Electronic Resource
Discussion on different numerical treatments on the loss of hyperbolicity for the two-layer shallow water system
| العنوان: | Discussion on different numerical treatments on the loss of hyperbolicity for the two-layer shallow water system |
|---|---|
| المؤلفون: | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII), Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI), Universidad de Sevilla. FQM120: Modelado Matemático y Simulación de Sistemas Medioambientales, Junta de Andalucía, European Union, Ministerio de Ciencia e Innovación (MICIN). España, Castro Díaz, Manuel Jesús, Fernández Nieto, Enrique Domingo, Garres-Díaz, José, Morales de Luna, Tomás |
| بيانات النشر: | Elsevier 2023 |
| نوع الوثيقة: | Electronic Resource |
| مستخلص: | This paper focus on the numerical approximation of two-layer shallow water system. First, a new approximation of the eigenvalues of the system is proposed, which satisfies some interesting properties. From this approximation, we give an accurate estimation of the non-hyperbolic region, which improves significantly the one computed with the classic eigenvalues approximation. In particular, we estimate both the lower and upper boundaries of the non-hyperbolic region. We also give a simple algorithm that allows us to compute bounds for the external eigenvalues, even when complex eigenvalues arise. We design an efficient FV solver depending on the hyperbolic nature of the system, that combines the PVM-2U-FL scheme and a new solver introduced in this work, named IFCP-FL, which degenerates to the Lax–Wendroff method in smooth areas. Different strategies for the numerical treatment for the loss of hyperbolicity are considered and discussed. Two of them are based on adding a friction term, depending on the classic or the new eigenvalues approximations, and the third one considers a simplified hyperbolic model in areas with complex eigenvalues. Some numerical tests are performed, including the case of two-layer fluids with different ratio of densities. The application to a two-layer model for submarine landslides is also considered. In the latter case, we show how the treatments based on adding friction are not appropriate for this kind of applications, whereas the treatment based on changing to a hyperbolic model produces much better results. |
| مصطلحات الفهرس: | Two-layer shallow water system, Hyperbolicity region, Finite volume, PVM methods, Submarine landslides, info:eu-repo/semantics/article |
| URL: | Advances in Water Resources, 182, 104587. PID2022-137637NB-C21 PID2022-137637NB-C22 |
| الاتاحة: | Open access content. Open access content http://creativecommons.org/licenses/by-nc/4.0 info:eu-repo/semantics/openAccess Atribución-NoComercial 4.0 Internacional |
| ملاحظة: | English |
| Other Numbers: | SUE oai:idus.us.es:11441/151702 Castro Díaz, M.J., Fernández-Nieto, E.D., Garres-Díaz, J. y Morales de Luna, T. (2023). Discussion on different numerical treatments on the loss of hyperbolicity for the two-layer shallow water system. Advances in Water Resources, 182, 104587. https://doi.org/10.1016/j.advwatres.2023.104587. 0309-1708 10.1016/j.advwatres.2023.104587 1416034715 |
| المصدر المساهم: | UNIV DE SEVILLA From OAIster®, provided by the OCLC Cooperative. |
| رقم الانضمام: | edsoai.on1416034715 |
| قاعدة البيانات: | OAIster |
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