A decade of progress on anisotropic mesh adaptation for computational fluid dynamics

Abstract

Please cite this article as: Alauzet F, Loseille A. A decade of progress on anisotropic mesh adaptation for computational fluid dynamics. Computer-Aided Design (2015), http://dx. AbstractIn the context of scientific computing, the mesh is used as a discrete support for the considered numerical methods. As a consequence, the mesh greatly impacts the e ciency, the stability and the accuracy of numerical methods. The goal of anisotropic mesh adaptation is to generate a mesh which fits the application and the numerical scheme in order to achieve the best possible solution. It is thus an active field of research which is progressing continuously. This review article proposes a synthesis of the research activity of the INRIA Gamma3 team in the field of anisotropic mesh adaptation applied to inviscid flows in computational fluid dynamics since 2000. It shows the evolution of the theoretical and numerical results during this period. Finally, challenges for the next decade are discussed.

An Adaptive Algorithm for the Time Dependent Transport Equation with Anisotropic Finite Elements and the Crank–Nicolson Scheme

“…Anisotropic adaptive meshes with large aspect ratio have proved to be extremely efficient for partial differential equations with free boundaries or boundary layers, see for instance [1][2][3] for applications in computational fluid dynamics. In most cases, the adaptive criteria are based on heuristics or interpolation error estimates rather than rigorous a posteriori error estimates.…”

“…The quality of our error estimator is first validated on non-adapted meshes and constant time steps. An adaptive algorithm is then B Marco Picasso marco.picasso@epfl.ch Samuel Dubuis samuel.dubuis@epfl.ch 1 Institute of Mathematics, Station 8, EPFL, 1015 Lausanne, Switzerland proposed, with goal to build a sequence of anisotropic meshes and time steps, so that the final error is close to a preset tolerance. Numerical results on adapted, anisotropic meshes and time steps show the efficiency of the method.…”

Goal-oriented error control of stochastic system approximations using metric-based anisotropic adaptations

“…This is a purely practical choice, well adapted for approximation of potentially discontinuous solutions, but there is no restriction in using a different p-norm. For deterministic problems, this kind of approach named "feature-based" mesh adaptation has been proposed to capture all the scales/singularities of the system, and has been applied to deterministic CFD problems [4,35,5]. In this case, a sensor is defined (for CFD applications a sensor will be a prescribed field: density, mach, ...) and some norm of the interpolation error associated to the sensor is controlled by anisotropic mesh refinement.…”

“…The extension of deterministic a posteriori goal-oriented error estimates has previously been applied to control numerical error in problems with uncertain input parameters [6,14,15,39]. Nevertheless, it is known that extracting anisotropic information from a posteriori estimates is a difficult task [5]. Moreover, only very few works demonstrate error splitting and automated adaptivity in both spaces, e.g.…”

“…While there is a cost associated to solving this additional adjoint problem, goal-based mesh adaptation allows for a faster convergence in the QoI. For a more complete overview of mesh adaptation the reader is referred to [20,5] and references therein.…”