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