Assessing the quality of curvilinear coordinate meshes by decomposing the Jacobian matrix
An algebraic decomposition of the Jacobian matrix [J] := @?x^i/@[email protected]^j which 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 decompostion 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 analysis (by G. H. K.)^1 of the mesh contribution to truncation error for the 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