A Multidimensional Flux Function with Applications to the Euler and Navier-Stokes Equations

Abstract

A grid-independent approximate Riemann solver has been developed for use in both two- and three-dimensional flows governed by the Euler or Navier-Stokes equations. Fluxes on grid faces are obtained via wave decomposition. By assuming that information propagates in the velocity-difference directions, rather than in the grids-normal directions as in a standard grid-aligned solver, this flux function more appropriately interprets and hence more accurately resolves shock and shear waves when these lie oblique to the grid. The model, which describes the difference in states at each grid interface by the action of five waves, produces a significant increase in accuracy for both supersonic and subsonic first-order spatially accurate computations. Second-order computations with the grid-independent flux function are generally only worth the additional effort for flowfields whose primary structures include shear waves that lie oblique to the grid. Included in this category is the viscous flow over an airfoil in which a separated shear layer emanates from the airfoil surface at an angle to the grid. Pressure distortions which can result from misinterpretation of the oblique waves by a grid-aligned solver are essentially eliminated by the grid-independent flux function.