On well-balanced finite volume methods for non-conservative non-homogeneous hyperbolic systems
In this work we introduce a general family of finite volume methods for non-homogeneous hyperbolic systems with non-conservative terms. We prove that all of them are “asymptotically well-balanced”: They preserve all smooth stationary solutions in all the domain but a set whose measure tends to zero...
| Authors: | , , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2007 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/32920 |
| Online Access: | http://hdl.handle.net/11441/32920 https://doi.org/10.1137/040607642 |
| Access Level: | Open access |
| Keyword: | Well-balanced Finite Volume Method upwinding shallow water source terms two-layer flows |
| Summary: | In this work we introduce a general family of finite volume methods for non-homogeneous hyperbolic systems with non-conservative terms. We prove that all of them are “asymptotically well-balanced”: They preserve all smooth stationary solutions in all the domain but a set whose measure tends to zero as ∆x tends to zero. This theory is applied to solve the bilayer Shallow-Water equations with arbitrary cross-section. Finally, some numerical tests are presented for simplified but meaningful geometries, comparing the computed solution with approximated asymptotic analytical solutions. |
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