Cell-vertex adaptive Euler method for cascade flows

This paper is concerned with the numerical solution of the two-dimensional steady Euler equations, using a multidimensional upwind cell-vertex residual distribution scheme. A solution-adaptive grid-refinement procedure is proposed, which combines with an efficient multigrid strategy based on an optimally smoothing explicit multistage scheme. A very accurate treatment of solid wall boundaries and a general approach for guaranteeing conservation on patched grids are developed within the present context of cell-vertex residual distribution schemes. The proposed approach is shown to be very efficient and sufficiently accurate to compute the transonic flow past a high-turning turbine cascade.