Accession Number : ADP001009

Title :   Orthogonal Coordinate Meshes with Manageable Jacobian,


Personal Author(s) : Christov,C. I.

Report Date : 1982

Pagination or Media Count : 11

Abstract : Recent the problem of numerical generating curvilinear coordinate meshes has received a vast exploration because of its outstanding importance in solving the partial differential equations of continuous mechanics. The major advantage of this method is that the boundary of the region becomes a coordinate line which decidedly simplifies the numerical schemes for approximate integration of boundary value problems. In some since the method of adapted coordinates is an alternative to the method of finite elements. In two dimension the most natural way to create curvilinear meshes was, perhaps, the inversion of conformal mapping. This approach was generalized by means of variational principle. The coordinates obtained in this way, however, were not orthogonal in general and the Jacobian assumed in some cases incomfortable values approaching zero or infinity. It was due to the rigid prescription of the boundary points. The orthogonality has been restored only after reducing the conditions on the boundary points to the natural ones for a conformal mapping. In present note an other approach ensuring the Jacobian to be a priory prescribed function is attempted. (Author)

Descriptors :   *Partial differential equations, Variational principles, Conformal mapping, Inversion, Orthogonality, Regions, Boundary value problems, Nonlinear differential equations

Distribution Statement : APPROVED FOR PUBLIC RELEASE