A Class Of Finite Volume Method On Unstructured Triangular Meshes And Its Convergence

The finite difference methods, specially TVD and ENO schemes, for hyperbolic conservation laws are very successful. But the finite difference methods require that computational domain is regular, and usually people construct the difference scheme for one dimension and then extend it to two or three dimensions in a dimension by dimension fashion. Due to the engineering problem and computational domain become more complicated and more complicated, the finite volume method on unstructured meshes for hyperbolic conservation laws is playing an important role in computational fluid dynamics, this method has no restriction for computational domain. The following work has been done in the thesis:In the presend paper , we constract a class of finite volume method statisfying the maximum principle for two dimensions scalar hyperbolic conservation law. The key idea of the new method is based upon first order monotone scheme and upon linear reconstrution with monotone limiting in every mesh, the resulting method is TVD-type and has second order accuracy. Analysis of convergence has been given.