ANTI-DIFFUSIVE ALTERNATE-DIRECTIONS SCHEMES FOR THE TRANSPORT OF STEP FUNCTIONS

Autor: Léa Batteux, Fabien Duval, Raphaële Herbin, Jean‐Claude Latché, Pascal Poullet
Přispěvatelé: Laboratoire de Mathématiques Informatique et Applications (LAMIA), Université des Antilles (UA), Institut de Radioprotection et de Sûreté Nucléaire (IRSN), Institut de Mathématiques de Marseille (I2M), Centre National de la Recherche Scientifique (CNRS)-École Centrale de Marseille (ECM)-Aix Marseille Université (AMU), Laboratoire de Mathématiques Informatique et Applications [UR1_1] (LAMIA), Laboratoire de l'Incendie et des Explosions (IRSN/PSN-RES/SA2I/LIE), Service des Agressions Internes et des risques Industriels (IRSN/PSN-RES/SA2I), Institut de Radioprotection et de Sûreté Nucléaire (IRSN)-Institut de Radioprotection et de Sûreté Nucléaire (IRSN), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)
Jazyk: angličtina
Rok vydání: 2021
Předmět:
Zdroj: International Journal for Numerical Methods in Fluids
International Journal for Numerical Methods in Fluids, 2022, 94 (8), pp.1155-1182. ⟨10.1002/fld.5086⟩
ISSN: 0271-2091
1097-0363
DOI: 10.1002/fld.5086⟩
Popis: International audience; The purpose in this paper is to design finite-volumes schemes on structured grids for the transport of piecewise-constant functions (typically, indicator functions) with as low diffusion as possible. We first propose an extension of the so-called Lagrange-projection algorithm, or downwind scheme with an Ultrabee limiter, for the transport equation in one space dimension with a non-constant velocity; as its constant velocity counterpart, this scheme is designed to capture the discontinuities separating two plateaus in only one cell, and is referred to as "anti-diffusive". It is shown to preserve the bounds of the solution. Then, for two and three dimensional problems, we introduce a conservative alternate-directions algorithm, an show that this latter enjoys a discrete maximum principle, provided that the underlying one-dimensional schemes satisfy a property which may be seen as a flux limitation, possibly incorporated a posteriori in any explicit scheme. Numerical tests of this alternate-directions algorithm are performed, with a variety of one-dimensional embedded schemes including the anti-diffusive scheme developed here and the so called THINC scheme. The observed numerical diffusion is indeed very low. With the anti-diffusive scheme, the above-mentionned a posteriori limitation is necessary to preserve the solution bounds, but, in the performed tests, does not introduce any visible additional diffusion.
Databáze: OpenAIRE
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