamics simulations
  • Numerical analysis

Background:

  • The convected vortex test case is a standard benchmark in fluid dynamics.
  • Existing initialization methods can lead to spurious relaxation and wave generation.
  • Athermal equations of state offer an alternative to isentropic assumptions.

Purpose of the Study:

  • To derive and implement a barotropic initialization for the convected vortex test case using an athermal equation of state.
  • To assess the performance of this new initialization on a lattice Boltzmann solver.
  • To reduce spurious wave generation and improve computational accuracy.

Main Methods:

  • Rigorous derivation of barotropic Euler equations with an athermal equation of state.
  • Initialization using a given velocity distribution and solving for a consistent density field.
  • Assessment on a D2Q9 lattice Boltzmann solver.

Main Results:

  • Significantly lower spurious relaxation compared to isentropic initialization.
  • Observed reduction attributed to spatial resolution, not approximated quantities.
  • Further reduction of spurious waves achieved by including off-equilibrium distribution functions.

Conclusions:

  • The proposed athermal initialization provides a more accurate and stable method for fluid dynamics simulations.
  • This technique minimizes spurious effects, leading to more reliable computational fluid dynamics results.
  • The findings are crucial for advancing numerical methods in fluid flow analysis.