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UGKS-BASED IMPLICIT ITERATIVE METHOD FOR MULTISCALE NONEQUILIBRIUM FLOW SIMULATIONS
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DOI：10.1137/21M1421398.png)
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The unified gas-kinetic scheme (UGKS) has been developed for rarefied and continuum flow simulations. To further enhance the computational efficiency of the implicit UGKS (IUGKS) [Y. Zhu, C. Zhong, and K. Xu, T. Comput. Phys., 315 (2016), pp. 16-38] for the steady-state solution, a two-step IUGKS is proposed in this paper. The multiscale solution of the UGKS is determined by the integral solution of the kinetic model equation, which is composed of the Lagrangian integration of the equilibrium and the free particle transport of the nonequilibrium state. With the implicit evaluation of the macroscopic variables in the first iterative step, the integration of the equilibrium can be directly used in the flux calculation of macroscopic flow variables in the second iterative step. This is equivalent to including the viscous flux in the implicit scheme to accelerate the convergence of the solution instead of using the Euler flux in the iterative process of the original IUGKS. In the present IUGKS, the update of macroscopic flow variables is closely coupled with the implicit evolution of the gas distribution function. At the same time, to get a more accurate physical solution the full Boltzmann collision term has been incorporated into the current scheme through the penalty method. Different iterative techniques, such as lower-upper symmetric Gauss-Seidel and multigrid, are used for solving the linear algebraic system of coupled macroscopic and microscopic equations. The efficiency of the current IUGKS has reached an outstanding level among all implicit schemes for the kinetic equations in the literature. Several numerical examples are used to validate the performance of the IUGKS. Accurate solutions have been obtained efficiently in all cases from rarefied to continuum regimes and from low to hypersonic speed.
Keyword:
unified gas-kinetic scheme
implicit iterative method
Boltzmann collision operator
multigrid
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