Journal of Computational Physics
Numerical hydrodynamics from gas-kinetic theory
Journal of Computational Physics
Numerical Navier-Stokes solutions from gas kinetic theory
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Journal of Computational Physics
On the construction of kinetic schemes
Journal of Computational Physics
Runge--Kutta Discontinuous Galerkin Method Using WENO Limiters
SIAM Journal on Scientific Computing
An improved gas-kinetic BGK finite-volume method for three-dimensional transonic flow
Journal of Computational Physics
A Runge-Kutta discontinuous Galerkin method for viscous flow equations
Journal of Computational Physics
Remapping-free ALE-type kinetic method for flow computations
Journal of Computational Physics
Higher-order quadrature-based moment methods for kinetic equations
Journal of Computational Physics
Hi-index | 31.46 |
This paper presents a discontinuous Galerkin BGK (DGBGK) method for both viscous and inviscid flow simulations under a DG framework with a gas-kinetic flux and WENO limiters. In the DGBGK method, the construction of the flux in the DG method is based on the particle transport and collisional mechanism which not only couples the convective and dissipative terms together, but also includes both discontinuous and continuous terms in the flux formulation. Due to the connection between the gas-kinetic BGK model and the Euler as well as the Navier-Stokes equations, both viscous and inviscid flow equations can be simulated by a unified formulation. WENO limiters are used to obtain uniform high-order accuracy and sharp non-oscillatory shock transition. In the current method, the time accuracy is achieved by the direct integration of both time-dependent flux function at a cell interface and the flow variables inside each element. Numerical examples in one and two space dimensions are presented to illustrate the robustness and accuracy of the present scheme.