Fast exact evaluation of particle interaction vectors in the finite volume particle method. (English) Zbl 1218.65094
Griebel, Michael (ed.) et al., Meshfree methods for partial differential equations V. Selected papers based on the presentations at the 5th international workshop, Bonn, Germany, August 17–19, 2009. Berlin: Springer (ISBN 978-3-642-16228-2/hbk; 978-3-642-16229-9/ebook). Lecture Notes in Computational Science and Engineering 79, 219-234 (2011).
Summary: The finite volume particle method (FVPM) is a mesh-free method which inherits many of the desirable properties of mesh-based finite volume methods. It relies on particle interaction vectors which are closely analogous to the intercell area vectors in the mesh-based finite volume method. To date, these vectors have been computed by numerical integration, which is not only a source of error but is also computationally by far the most expensive part of the algorithm. We show that by choosing an appropriate particle weight or kernel function, it is possible to evaluate the particle interaction vectors exactly and relatively quickly. The new formulation is validated for 2D viscous flow, and shown to enable modelling of free-surface flow.
For the entire collection see [Zbl 1202.65004].
For the entire collection see [Zbl 1202.65004].
MSC:
| 65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |
| 35L65 | Hyperbolic conservation laws |
| 76B07 | Free-surface potential flows for incompressible inviscid fluids |
| 76M12 | Finite volume methods applied to problems in fluid mechanics |
| 76M28 | Particle methods and lattice-gas methods |
| 65M75 | Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs |
