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The Finite Volume Particle Method

Collaborators: D. Hietel, R. Keck, J. Kuhnert, J. Struckmeier, D. Teleaga
Key words: finite volume methods, partition of unity, overlapping cells, mesh-free methods
Support: DFG

    In the Finite-Volume-Particle Method (FVPM), 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 not taken as characteristic functions of the control volumes in a spatial grid, but are chosen from a partition of unity with smooth and overlapping partition functions (the particles), which can 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.


    Meshless methods for conservation laws,
    Analysis and Numerics for Conservation Laws (G. Warnecke Edt.), 339-362, Springer, 2005
    with D. Hietel, J. Kuhnert, S. Tiwari
    Do finite volume methods need a mesh?
    Springer Lecture Notes in Computational Science and Engineering, 26, 223-238, 2002
    The Finite-Volume-Particle Method for Conservation Laws
    proceedings of GAMM Workshop "Discrete Modelling and discrete Algorithms in Continuum Mechanics", Logos Verlag, 2001
    with D. Hietel, R. Keck and D. Teleaga
    Consistency analysis of mesh-free methods for conservation laws
    Mitt. Ges. Angew. Math. Mech., 24, No.2, 99-126, 2001
    with J. Struckmeier