Theoretical and numerical analysis of nonconforming grid interface for unsteady flows

A framework is proposed for the spectral analysis of the numerical scheme applied on a nonconforming grid interface between two structured blocks for the two-dimensional advection equation, in a cell-centered finite-volume formalism. The conservative flux computation on the nonconforming grid interface is based on the sum of partial fluxes computed with the same numerical scheme used for a standard cell interface. This framework is used to analyze the effect of grid refinement or coarsening on the stability of the second-order centered scheme. New theoretical results are given and compared to numerical results. Considering the convection of a two-dimensional isentropic vortex, the refinement/coarsening are shown to be the cause of instabilities, poor accuracy and reflection of high-frequency waves. A new approach to compute partial fluxes, which is based both on a high-order extrapolation that accounts for the local metric and on a Riemann solver, is then proposed to reduce spurious modes.