Multi‐scale Adaptation for Unsteady Flows
Alain Dervieux, Frédéric Alauzet, Adrien Loseille, Bruno Koobus · 2022
This chapter describes an extension of the multiscale feature-based mesh adaptation method for the calculation of an unsteady flow. It considers adaptation methods changing the spatial mesh during the simulation time frame. The chapter describes the adequation of the mesh with the concerned time levels is obtained by a fixed point algorithm, which generalizes to time advancing the Hessian-based steady-state fixed point. It introduces and analyzes the transient fixed-point in order to approach the early capturing property for spatial error and, at least, to show a predictable mesh convergence rate that will be better than with non-adaptive approaches. The chapter provides the basic option of a feature-based adaptation, that is, we make the assumption that the discretization error can be controlled by the interpolation error of some features prescribed by the user. It describes a method for controlling, time interval after time interval, the error of transient flows.