Meshing, Geometric Modeling and Numerical Simulation 3

Chapter 5Visualization of a Solution Field Related to a High-Degree Mesh

We have a mesh of degree 1 (or 1 × 1, quadrilateral case) or, more generally of any degree and the solution computed from this mesh, which for its part is a first-degree (or 1 × 1) solution or of any degree. In this chapter, it will be shown how this (discrete) solution can be represented and precisely when its degree is not 1, for example, when it is of 1 × 1 degree or of any degree. These cases are already covered by some software programs but, and even just at degree 1, the drawing method is not always documented.

The functions that we are considering are scalar (temperatures, pressure, etc.), vector (movements, normals, velocities, etc.) or still tensor functions (stress tensors, reference frames, metric fields, etc.). Depending on these types, the representation sought for may appear under different forms. It seems natural to visualize a scalar field via colors or via curves (or surfaces) of isovalues, a vector field via vectors (small arrows) and a tensor field in the same way via (small) frames of reference or, for example, for a metric field, via drawing ellipses or ellipsoids. In the surface case, we can use normals to take shading into account, so this case is also discussed in this chapter.

These functions are known discretely, usually at the nodes of the mesh being considered, but may also be known element by element (for example, one by element that may be supposed to be associated with its ...