Accession Number : ADP001003

Title :   Assessing the Quality of Curvilinear Coordinate Meshes by Decomposing the Jacobian Matrix,

Corporate Author : NIELSEN ENGINEERING AND RESEARCH INC MOUNTAIN VIEW CA

Personal Author(s) : Kerlick,G. David ; Klopfer,Goetz H.

Report Date : 1982

Pagination or Media Count : 21

Abstract : An algebraic decomposition of the Jacobian matrix relates physical and computational variables is presented. This invertible decomposition parameterizes the mesh by the physically intuitive qualities of cell orientation, cell orthogonality, cell volume, and cell aspect ratio. This decomposition can be used to analyze numerically generated curvilinear coordinate meshes and to assess the contribution of the mesh to the truncation error for any specific differential operator and algorithm. This is worked out in detail for Laplace's equation in nonconservative and conservative forms. An full potential code TAIR is given in abbreviated form. The variables introduced here, and their derivatives are also natural Lagrange multipliers for adaptive mesh algorithms based on a variational principle. (Author)

Descriptors :   *Grids(Coordinates), *Matrices(Mathematics), *Decomposition, Algebra, Numerical analysis, Variables, Mesh, Truncation, Errors, Derivatives(Mathematics), Lagrangian functions, Partial differential equations, Finite difference theory, Laplace transformation, Airfoils

Distribution Statement : APPROVED FOR PUBLIC RELEASE