A Discussion of Boundary-Fitted Coordinate Systems and their Applicability to the Numerical Modeling of Hydraulic Problems.

摘要

A procedure for the numerical solution of nonorthogonal boundary-fitted coordinate systems, i.e., a coordinate line coincides with the boundary, is presented. This method generates curvilinear coordinates as the solution of two elliptic partial differential equations with Dirichlet boundary conditions, one coordinate being specified to be constant on each of the boundaries, and a distribution of the other specified along the boundaries. No restrictions are placed on the irregularity of the boundaries, which are even allowed to be time dependent, such as might occur in problems involving the computation of the location of the free surface, flooding boundaries, and streambank erosion problems. In addition, fields containing multiple bodies or branches can be handled as easily as simple geometries. Regardless of the shape and number of bodies and regardless of the spacing of the curvilinear coordinate lines, all numerical computations, both to generate the coordinate system and to subsequently solve the system of partial differential equations of interest, e.g., the vertically integrated hydrodynamic equations, are done on a rectangular grid with square mesh.