Mesh Adaptation for Computational Fluid Dynamics, Volume 2

1Nonlinear Corrector for CFD

This chapter examines methods for improving an already obtained numerical solution with a reasonable computational effort. In the case of a Poisson problem, two types of approaches are identified. First, the corrector can rely on an a priori estimate. Second, the corrector can rely on a fictitious computation on a twice finer mesh through the defect correction (DC) process. A nonlinear version is the central point in the discussion. The description of nonlinear methods is focused on the Reynolds-averaged Navier–Stokes (RANS) equations. Examples of applications are RANS computations around airfoil and wing and the Euler evaluation of a supersonic flow around low-boom aircraft.

1.1. Introduction

The numerical simulation of engineering problems involves a discrete solution, which is alleged to converge toward the continuous solution of the problem as the size of the elements of the mesh decreases. As the exact solution of the continuous problem is sought, the difference between the numerical and the analytical solution is often seen as an unavoidable noise. But in an engineering context, this error can have disastrous consequences on the numerical prediction which can, in turn, lead to actual accidents or misconceptions (Collins et al. 1997; Jakobsen and Rosendahl 1994; Feghaly et al. 2008). It is thus essential not only to reduce but also to estimate this error. This is usually done by applying a mesh convergence study, see the previous chapter and ...