p-Adaptive simulations of Richards’ equation with discontinuous Galerkin method

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21220%2F22%3A00363727" target="_blank" >RIV/68407700:21220/22:00363727 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.kme.zcu.cz/compmech/download/proceedings/CM2022_Conference_Proceedings.pdf" target="_blank" >https://www.kme.zcu.cz/compmech/download/proceedings/CM2022_Conference_Proceedings.pdf</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

p-Adaptive simulations of Richards’ equation with discontinuous Galerkin method

Popis výsledku v původním jazyce

This paper focus on numerical discretization of Richards’ equation. This problem is widely used to study groundwater dynamics of saturated/unsaturated porous media. The numerical solution of Richards’ equation can be troublesome and costly because of abrupt changes in the nonlinear hydraulic properties. Typically, Richards’ equation exhibits sharp wetting fronts moving dynamically in the unsaturated zone while the saturated zone remains relatively smooth. As high-order methods are known to reach accuracy with a reduced cost compared to low-order methods, the use of local space order approximation seems as a quite natural direction to be explored in order to assess the possible gains for the solution of Richards’ equation. In this paper the discontinuous Galerkin methods are employed with the p-adaptive algorithm kept as simple as possible in order to prevent computational complexity. The Richard's equation is discretized with a DG method in space and with Backward Differentiation Formula methods in time. The adaptivity algorithm is outlined. Finally, the applicability of the method is demonstrated on a test-case.

Název v anglickém jazyce

p-Adaptive simulations of Richards’ equation with discontinuous Galerkin method

Popis výsledku anglicky

This paper focus on numerical discretization of Richards’ equation. This problem is widely used to study groundwater dynamics of saturated/unsaturated porous media. The numerical solution of Richards’ equation can be troublesome and costly because of abrupt changes in the nonlinear hydraulic properties. Typically, Richards’ equation exhibits sharp wetting fronts moving dynamically in the unsaturated zone while the saturated zone remains relatively smooth. As high-order methods are known to reach accuracy with a reduced cost compared to low-order methods, the use of local space order approximation seems as a quite natural direction to be explored in order to assess the possible gains for the solution of Richards’ equation. In this paper the discontinuous Galerkin methods are employed with the p-adaptive algorithm kept as simple as possible in order to prevent computational complexity. The Richard's equation is discretized with a DG method in space and with Backward Differentiation Formula methods in time. The adaptivity algorithm is outlined. Finally, the applicability of the method is demonstrated on a test-case.

Druh

O - Ostatní výsledky

CEP obor

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OECD FORD obor

10102 - Applied mathematics

Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů