Abstract
The purpose of this paper is to present a synthesis of our recent studies related to the design of multi-dimensional non-oscillatory schemes, applying to non-structured finite-element simplicial meshes (triangles, tetrahedra). While the direct utilization of 1-D concepts may produce robust and accurate schemes when applied to non-distorted structured meshes, it cannot when non-structured triangulations are to be used. The subject of the paper is to study the adaptation of the so-called TVD methods to that context. TVD methods have been derived for the design of hybrid first-order/second-order accurate schemes which present in simplified cases monotonicity properties (see, for example, the review [2]). A various collection of first-order accurate schemes can be used, they are derived from an artificial viscosity model or from an approximate Riemann solver. However, the main feature in the design is the choice of the second-order accurate scheme; this choice can rely either on central differencing or on upwind differencing.
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© 1989 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig
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Arminjon, P., Dervieux, A., Fezoui, L., Steve, H., Stoufflet, B. (1989). Non-Oscillatory Schemes for Multidimensional Euler Calculations with Unstructured Grids. In: Ballmann, J., Jeltsch, R. (eds) Nonlinear Hyperbolic Equations — Theory, Computation Methods, and Applications. Notes on Numerical Fluid Mechanics, vol 24. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-87869-4_1
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DOI: https://doi.org/10.1007/978-3-322-87869-4_1
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