Stable boundary conditions and difference schemas for Navier-Stokes equations
SIAM Journal on Numerical Analysis
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Journal of Computational Physics
Boltzmann type schemes for gas dynamics and the entropy property
SIAM Journal on Numerical Analysis
Numerical hydrodynamics from gas-kinetic theory
Journal of Computational Physics
Kinetic flux-vector splitting for the Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
A discontinuous hp finite element method for diffusion problems
Journal of Computational Physics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
Journal of Computational Physics
On the construction of kinetic schemes
Journal of Computational Physics
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Discontinuous Galerkin BGK Method for Viscous Flow Equations: One-Dimensional Systems
SIAM Journal on Scientific Computing
An improved gas-kinetic BGK finite-volume method for three-dimensional transonic flow
Journal of Computational Physics
Journal of Scientific Computing
Journal of Computational Physics
Hi-index | 31.45 |
Kinetic schemes for compressible flow of gases are constructed by exploiting the connection between Boltzmann equation and the Navier-Stokes equations. This connection allows us to construct a flux splitting for the Navier-Stokes equations based on the direction of molecular motion from which a numerical flux can be obtained. The naive use of such a numerical flux function in a discontinuous Galerkin (DG) discretization leads to an unstable scheme in the viscous dominated case. Stable schemes are constructed by adding additional terms either in a symmetric or non-symmetric manner which are motivated by the DG schemes for elliptic equations. The novelty of the present scheme is the use of kinetic fluxes to construct the stabilization terms. In the symmetric case, interior penalty terms have to be added for stability and the resulting schemes give optimal convergence rates in numerical experiments. The non-symmetric schemes lead to a cell energy/entropy inequality but exhibit sub-optimal convergence rates. These properties are studied by applying the schemes to a scalar convection-diffusion equation and the 1-D compressible Navier-Stokes equations. In the case of Navier-Stokes equations, entropy variables are used to construct stable schemes.