Simulation of three-dimensional forced compressible isotropic turbulence by a redesigned discrete unified gas kinetic scheme

Chen T. Wen X. Wang L.-P. Guo Z. Wang J. Chen S. Zhakebayev D.B.
1 February 2022 American Institute of Physics Inc.

Physics of Fluids
2022 #34 Issue 2

In this paper, we implemented the Boltzmann-equation-based mesoscopic model, developed recently by Chen et al. [Inverse design of mesoscopic models for compressible flow using the Chapman-Enskog analysis,Adv. Aerodyn. 3, 5 (2021)], to simulate three-dimensional (3D) forced compressible isotropic turbulence. In this model, both the Prandtl number and the ratio of bulk to shear viscosity can be arbitrary prescribed. The statistically stationary turbulent flow is driven by a large-scale momentum forcing in the Fourier space, with the internal heating due to the viscous dissipation at small scales being removed by a thermal cooling function. Under the framework of discrete unified gas kinetic scheme (DUGKS), a 3D direct numerical simulation code has been developed, incorporating a generalized Strang-splitting scheme. The weighted essentially non-oscillatory (WENO) scheme is used to increase local spatial accuracy in the reconstruction of particle distribution functions at the cell interface. A 3D discrete particle velocity model with a ninth-order Gauss-Hermite quadrature accuracy is used to ensure accurate evaluation of viscous stress and heat flux in the continuum regime. We simulate forced compressible isotropic turbulence at both low and high turbulent Mach numbers. A direct comparison is performed with the results obtained from a hybrid compact finite difference-WENO scheme solving directly the Navier-Stokes-Fourier system. The comparison validates our DUGKS code and indicates that DUGKS is a reliable and promising tool for simulating forced compressible isotropic turbulence. The work represents a first study to directly simulate forced compressible turbulence by a mesoscopic method based on the Boltzmann equation.

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Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Center for Complex Flows and Soft Matter Research, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong, 518055, China
Department of Mechanical Engineering, 126 Spencer Laboratory, University of Delaware, Newark, 19716-3140, DE, United States
Southern Marine Science and Engineering Guangdong Laboratory (Guangzhou), 1119 Haibin Road, Nansha District, Guangzhou, 511458, China
Guangdong-Hong Kong-Macao Jt. Lab. for Data-Driven Fluid Mechanics and Engineering Applications, Southern University of Science and Technology, Shenzhen, 518055, China
State Key Laboratory of Coal Combustion, School of Energy and Power Engineering, HuaZhong University of Science and Technology, Wuhan, Hubei, 430074, China
Department of Mathematical and Computer Modelling, Faculty of Mechanics and Mathematics, Al-Farabi Kazakh National University, Almaty, 050000, Kazakhstan

Guangdong Provincial Key Laboratory of Turbulence Research and Applications
Department of Mechanical Engineering
Southern Marine Science and Engineering Guangdong Laboratory (Guangzhou)
Guangdong-Hong Kong-Macao Jt. Lab. for Data-Driven Fluid Mechanics and Engineering Applications
State Key Laboratory of Coal Combustion
Department of Mathematical and Computer Modelling

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