Implementation of dual time-stepping strategy of the gas-kinetic scheme for unsteady flow simulations

Abstract

In our study, the dual time-stepping strategy of the gas-kinetic scheme is constructed and used for the simulation of unsteady flows. In comparison to the previous implicit gas-kinetic scheme, both the inviscid and viscous flux Jacobian are considered in our work, and the linear system of the pseudo-steady-state is solved by applying generalized minimal residual algorithm. The accuracy is validated by several numerical cases, the incompressible flow around blunt bodies (stationary circular cylinder and square cylinder), and the transonic buffet on the NACA0012 airfoil under hybrid mesh. The numerical cases also demonstrate that the present method is applicable to approach the fluid flows from laminar to turbulent and from incompressible to compressible. Finally, the case of acoustic pressure pulse is carried out to evaluate the effects of enlarged time step, and the side effect of enlarged time step is explained. Compared with the explicit gas-kinetic scheme, the proposed scheme can greatly accelerate the computation and reduce the computational costs for unsteady flow simulations.

GKS and UGKS for High-Speed Flows

“…Another distinguishable feature of the GKS is the multi-dimensional property of the flux function [3,8], which incorporates both normal and tangential variations of the flow field in the flux computation, and makes the GKS suitable for flow simulations on unstructured mesh. In order to simulate high-speed flow, the GKS has been further developed in the aspects of physical modeling and numerical algorithms, such as the kinetic boundary condition [9,10], multiple temperature model [11][12][13][14][15][16][17][18][19][20], multi-component and reactive flow [21][22][23][24][25], and implicit scheme and multigrid acceleration [3,[26][27][28][29][30][31][32][33]. By employing a modified relaxation time [10,13,34], the corresponding constitutive relationship in the GKS have been improved so that the GKS can be applied in the near continuum regime.…”

Discrete Boltzmann model for implosion- and explosionrelated compressible flow with spherical symmetry

“…In recent years, a variety of kinetic models based on Boltzmann equation are proposed to simulate non-equilibrium flows [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. The Discrete Boltzmann Method (DBM) [24][25][26][27][28][29][30][31][32][33][34][35][36][37] recently developed from the Lattice Boltzmann Method (LBM) [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52] belongs to this category.…”

An implicit gas-kinetic scheme for turbulent flow on unstructured hybrid mesh

“…As mentioned above, several kinds of IGKS have been applied for compressible flow simulations [6,7]. For unsteady flows, a dual time-stepping strategy of gas-kinetic scheme is proposed by Li et al [8]. In their works, fluid flows from laminar to turbulent and from incompressible to compressible are accurately simulated with better efficiency than previous method.…”

“…In particular, the one-equation Splalart-Allmaras (SA) model [14] became quite popular because of its satisfactory results for a wide range of flow problems and its reliable numerical properties. On the basis of the explicit GKS, we have successfully carried out the simulation of compressible turbulent flows with shock waves on unstructured meshes, in which the SA turbulence model [13] and SST turbulence model [8] are incorporated to include the effect of turbulence. In this study, the SA turbulence model is also selected on account of its good accurate and stability under relatively coarse grid near the wall, as well as its low computational cost.…”