A method for generating boundary-orthogonal curvilinear coordinate systems using the biharmonic equation (Q1073558)

The author presents a new method for the generation of a boundary-fitted curvilinear coordinate system which uses the biharmonic operator to generate a coordinate system with a prescribed mesh point distribution on the domain boundary. This coordinate system has coordinate lines that are normal to the domain boundary. This boundary-orthogonal coordinate system generally simplifies the application of boundary conditions expressed in the normal direction to the field boundary. The solution of the biharmonic equation is accomplished by the coupled approach that splits the problem into the solution of a Poisson and a Laplace equation. The solution of these equations is carried out in the transformed domain in a similar manner with the well-established methods of boundary-fitted coordinate system generation based on the Laplace operator, and thus retains the extremum principal. The method may also be used for the generation of meshes in segmented fields. Finally the method can be easily extended to three dimensions.