Consistency by Coefficient-Correction in the Finite-Volume-Particle Method

In the Finite-Volume-Particle Method, the weak formulation of a hyperbolic conservation law is discretized by restricting it to a discrete set of test functions. In contrast to the usual Finite-Volume approach, the test functions are chosen from a partition of unity with smooth and overlapping partition functions, which may even move along prescribed velocity fields. The information exchange between particles is based on standard numerical flux functions. Geometrical information, similar to the surface area of the cell faces in the Finite-Volume Method and the corresponding normal directions are given as integral quantities of the partition functions.These quantities fulfill certain properties, which are heavily used in showing Lax-Wendroff consistency and stability estimates. We present a method which enforces the properties to be fulfilled in numerical computations. Moreover, we show a coupling among the coefficients and finally consistency of the method in space.