A multi-prediction implicit scheme for steady state solutions of gas flow in all flow regimes

Abstract

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.