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Gas kinetic flux solver based high-order finite-volume method for simulation of two-dimensional compressible flows
1Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Yudao Street, Nanjing 210016, Jiangsu, China.
Physical Review. E
|August 20, 2021
Summary
A new high-order gas kinetic flux solver (GKFS) simulates 2D compressible flows. This advanced method uses asymptotic solutions for improved accuracy over traditional schemes.
Area of Science:
- Computational Fluid Dynamics
- Kinetic Theory
- Numerical Analysis
Background:
- Accurate simulation of compressible flows is crucial in various engineering fields.
- Existing gas kinetic schemes rely on integral solutions, limiting accuracy.
- High-order methods are needed for precise flow field predictions.
Purpose of the Study:
- To develop a high-order gas kinetic flux solver (GKFS) for two-dimensional (2D) compressible flows.
- To evaluate numerical fluxes using local asymptotic solutions of the Boltzmann equation.
- To enhance simulation accuracy and efficiency.
Main Methods:
- Developed a high-order gas kinetic flux solver (GKFS).
- Employed local asymptotic solutions of the Boltzmann equation, including equilibrium distribution function and its substantial derivative.
- Utilized a second-order in time and fourth-order in space discretization for the substantial derivative.
- Applied Taylor series expansion for simplification.
Main Results:
- Achieved explicit numerical fluxes for macroscopic governing equations.
- Demonstrated high-order accuracy on both quadrilateral and triangular meshes.
- Outperformed second-order counterparts in numerical simulations.
Conclusions:
- The developed high-order GKFS accurately simulates 2D compressible flows.
- The method offers superior performance compared to existing second-order schemes.
- Applicable to complex flow simulations requiring high fidelity.
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