Abstract
An inflow-based gradient is proposed to solve a propagation in a normal direction with a cell-centered finite volume method. The proposed discretization of the magnitude of gradient is an extension of Rouy–Tourin scheme (SIAM J Numer Anal 29:867–884, 1992) and Osher–Sethian scheme (J Comput Phys 79:12–49, 1988) in two cases; the first is that the proposed scheme can be applied in a polyhedron mesh in three dimensions and the second is that its corresponding form on a regular structured cube mesh uses the second order upwind difference. Considering a practical application in three dimensional mesh, we use the simplest decomposed domains for a parallel computation. Moreover, the implementation is straightforwardly and easily combined with a conventional finite volume code. A higher order of convergence and a recovery of signed distance function from a sparse data are illustrated in numerical examples on hexahedron or polyhedron meshes.
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Acknowledgements
We would like to thank to Dr. Peter Priesching in AVL LIST GmbH, Graz, Austria and Dr. Kiwan Jeon in National Institute for Mathematical Sciences, Daejeon, South Korea for and to Dr. Peter Sampl and MSc. Dirk Martin in AVL LIST GmbH, Graz, Austria, for generating polyhedron and hexahedron meshes of the Stanford bunny and Dragon examples. We sincerely appreciate valuable comments and feedback from anonymous referee.
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Karol Mikula was supported by VEGA 1/0808/15 and APVV-15-0522. Peter Frolkovič was supported by VEGA 1/0728/15 and APVV-15-0522.
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Hahn, J., Mikula, K., Frolkovič, P. et al. Inflow-Based Gradient Finite Volume Method for a Propagation in a Normal Direction in a Polyhedron Mesh. J Sci Comput 72, 442–465 (2017). https://doi.org/10.1007/s10915-017-0364-4
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DOI: https://doi.org/10.1007/s10915-017-0364-4