A comparative study of various adaptive meshless methods for steady and unsteady flow calculations

Abstract

Three di erent adaptive methods are presented for meshless calculation of steady and unsteady ows. Two approaches of point re nement/coarsening and point movement have their ground in the mesh-based methods that, in the present work, are extended for meshless calculations. However, the third approach is a new concept, socalled adaptive neighboring scheme, that concerns the optimum selection of the neighbors for each point in the meshless framework. This means that the selection of the neighboring region for each particular point is a ected by the flow features in the domain. In this paper, an explicit meshless method based on the least square scheme is used. The results are presented for di erent steady and unsteady flows and the e ciency of the methods in terms of computational cost and accuracy is investigated. It is observed that using these adaptive approaches decrease the computational cost of the method by about 60% as compared with the un-adapted results while improving the accuracy of results at the same time.