ENO Finite Volume Method On 2D Unstructured Meshs

Being improved by finite difference method and finite element method, finite volume method absorb the advantages of the finite difference method,which is simple and is developed well. It avoids some limitations of the finite difference method and becomes populary. Since 1980, finite volume method are very succesful with the development of the adaptive meshes, structured meshes and unstructured meshes, such as Upwing schemes Godunov schemes, Riemann schemes and TVD schemes. ENO and WENO schemes on unstrutured meshes has attracted much attention with high order accuracy. In this thesis, we study the finite volume schemes for 2D hyperbolic conservation laws on unstrutured meshes. Several parts are included in this thesis:We briefly review the developments for the partial differential eguation,and introduce the finite volume methods on 2D unstrutured meshes. We study the mesh generation on the 2D unstructured meshes in the chapter 1,2 and 3.In chapter 4, we present the constructions of the ENO schemes and construct a new quadratic reconstructed function. Then we get a third-order ENO finite volume schemes on unstructured mesh.In chapter 5, we construct the WENO schemes on unstructured meshes with nonlinear weights based on the quadratic interpolation polynomials in chapter 4.Finally,numerical experiments are performed to demonstrate the accuracy of the two methods.The results show that the methods have high-order accuracy.