Hessian 3D remeshing

Author: Vicente Mataix Ferrándiz

Kratos version: 7.1

Source files: Hessian 3D

Case Specification

In this test case,

The following applications of Kratos are used:

• MeshingApplication with the MMG module

The problem corresponds with the example proposed in reference, translated to 3D. The objective is to remesh the following unstructured mesh of a domain 1x1x0.1:

We want again adapt the mesh to the following test function :

The challenge consists in using the Hessian function of the test function as error measure and adapt the mesh in a proper manner. In this case the original mesh is coarse, so two remeshing steps will be necessaries.

Results

The results obtained after remeshing can be see in the following figures:

• First iteration:

• Second iteration:

The color map of the test function:

In 3D:

References

Frédéric Alauzet. Metric-Based Anisotropic Mesh Adaptation. Course material, CEA-EDF-INRIA Schools. Numerical Analysis Summer School. https://www.rocq.inria.fr/gamma/Frederic.Alauzet/cours/cirm.pdf

Pascal Tremblay 2-D, 3-D and 4-D Anisotropic Mesh Adaptation for the Time-Continuous Space-Time Finite Element Method with Applications to the Incompressible Navier-Stokes Equations. PhD thesis Ottawa-Carleton Institute for Mechanical and Aerospace Engineering, Department of Mechanical Engineering, University of Ottawa. 2007. http://aix1.uottawa.ca/~ybourg/thesis/PhDThesis_Pascal_Tremblay_Final.pdf