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

• Published in: Communications in nonlinear science & numerical simulation Vol. 92; p. 105470
• Main Authors: Yuan, Ruifeng, Liu, Sha, Zhong, Chengwen
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.01.2021; Elsevier Science Ltd
• Subjects: Accelerated tests; Computational fluid dynamics; Continuum flow; Convergence; Discrete velocity method; Gas flow; Implicit methods; Implicit scheme; Kinetic scheme; Kinetics; Multiscale analysis; Multiscale scheme; Navier-Stokes equations; Rarefied gas flow; Steady state; Velocity; Kinetic scheme; Rarefied gas flow; Discrete velocity method; Implicit scheme; Multiscale scheme
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2020.105470

•A second order macroscopic scheme with NS accuracy is applied to predict macroscopic variables for the DVM-framework gas-kinetic numerical system.•High efficiency is achieved in all flow regimes, especially in the continuum regime where the present method is thousands of times faster than the explicit DVM-framework method.•Multiscale kinetic solver is used to evaluate the residual and ensure the accuracy of the solution in all flow regimes.•The comparison of entropy generation rates calculated by the NS constitutive relations and the distribution function is conducted at various Kn numbers. 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.