Model Adaptation Enriched with an Anisotropic Mesh Spacing for Nonlinear Equations: Application to Environmental and CFD Problems

Goal of this paper is to suitably combine a model with an anisotropic mesh adaptation for the numerical simulation of nonlinear advection-diffusion-reaction systems and incompressible flows in ecological and environmental applications.Using the reduced-basis method terminology,the proposed approach leads to a noticeable computational saving of the online phase with respect to the resolution of the reference model on nonadapted grids.The search of a suitable adapted model/mesh pair is to be meant,instead,in an offline fashion.

Quadrilateral Cell-Based Anisotropic Adaptive Solution for the Euler Equations

An anisotropic solution adaptive method based on unstructured quadrilateral meshes for inviscid compressible flows is proposed.The data structure,the directional refinement and coarsening,including the method for initializing the refined new cells,for the anisotropic adaptive method are described.It provides efficient high resolution of flow features,which are aligned with the original quadrilateral mesh structures.Five different cases are provided to show that it could be used to resolve the anisotropic flow features and be applied to model the complex geometry as well as to keep a relative high order of accuracy on an efficient anisotropic mesh.