Numerical treatment of grid interfaces for viscous flows

Abstract

Numerical treatment of grid interfaces is one of the most important considerations for algorithms that employ different grids within the computational domain. The issue of numerical treatment of quadrilateral grid interfaces with a representative finite-volume Navier-Stokes integration scheme is addressed. Interfaces are created by local embedding of quadrilateral grids and are the borders between different grids. Grid embedding is one of the basic functions of adaptive algorithms that have been developed in order to increase both accuracy and efficiency of computations. The present work both develops and investigates interface treatment schemes that have certain properties such as accuracy and conservation. It is a novel study of interfaces for the case of viscous flow computations. Various treatments are proposed and evaluated with the emphasis being on a comparison between accurate and conservative treatments. Two methodologies have been followed in order to study interface treatments. The first is analytical and yields orders of possible numerical errors, while the second approach employs model test cases, which are especially designed to evaluate certain aspects of the described interface treatments. Also, a transonic airfoil flow case is included as an example of accuracy and robustness of a particular interface treatment scheme. All numerical treatment schemes that are discussed have been coded and evaluated.