Grid-characteristic method on tetrahedral unstructured meshes with large topological inhomogeneities
A. V. Vasyukov, I. B. Petrov
Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Russia
A key difficulty faced when grid-characteristic methods on tetrahedral meshes are used to compute structures of complex geometry is the high computational cost of the problem. Formally, grid-characteristic methods can be used on any tetrahedral mesh. However, a direct generalization of these methods to tetrahedral meshes leads to a time step constraint similar to the Courant step for uniform rectangular grids. For computational domains of complex geometry, meshes nearly always contain very small or very flat tetrahedra. From a practical point of view, this leads to unreasonably small time steps (1-3 orders of magnitude smaller than actual structures) and, accordingly, to unreasonable growth of the amount of computations. In their classical works, A.S. Kholodov and K.M. Magomedov proposed a technique for designing grid-characteristic methods on unstructured meshes with the use of skewed stencils. Below, this technique is used to construct a numerical method that performs efficiently on tetrahedral meshes.
grid-characteristic method, tetrahedral mesh, skewed stencil.
Computational Mathematics and Mathematical Physics, 2018, 58:8, 1259–1269
A. V. Vasyukov, I. B. Petrov, “Grid-characteristic method on tetrahedral unstructured meshes with large topological inhomogeneities”, Zh. Vychisl. Mat. Mat. Fiz., 58:8 (2018), 62–72; Comput. Math. Math. Phys., 58:8 (2018), 1259–1269
Citation in format AMSBIB
\by A.~V.~Vasyukov, I.~B.~Petrov
\paper Grid-characteristic method on tetrahedral unstructured meshes with large topological inhomogeneities
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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