Cell-vertex adaptive Euler method for cascade flows

Abstract

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.

Third-order-accurate fluctuation splitting schemes for unsteady hyperbolic problems

“…Fluctuation splitting (FS) schemes using a compact stencil have been developed and applied successfully for the last 15 years to compute a wide range of compressible steady flows with shocks [1][2][3][4][5][6][7][8][9]. The FS (also called residual distribution) approach is based on a cell-vertex tessellation of the computational domain and on a continuous reconstruction of the solution over linear (triangular/tetrahedral) elements.…”

A second-order-accurate monotone implicit fluctuation splitting scheme for unsteady problems

“…(11) and (17) one has: Eq. (29): (i) combined with condition (27) leads to c i,j = 1/3, providing a second-order-accurate scheme;…”

“…1(b)) the unsteady term is distributed only between the downstream nodes according to Eq. (11). Let us consider the triangle in Fig.…”