A study of point moving adaptivity in gridless method

In this paper, an adaptive gridless algorithm is presented to solve Euler equations. The adaptive procedure is realized through the movement of points in order to fix the number of the points for capturing physical features like shock waves with high resolution. To carry out the adaptive point movement, weighted reference radius equidistribution is introduced into the clouds of points updated during the gridless computation. The features of the flow field are firstly measured by a weighted function based on local gradients, and then the point gathering in the vicinity of the measured feature is realized by adjusting the reference radius of the clouds. No points are inserted or removed during the adaptive procedure, therefore the number of the points can be kept the same. It can be noted that the points gradually approach the vicinity of the important physical features, and hence the resolution of the flow filed is increased. Compressible flows in channels governed by Euler equations are solved to validate this new methodology. The numerical results show that the shock waves are accurately captured and agree well with the reference works.