Finite-difference algorithm with local time-space grid refinement for simulation of waves
نویسندگان
چکیده
This paper presents a new approach to a local time-space grid refinement for a staggered-grid finitedifference simulation of waves. The approach is based on approximation of a wave equation at the interface where two grids are coupled. As no interpolation or projection techniques are used, the finite-difference scheme preserves second order of convergence. We have proved that this approach is low-reflecting, the artificial reflections are about 10−4 of an incident wave. We have also shown that if a successive refinement is applied, i.e. temporal and spatial steps are refined at different interfaces, this approach is stable.
منابع مشابه
Automatic Grid Control in Device Simulation
Automatic grid control for finite differences meshes is a difficult task because only very few mathematically founded criteria for adaptive grid refinement can be given which may be implemented in a computer program with reasonable effort. Especially for the solution of the semiconductor equations, a coupled system of nonlinear partial differential equations, most strategies for fully automatic...
متن کاملAutomatic Grid Generation for 3 d Device Simulation
The concepts of an automatic 3d grid generator for the solution of the semiconductor equations are presented. The grid generator allows to mix elements of different shapes. An algorithm for the refinement of a grid according to a given point density function is outlined. Local heuristics for the improvement of the quality of the elements with worst aspect ratio obtained during the refinement ar...
متن کاملImplicit , Time - Dependent Variable Grid Finite Difference Methods for the Approximation
An implicit, time-dependent variable grid finite difference method based on the addition of an artificial diffusivity is introduced and analyzed for approximating the solution of a scalar conservation law in a single space variable. No relation between the grids at successive time steps is required for convergence. Two adaptive grid selection procedures are shown to be covered by the analysis. ...
متن کاملWater hammer simulation by explicit central finite difference methods in staggered grids
Four explicit finite difference schemes, including Lax-Friedrichs, Nessyahu-Tadmor, Lax-Wendroff and Lax-Wendroff with a nonlinear filter are applied to solve water hammer equations. The schemes solve the equations in a reservoir-pipe-valve with an instantaneous and gradual closure of the valve boundary. The computational results are compared with those of the method of characteristics (MOC), a...
متن کاملHULK - Simple and fast generation of structured hexahedral meshes for improved subsurface simulations
Short for Hexahedra from Unique Location in (K)convex Polyhedra – HULK is a simple and efficient algorithm to generate hexahedral meshes from generic STL files describing a geological model to be used in simulation tools based on the finite difference, finite volume or finite element methods. Using binary space partitioning of the input geometry and octree refinement on the grid, a successive i...
متن کامل