Using a Separable Mathematical Entropy to Construct Entropy-Stable Schemes for a Reduced Blood Flow Model
The aim of this paper is to derive a separable entropy for a one-dimensional reduced blood flow model, which will be used to treat the symmetrizability of the model in full generality and for constructing entropy conservative fluxes, which are one of the essential building blocks of designing entrop...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/18/3314 |
| _version_ | 1797485204172963840 |
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| author | Sonia Valbuena Carlos A. Vega |
| author_facet | Sonia Valbuena Carlos A. Vega |
| author_sort | Sonia Valbuena |
| collection | DOAJ |
| description | The aim of this paper is to derive a separable entropy for a one-dimensional reduced blood flow model, which will be used to treat the symmetrizability of the model in full generality and for constructing entropy conservative fluxes, which are one of the essential building blocks of designing entropy-stable schemes. Time discretization is conducted by implicit–explicit (IMEX) Runge–Kutta schemes, but solutions for nonlinear systems will not be required due to the particular form of the source term. To validate the numerical schemes obtained, some numerical tests are presented. |
| first_indexed | 2024-03-09T23:15:24Z |
| format | Article |
| id | doaj.art-3b4ff82f5e954adba14b2a2b6784e4d0 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:15:24Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-3b4ff82f5e954adba14b2a2b6784e4d02023-11-23T17:36:30ZengMDPI AGMathematics2227-73902022-09-011018331410.3390/math10183314Using a Separable Mathematical Entropy to Construct Entropy-Stable Schemes for a Reduced Blood Flow ModelSonia Valbuena0Carlos A. Vega1Grupo de Investigación GIMED, Universidad del Atlántico, Barranquilla 080001, ColombiaDepartamento de Matemáticas y Estadística, Universidad del Norte, Barranquilla 080001, ColombiaThe aim of this paper is to derive a separable entropy for a one-dimensional reduced blood flow model, which will be used to treat the symmetrizability of the model in full generality and for constructing entropy conservative fluxes, which are one of the essential building blocks of designing entropy-stable schemes. Time discretization is conducted by implicit–explicit (IMEX) Runge–Kutta schemes, but solutions for nonlinear systems will not be required due to the particular form of the source term. To validate the numerical schemes obtained, some numerical tests are presented.https://www.mdpi.com/2227-7390/10/18/3314blood flow modelentropy pairsymmetrizabilityentropy conservative fluxIMEX schemes |
| spellingShingle | Sonia Valbuena Carlos A. Vega Using a Separable Mathematical Entropy to Construct Entropy-Stable Schemes for a Reduced Blood Flow Model Mathematics blood flow model entropy pair symmetrizability entropy conservative flux IMEX schemes |
| title | Using a Separable Mathematical Entropy to Construct Entropy-Stable Schemes for a Reduced Blood Flow Model |
| title_full | Using a Separable Mathematical Entropy to Construct Entropy-Stable Schemes for a Reduced Blood Flow Model |
| title_fullStr | Using a Separable Mathematical Entropy to Construct Entropy-Stable Schemes for a Reduced Blood Flow Model |
| title_full_unstemmed | Using a Separable Mathematical Entropy to Construct Entropy-Stable Schemes for a Reduced Blood Flow Model |
| title_short | Using a Separable Mathematical Entropy to Construct Entropy-Stable Schemes for a Reduced Blood Flow Model |
| title_sort | using a separable mathematical entropy to construct entropy stable schemes for a reduced blood flow model |
| topic | blood flow model entropy pair symmetrizability entropy conservative flux IMEX schemes |
| url | https://www.mdpi.com/2227-7390/10/18/3314 |
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