Assessment of grid interface treatments for multi-block incompressible viscous flow computation

Abstract

In the multi-block computation of the Navier-Stokes equations, the interface treatment is a key issue. In the present work, we investigate this issue in the context of a pressure-based method using a non-orthogonal grid. For the momentum equations, a straightforward bilinear interpolation seems satisfactory as the interface treatment; on the other hand, because the pressure field depends on the satisfaction of the mass continuity equation, a conservative interface treatment has been found necessary for the pressure-correction equation. Two alternative interface treatments for the pressure-correction equation, one employing the Neumann boundary condition in both grid blocks, based on explicit local, cell-by-cell mass flux conservation, and the other utilizing Neumann-Dirichlet boundary conditions, allowing the interface condition in one block to be derived by interpolating the pressure field from the adjacent block, are assessed in the present work. To evaluate these interface schemes, the laminar flow inside a lid-driven cavity flow, and the turbulent flow around cascades of multiple airfoils have been investigated. For the case tested, both interface treatments give comparable accuracy. The finding that more than one type of interface treatment can work well allows one to devise a flexible multi-block strategy for complex flow computations.