Gas-kinetic finite volume methods, flux-vector splitting, and artificial diffusion
The authors found that the gas-kinetic discretization can be explained in terms of standard central difference and upwind schemes. Artificial viscosity concepts are reviewed and linked to the grid size and to the physical length scale of the discontinuity. Also, a new three-dimensional gas-kinetic scheme for the Navier-Stokes equations, whose solution satisfies the entropy condition, is presented. Two limiting cases of the scheme are discussed. The first one is the one-step Lax-Wendroff scheme, and the second one is the kinetic flux-vector splitting scheme. A new relaxation scheme for steady state calculations is also formulated and implemented in the frame of multigrid time stepping technique of Jameson. When applied to the Euler equations, the proposed method yields high accuracy and fast convergence to the steady state.
scientific article; zbMATH DE number 819430