The Finite Mass Method

The nite mass method, a new Lagrangian method for the numerical simulation of gas ows, is presented and analyzed. In contrast to the nite volume and the nite element method, the nite mass method is founded on a discretization of mass, not of space. Mass is subdivided into small mass packets of nite extension each of which is equipped with nitely many internal degrees of freedom. These mass packets move under the innuence of internal and external forces and the laws of thermodynamics and can undergo arbitrary linear deformations. The method is based on an approach recently developed by the last author and can attain a very high accuracy.