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General mechanisms for stabilizing weakly compressible models.

Jinhua Lu1, Nikolaus A Adams1,2

  • 1Department of Mechanical Engineering, Chair of Aerodynamics and Fluid Mechanics, Technical University of Munich, Boltzmannstraße 15, Garching 85748, Germany.

Physical Review. E
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Summary
This summary is machine-generated.

This study unifies weakly compressible models for simulating incompressible flows, revealing common stabilization mechanisms. The proposed solvers demonstrate excellent stability and accuracy for both isothermal and thermal flow simulations.

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Area of Science:

  • Computational fluid dynamics
  • Numerical analysis

Background:

  • Weakly compressible models are used to simulate incompressible flows, but lack a unified framework.
  • Existing models possess intrinsic computational stabilization mechanisms that are not fully understood.

Purpose of the Study:

  • To establish general mechanisms for stabilizing computations in weakly compressible models.
  • To develop a unified framework for these models.
  • To propose two general weakly compressible solvers for isothermal and thermal flows.

Main Methods:

  • Analysis of existing weakly compressible models to identify common stabilization terms.
  • Derivation of new solvers from standard governing equations, implicitly incorporating stabilization.
  • Numerical investigations to assess solver performance.

Main Results:

  • Identified common numerical dissipation, mass diffusion, and bulk viscosity terms across models.
  • Demonstrated that these terms provide general computational stabilization.
  • Developed two general weakly compressible solvers with good numerical stability and accuracy for isothermal and thermal flows.

Conclusions:

  • The identified general mechanisms effectively stabilize computations in weakly compressible models.
  • The proposed approach provides a unified and simple framework for constructing such solvers.
  • The developed solvers are robust and accurate for both isothermal and thermal flow simulations.