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A multi-prediction implicit scheme for steady state solutions of gas flow in all flow regimes
Communications in Nonlinear Science and Numerical Simulation ( IF 3.9 ) Pub Date : 2020-07-31 , DOI: 10.1016/j.cnsns.2020.105470
Ruifeng Yuan , Sha Liu , Chengwen Zhong

An implicit multiscale method with multiple macroscopic prediction for steady state solutions of gas flow in all flow regimes is presented. The method is based on the finite volume discrete velocity method (DVM) framework. At the cell interface, a numerical flux with construction similar to discrete unified gas-kinetic scheme (DUGKS) is applied to ensure multiscale property and make the scheme free from the influence of cell Knudsen number. The idea of the macroscopic variable prediction is adopted and further developed to form an efficient implicit method, where a second order prediction scheme based on the Navier-Stokes (NS) equation is constructed to predict macroscopic variables from macroscopic residuals for the microscopic implicit system, and then a multiple prediction structure is formed. The accurate prediction procedure endows the implicit numerical system with high convergence speed in all flow regimes, especially in the continuum flow regime where NS solution is directly predicted and the convergence is accelerated greatly. Test cases show that the present method is accurate and efficient, and is one order of magnitude faster than the previous prediction-based implicit multiscale scheme in the continuum flow regime.



中文翻译:

在所有流态下的气体稳态求解的多预测隐式方案

提出了一种具有多重宏观预测的隐式多尺度方法,用于在所有流态下的气体稳态求解。该方法基于有限体积离散速度方法(DVM)框架。在单元界面处,使用具有类似于离散统一气体动力学方案(DUGKS)的构造的数值通量来确保多尺度性质,并使该方案不受单元Knudsen数的影响。采用并进一步发展了宏观变量预测的思想,以形成一种有效的隐式方法,其中构造了基于Navier-Stokes(NS)方程的二阶预测方案,以便从微观隐式系统的宏观残差预测宏观变量,然后形成多重预测结构。精确的预测程序使隐式数值系统在所有流态下都具有较高的收敛速度,尤其是在直接预测NS解且极大地加速收敛的连续流态下。测试案例表明,该方法准确有效,比连续流模型中基于预测的隐式多尺度方案要快一个数量级。

更新日期:2020-07-31
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