Adjustment: meshing by relaxation (on the geometric entities)

Introduction

Relaxation permits to smooth the mesh distribution on:

• lines
• faces
• volumes

Principle

Relaxation permits to create the biggest possible good quality elements in function of the size of the geometric entities (lines, faces or volumes).

The mesh will be dense for smaller size entities and more relaxed for bigger size entities.

Repartition by relaxation

To carry out the mesh relaxation, Flux modifies the weight of each consecutive mesh node to progressively pass from a small element to a larger one.

In the figure below, the weights on line (1) are smaller and influence the weight on line (2).

The stronger the relaxation is, the faster the weights of line (2) will grow.

Operation

On a first step, larger weights are attributed to each node of the mesh. A relaxation algorithm facilitates the distribution of the node weights according to the geometry configuration.

The smaller weights influence the bigger weights.

The stronger the relaxation is, the more important the difference is between the biggest and the smallest weight . The mesh is then strongly relaxed in the larger zones.

Aided mesh

For each project, the software creates an aided_relaxline instance (for the relaxation on the lines), an aided relaxface (for the relaxation on the faces) and an aided relaxvolume (for the relaxation on the volumes in 3D) dedicated to the Aided mesh.