Fast Algorithm for Moving-Adaptive-Grid Generation in One- and Multiple-Dimensions

Abstract

Solution adaptive grid (SAG) method is a step that improves the accuracy of numerical method, and is very effective for singular problems, such as the advection of shock waves and/or interfaces. Some sorts of SAG methods in one- and/or multiple-dimensions have proposed in the past decade [1–10]. Among these methods, the SAG methods based on elliptic partial differential equations (EPDEs) [5,7,10] provide stabler resulting grids rather than that of other methods. However, SAG methods of this type have some faults in their use. One is that it takes long CPU time to solve the EPDEs used in the SAG methods. The other is that it is difficult to control the clustering, although, especially in explicit simulations, it is important to avoid the excessive grid clustering. Most of SAG methods with other approaches [4,6,8,9] are superior on these points, but they are inferior on other points, such as the stability of resulting grid and/or the extent of its application, to that with EPDEs.