Anisotropic mesh adaptation: towards user‐independent, mesh‐independent and solver‐independent CFD. Part II. Structured grids

Abstract

SUMMARYThe present paper is the second article in a three-part series on anisotropic mesh adaptation and its application to (2-D) structured and unstructured meshes. In the ÿrst article, the theory was presented, the methodology detailed and brief examples given of the application of the method to both types of grids. The second part details the application of the mesh adaptation method to structured grids. The adaptation operations are restricted to mesh movement in order to avoid the creation of hanging nodes. Being based on a spring analogy with no restrictive orthogonality constraint, a wide grid motion is allowed. The adaptation process is ÿrst validated on analytical test cases and its high e ciency is shown on relevant transonic and supersonic benchmarks. These latter test cases are also solved on adapted unstructured grids to provide a reference for comparison studies. The third part of the series will demonstrate the capability of the methodology on 2-D unstructured test cases.

An interpolation error estimate in $\mathcal{R}^2$ based on the anisotropic measures of higher order derivatives

“…Numerous examples have shown that long and thin elements are useful in computation of problems with boundary or internal layers [1,2,14,15,19,22]. A practical question is in what direction an element should be long and how long and thin it should be.…”

Anisotropic hp-adaptive method based on interpolation error estimates in the H 1-seminorm

“…⊲ anisotropic mesh adaptation techniques, generating anisotropic elements (i.e., long and thin triangles), which are suitable in computation of problems with boundary or internal layers, see, e.g., [1], [2], [9], [14], [16], [20], [21], [29].…”

Mesh Smoothing Based on Riemannian Metric Non-Conformity Minimization

“…Examples of other size distribution methods include physical analogies such as the spring analogy [3,4] and particle potential minimization [5], methods based on the elliptical Poisson system [6,7,8,9] as well as "center of mass" methods [10,11]. These methods have been used in adaptive setting: they all have some kind of weight function or concentration function that allows for spacing or size specification.…”

“…The concepts of Riemannian metrics and non-conformity are explained next, in Sect. 3. The paper then goes on to explain the smoothing method used to optimize the non-conformity of a mesh (Sect.…”