Convection by means of least squares projection for ALE calculations

ABSTRACT: Element result data are in general discontinuous across element boundaries. In the ALE method convection of these data with respect to the element grid is required. In this paper we present a convection method, which is based on a least squares projection. For moderate convective displacements it is reformulated in terms of a field integral and boundary flux terms. For one dimen-sional problems the method can be shown to be third order in space. For two dimensional problems the method is stable for Courant numbers upto 1.05. Based on this method a simplification is suggested where the calculation of gradients of fields in upwind el-ements is not needed. This simplification is paid for by a slight decrease in stability. A maximum Courant number of 0.72 is still attainable. The methods are outlined in one dimension, results are shown of two dimensional calculations. Key words: ALE, transient convection, least squares