Particles of variable size

A problem of all particle methods is that they produce large vacuum regions when they are applied to a free gas ow, for example. With the approach recently proposed by the author Numer. Math., in press], this diiculty can be avoided. One can let the particles adapt their size to the local state of the uid. How, is described in the present article. The diameter as an additional degree of freedom strongly improves the performance of the numerical methods based on this particle model.