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 by far the most computationally 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 freesurface flow.
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Acknowledgement
The research leading to these results has received funding from the European Community’s Seventh Framework Programme (FP7/2007-2013) under grant agreement 225967 NextMuSE. Ruairi Nestor was supported by the IRCSET Embark Initiative.
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Quinlan, N.J., Nestor, R.M. (2011). Fast exact evaluation of particle interaction vectors in the finite volume particle method. In: Griebel, M., Schweitzer, M. (eds) Meshfree Methods for Partial Differential Equations V. Lecture Notes in Computational Science and Engineering, vol 79. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16229-9_14
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DOI: https://doi.org/10.1007/978-3-642-16229-9_14
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