In this paper, we focus on finite volume approximation schemes to solve a non-local material flow model in two space dimensions. Based on the numerical discretisation with dimensional splitting, we prove the convergence of the approximate solutions, where the main difficulty arises in the treatment of the discontinuity occurring in the flux function. In particular, we compare a Roe-type scheme to the well-established Lax-Friedrichs method and provide a numerical study highlighting the benefits of the Roe discretisation. Besides, we also prove the L1-Lipschitz continuous dependence on the initial datum, ensuring the uniqueness of the solution.

Well-posedness of a non-local model for material flow on conveyor belts / Rossi, E.; Weissen, J.; Goatin, P.; Gottlich, S.. - In: MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE. - ISSN 0764-583X. - 54:2(2020), pp. 679-704. [10.1051/m2an/2019062]

Well-posedness of a non-local model for material flow on conveyor belts

Rossi E.
;
2020

Abstract

In this paper, we focus on finite volume approximation schemes to solve a non-local material flow model in two space dimensions. Based on the numerical discretisation with dimensional splitting, we prove the convergence of the approximate solutions, where the main difficulty arises in the treatment of the discontinuity occurring in the flux function. In particular, we compare a Roe-type scheme to the well-established Lax-Friedrichs method and provide a numerical study highlighting the benefits of the Roe discretisation. Besides, we also prove the L1-Lipschitz continuous dependence on the initial datum, ensuring the uniqueness of the solution.
2020
54
2
679
704
Well-posedness of a non-local model for material flow on conveyor belts / Rossi, E.; Weissen, J.; Goatin, P.; Gottlich, S.. - In: MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE. - ISSN 0764-583X. - 54:2(2020), pp. 679-704. [10.1051/m2an/2019062]
Rossi, E.; Weissen, J.; Goatin, P.; Gottlich, S.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1224588
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