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High-order kinetic flow solver based on the flux reconstruction framework.

Ji Li1, Chengwen Zhong1, Sha Liu1

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This study introduces a high-order numerical method combining the kinetic inviscid flux (KIF) and flux reconstruction (FR) frameworks. This approach balances the benefits of gas-kinetic schemes with reduced computational costs, showing promise for simulating turbulent flows.

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Area of Science:

  • Computational Fluid Dynamics
  • Numerical Methods
  • Gas Kinetic Theory

Background:

  • The gas-kinetic scheme (GKS) offers excellent merits but can be computationally expensive.
  • Existing numerical frameworks require methods that balance accuracy with efficiency.
  • Integrating advanced kinetic theories into established numerical schemes is an ongoing challenge.

Purpose of the Study:

  • To develop a high-order numerical method using the kinetic inviscid flux (KIF) and flux reconstruction (FR) frameworks.
  • To create a method that retains the advantages of the gas-kinetic scheme (GKS) while reducing computational costs.
  • To enhance the efficiency of numerical simulations based on gas-kinetic theory.

Main Methods:

  • Developed a novel numerical method by integrating the kinetic inviscid flux (KIF) with the flux reconstruction (FR) framework.
  • KIF combines the totally thermalized transport (TTT) scheme and kinetic flux vector splitting (KFVS) method.
  • Replaced the Riemann flux solver at element interfaces with the KIF method, computing common solutions based on gas-kinetic theory.

Main Results:

  • The combined KIF-FR method demonstrated accuracy and efficiency in numerical simulations.
  • Adaptive weighting of TTT and KFVS fluxes was achieved using a coefficient related to time step and collision time.
  • The Taylor-Green vortex problem was used to validate the method's capability in simulating turbulent flows.

Conclusions:

  • The KIF-FR method provides a robust, efficient, and accurate high-order numerical approach.
  • The integration of gas-kinetic theory principles into the FR framework is feasible and beneficial.
  • The developed method shows significant potential for simulating complex fluid dynamics problems, including turbulence.