A study of convective flux schemes for aerospace flows

this paper presents the effects of some convective flux computation schemes on boundary layer and shocked flow solutions. second-order accurate centered and upwind convective flux computation schemes are discussed. the centered jameson scheme, plus explicitly added artificial dissipation terms are considered. three artificial dissipation models, namely a scalar and a matrix version of a switched model, and the cusp scheme are available. some implementation options regarding these methods are proposed and addressed in the paper. for the upwind option, the roe flux-difference splitting scheme is used. the cusp and roe schemes require property reconstructions to achieve second-order accuracy in space. a multidimensional limited muscl interpolation method is used to perform property reconstruction. extended multidimensional limiter formulation and implementation are here proposed and verified. theoretical flow solutions are used in order to provide a representative testbed for the current study. it is observed that explicitly added artificial dissipation terms of the centered scheme may nonphysically modify the numerical solution, whereas upwind schemes seem to better represent the flow structure.