Reliable flow solver based on the high order control volume Padé-type differences

Barrier variational generation of quasi‐isometric grids

“…Ka porin, was found to be the best regularizator for (14), (15). A similar penalty function was suggested in [26] in the context of triangular grid generation using nonlinear net of springs analogy …”

“…It arises quite naturally when using finite element methods but usually it is excessive for the fi nite volume methods, where the barriers can be constructed using the cell volume positivity constraint, a set of suitable cell shape constraints along with the Linear Preservation (LP) constraint which is the counterpart of the patch test for finite volume methods. In [15] it was shown that the least restrictive condition is the pos itiveness of the jacobian of trilinear mapping in the logical face centers, which in a sense means that the cell is not turned inside out. However the negative values of det S in the vertices and on the egdes are allowed which makes the trilinear mapping itself meaningless.…”

“…However the negative values of det S in the vertices and on the egdes are allowed which makes the trilinear mapping itself meaningless. Such barrier approximation was suggested in [15]. It is illustrated on Figure 5, where two triples of the covariant basis vectors gi.g-j.g:» from 24 possible combina tions are shown.…”

“…In [15] in the case of harmonic functional it was shown that the best way to contruct barriers suitable for high order control volume methods is to do it in the hierarchical manner, by adding the constraints originating from the high order approximation schemes to the basic set of constraints associated with the conventional low order control volume methods. This is somewhat contrary to the idea of the "high order" [18] it was demonstrated that finite element approximation to Winslow functional with bi-quadratic bases may result in grid folding for quite simple domains.…”