The Finite Mass Method on Domains with Boundary

The finite mass method is a gridless Lagrangian method to simulate compressible flows that has been introduced in a recent paper from Gauger, Leinen, and Yserentant [SIAM J. Numer. Anal., 37 (2000), pp. 1768–1799]. It is based on a discretization of mass, not of space as with classical discretization schemes. Mass is subdivided into little mass packets of finite extension each of which is equipped with finitely many internal degrees of freedom. These mass packets move under the influence of internal and external forces and the laws of thermodynamics and can change their shape to follow the motion of the fluid. Only free flows in vacuum have been considered so far. In this article, a concept is presented to extend the method to flows in domains having boundaries. It maintains the second order accuracy of the basic method and can be implemented along the same lines.