Abstract
AbstractA general framework for the development of high-order compact schemes has been proposed recently. The core steps of the schemes are composed of the following. 1). Based on a kinetic model equation, from a generalized initial distribution of flow variables construct a time-accurate evolution solution of gas distribution function at a cell interface and obtain the corresponding flux function; 2). Introduce the WENO-type weighting functions into the high-order time-derivative of the cell interface flux function in the multistage multi-derivative (MSMD) time stepping scheme to cope with the possible impingement of a shock wave on a cell interface within a time step, and update the cell-averaged conservative flow variables inside each control volume; 3). Model the time evolution of the gas distribution function on both sides of a cell interface separately, take moments of the inner cell interface gas distribution function to get flow variables, and update the cell-averaged gradients of flow variables inside each control volume; 4). Based on the cell-averaged flow variables and their gradients, develop compact initial data reconstruction to get initial condition of flow distributions at the beginning of next time step. A compact gas-kinetic scheme (GKS) up to sixth-order accuracy in space and fourth-order in time has been constructed on 2D unstructured mesh. In this paper, the compact GKS up to fourth-order accuracy on three-dimensional tetrahedral mesh will be further constructed with the focus on the WENO-type initial compact data reconstruction. Nonlinear weights are designed to achieve high-order accuracy for the smooth Navier-Stokes solution and keep super robustness in 3D computation with strong shock interactions. The fourth-order compact GKS uses a large time step with a CFL number 0.6 in the simulations from subsonic to hypersonic flow. A series of test cases are used to validate the scheme. The high-order compact GKS can be used in 3D applications with complex geometry.
Funder
Hong Kong research grant council
Center for Ocean Research in Hong Kong and Macau
National Science Foundation of China
Publisher
Springer Science and Business Media LLC
Subject
Mechanical Engineering,Aerospace Engineering,Modeling and Simulation,Renewable Energy, Sustainability and the Environment,Civil and Structural Engineering
Cited by
4 articles.
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