An efficient adaptive multiresolution finite difference scheme is developed for hyperbolic conservation laws. Based on discrete multiresolution analysis of numerical solution on a nested grid structure,the scheme builds up an one-to-one relationship between wavelet coefficients with multiple nested grid point. At grid points where magnitude of wavelet coefficients are great,high-order WENO scheme is used for time evolution. While in the rest computational region,we use polynomial interpolation directly. Numerical experiments show that the method can reduce CPU time significantly,while maintaining accuracy and resolution of original regular grid method.

A constrained boundary recovery algorithm for 3D unstructured meshes which combines vector boundary advancing triangulation method(VBATM) with Steiner point perturbation is presented.From conforming mesh,constrained edges and faces could be recovered by Steiner point perturbation and VBATM to reconstruct triangulation on constrained faces.The tetrahedral-eating method can be used to get rid of Steiner points as many as possible.Different from existing methods,the algorithm does not need edges/faces swapping(flip) method and side compress method.Convergence and stability of the method are theoretically studied.Numerical examples are provided to illustrate effectiveness of the method.

Two constrained Delaunay triangulation methods based on local reconstruction and side-swapping method are presented.Their convergence are shown.Appointed fields are renewed by boundary indicating method.It updates field scales by analysis of boundary curvature,axial and mutual smooth gradient of the domain.Based on Spring method,boundary points according to field scales are generated.By sign-area function and probability filer,initial points of field are obtained.Structure of meshes is optimized by Spring-Laplace method,side-swapping and side-collapse methods.The methods can be adaptive refined and made sparse successfully.They can be used to moving mesh and surface mesh generation of reflection surface.

We present a method, vector boundary advancing method, to generate unstructured triangle meshes, and prove its feasibility. It lays out boundary points based on domain scales and generates background meshes with vector boundary advancing method. With sign-area function and probability filer, it obtains initial points in the domain. Spring-Laplace method and side-swapping method adjust location and structure of the mesh and prevent points from getting out of the domain. The method can do adaptive refine and derefine successfully and can deal with fixed-points, fixed-lines and inner-boundary. An efficient smooth adaptive triangulation divided in two-dimensional domain according to scales is realized.

Based on the theory of Sweby an implicit TVD scheme is obtained. The new method is first-order accurate with a truncation error of O The efficiency of this new scheme is demonstrated by some numerical computations of single Burgers equation and two-dimensional SNS equations.