The solution of the Navier-Stokes equations using Gauss-Seidel line relaxation
Computers and Fluids - In honour of Gino Moretti on the occasion of his 70th birthday
Journal of Computational Physics
On the construction of kinetic schemes
Journal of Computational Physics
The kinetic scheme for the full-Burnett equations
Journal of Computational Physics
A compressible Navier-Stokes flow solver with scalar transport
Journal of Computational Physics
An adaptive grid method for two-dimensional viscous flows
Journal of Computational Physics
On the multidimensional gas-kinetic BGK scheme
Journal of Computational Physics
An improved gas-kinetic BGK finite-volume method for three-dimensional transonic flow
Journal of Computational Physics
A unified moving grid gas-kinetic method in Eulerian space for viscous flow computation
Journal of Computational Physics
A Runge-Kutta discontinuous Galerkin method for viscous flow equations
Journal of Computational Physics
A comparative study of the LBE and GKS methods for 2D near incompressible laminar flows
Journal of Computational Physics
Journal of Computational Physics
A gas-kinetic BGK scheme for semiclassical Boltzmann hydrodynamic transport
Journal of Computational Physics
Gas-kinetic numerical studies of three-dimensional complex flows on spacecraft re-entry
Journal of Computational Physics
Journal of Computational Physics
A numerical study of temporal shallow mixing layers using BGK-based schemes
Computers & Mathematics with Applications
A high-order gas-kinetic Navier-Stokes flow solver
Journal of Computational Physics
A unified gas-kinetic scheme for continuum and rarefied flows
Journal of Computational Physics
Journal of Computational Physics
A gas-kinetic BGK scheme for gas-water flow
Computers & Mathematics with Applications
Computers & Mathematics with Applications
Gas-kinetic numerical study of complex flow problems covering various flow regimes
Computers & Mathematics with Applications
WENO-enhanced gas-kinetic scheme for direct simulations of compressible transition and turbulence
Journal of Computational Physics
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This paper concerns the development and application of a gas-kinetic scheme based on the Bhatnagar-Gross-Krook (BGK) model for the Navier-Stokes equations in the study of hypersonic viscous flow. Firstly, we extend the gas-kinetic Navier-Stokes solver [K. Xu, A gas-kinetic BGK scheme for the Navier-Stokes equations and its connection with artificial dissipation and Godunov method, J. Comput. Phys. 171 (2001) 289-335] by implementing a multidimensional particle propagation mechanism in the flux evaluation, where the gradients of flow variables in both normal and tangential directions of a cell interface are explicitly included. With the construction of a time averaged flux function, an implicit BGK scheme with LU-SGS method is constructed. The main purpose of the current research is to pave the way to extend the current approach directly to the flow computation with unstructured mesh, where the flow gradients in both parallel and perpendicular directions around a cell interface can be explicitly taken into account in a viscous flow computation. In the numerical parts, we concentrate on the computation of heat flux in laminar hypersonic viscous flows, where complicated flow phenomena, i.e., shock boundary layer interaction, flow separation, and viscous/inviscid interaction, will be encountered. The cases studied include the type IV shock-shock interaction around a circular cylinder and hypersonic flow passing through a double-cone geometry. In the hypersonic viscous flow, in comparison with the capturing of velocity and pressure fields, the accurate computation of stress and heat flux bears large difficulties. In all cases studied here, the heat fluxes obtained across body surfaces have good agreement with the experimental measurements.