Compact finite volume schemes on boundary-fitted grids

Abstract

The paper focuses on the development of a framework for high-order compact finite volume discretization of the three-dimensional scalar advection–diffusion equation. In order to deal with irregular domains, a coordinate transformation is applied between a curvilinear, non-orthogonal grid in the physical space and the computational space. Advective fluxes are computed by the fifth-order upwind scheme introduced by Pirozzoli [S. Pirozzoli, Conservative hybrid compact-WENO schemes for shock–turbulence interaction, J. Comp. Phys. 178 (2002) 81] while the Coupled Derivative scheme [M.H. Kobayashi, On a class of Padé finite volume methods, J. Comp. Phys. 156 (1999) 137] is used for the discretization of the diffusive fluxes.Numerical tests include unsteady diffusion over a distorted grid, linear free-surface gravity waves in a irregular domain and the advection of a scalar field. The proposed methodology attains high-order formal accuracy and shows very favorable resolution characteristics for the simulation of problems with a wide range of length scales.