A High–Order WENO Scheme Based on Different Numerical Fluxes for the Savage–Hutter Equations
The study of rapid free surface granular avalanche flows has attracted much attention in recent years, which is widely modeled using the Savage–Hutter equations. The model is closely related to shallow water equations. We employ a high-order shock-capturing numerical model based on the weighted esse...
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MDPI AG
2022-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/9/1482 |
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| author | Min Wang Xiaohua Zhang |
| author_facet | Min Wang Xiaohua Zhang |
| author_sort | Min Wang |
| collection | DOAJ |
| description | The study of rapid free surface granular avalanche flows has attracted much attention in recent years, which is widely modeled using the Savage–Hutter equations. The model is closely related to shallow water equations. We employ a high-order shock-capturing numerical model based on the weighted essential non-oscillatory (WENO) reconstruction method for solving Savage–Hutter equations. Three numerical fluxes, i.e., Lax–Friedrichs (LF), Harten–Lax–van Leer (HLL), and HLL contact (HLLC) numerical fluxes, are considered with the WENO finite volume method and TVD Runge–Kutta time discretization for the Savage–Hutter equations. Numerical examples in 1D and 2D space are presented to compare the resolution of shock waves and free surface capture. The numerical results show that the method proposed provides excellent performance with high accuracy and robustness. |
| first_indexed | 2024-03-10T03:57:01Z |
| format | Article |
| id | doaj.art-de5611faa69f424d86a82f0dad2f3372 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:57:01Z |
| publishDate | 2022-04-01 |
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| series | Mathematics |
| spelling | doaj.art-de5611faa69f424d86a82f0dad2f33722023-11-23T08:45:01ZengMDPI AGMathematics2227-73902022-04-01109148210.3390/math10091482A High–Order WENO Scheme Based on Different Numerical Fluxes for the Savage–Hutter EquationsMin Wang0Xiaohua Zhang1College of Civil Engineering & Architecture, China Three Gorges University, Yichang 443002, ChinaThree Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, ChinaThe study of rapid free surface granular avalanche flows has attracted much attention in recent years, which is widely modeled using the Savage–Hutter equations. The model is closely related to shallow water equations. We employ a high-order shock-capturing numerical model based on the weighted essential non-oscillatory (WENO) reconstruction method for solving Savage–Hutter equations. Three numerical fluxes, i.e., Lax–Friedrichs (LF), Harten–Lax–van Leer (HLL), and HLL contact (HLLC) numerical fluxes, are considered with the WENO finite volume method and TVD Runge–Kutta time discretization for the Savage–Hutter equations. Numerical examples in 1D and 2D space are presented to compare the resolution of shock waves and free surface capture. The numerical results show that the method proposed provides excellent performance with high accuracy and robustness.https://www.mdpi.com/2227-7390/10/9/1482granular avalanche flowSavage–Hutter equationsWENO finite volume methodnumerical flux |
| spellingShingle | Min Wang Xiaohua Zhang A High–Order WENO Scheme Based on Different Numerical Fluxes for the Savage–Hutter Equations Mathematics granular avalanche flow Savage–Hutter equations WENO finite volume method numerical flux |
| title | A High–Order WENO Scheme Based on Different Numerical Fluxes for the Savage–Hutter Equations |
| title_full | A High–Order WENO Scheme Based on Different Numerical Fluxes for the Savage–Hutter Equations |
| title_fullStr | A High–Order WENO Scheme Based on Different Numerical Fluxes for the Savage–Hutter Equations |
| title_full_unstemmed | A High–Order WENO Scheme Based on Different Numerical Fluxes for the Savage–Hutter Equations |
| title_short | A High–Order WENO Scheme Based on Different Numerical Fluxes for the Savage–Hutter Equations |
| title_sort | high order weno scheme based on different numerical fluxes for the savage hutter equations |
| topic | granular avalanche flow Savage–Hutter equations WENO finite volume method numerical flux |
| url | https://www.mdpi.com/2227-7390/10/9/1482 |
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