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**Finite element modelling of flow and temperature regime in shallow lakes.**
*(English)*
Zbl 1340.76052

Brandts, J. (ed.) et al., Proceedings of the international conference ‘Applications of mathematics’, Prague, Czech Republic, May 15–17, 2013. In honor of the 70th birthday of Karel Segeth. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics (ISBN 978-80-85823-61-5). 177-184 (2013).

The authors study numerically a two-dimensional depth-averaged flow and temperature model. The continuity equation is rearranged to the Helmholtz equation form. The system of shallow water and temperature evolution equations is discretized with the modified Utnes scheme, which is characterized by a semi-decoupling algorithm. The upwinding Tabata method is used to approximate convective terms. Simulations are carried out to study the circulation patterns in the Oder Lagoon located on the border between Germany and Poland. Averaged flow fields under prevailing wind conditions in August are calculated. The temperature variations are simulated during the flood period in summer 1997. Finally, limitations of the model are also discussed.

For the entire collection see [Zbl 1277.00032].

For the entire collection see [Zbl 1277.00032].

Reviewer: Peicheng Zhu (Leioa)

### MSC:

76M10 | Finite element methods applied to problems in fluid mechanics |

65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |

65Z05 | Applications to the sciences |

### Keywords:

depth-averaged flow; system of shallow water; continuity equation; temperature equation; Utnes scheme; upwinding Tabata method
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\textit{V. Podsechin} and \textit{G. Schernewski}, in: Proceedings of the international conference `Applications of mathematics', Prague, Czech Republic, May 15--17, 2013. In honor of the 70th birthday of Karel Segeth. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics. 177--184 (2013; Zbl 1340.76052)

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