Function opensn::FaceSideLength

Function Documentation

double opensn::FaceSideLength(const Mesh &grid, const Cell &cell, unsigned int f)

Side length of face f of cell for the PWLD basis: twice the smallest height of the face’s side simplices over their face part, \(2 \min_k d |S_k| / |T_k|\).

In 3D \(S_k\) is the tetrahedron (edge k of the face, face centroid, cell centroid) and \(T_k\) its triangle on the face; in 2D \(S\) is the triangle (face edge, cell centroid) and \(T\) the edge. PWLD is linear on each side simplex, so \(\|\partial_n v\|^2_{T_k} \le (d / h_k) \|\nabla v\|^2_{S_k}\) exactly, with \(h_k = d|S_k|/|T_k|\), and the side simplices of different faces are disjoint: a penalty \(\propto D/h\) with this length bounds the consistency terms on any cell shape. Equal to \(V/A_f\) on a square or a cube. Slab cells: the cell length.