Stable Algorithm Based On Lax-Friedrichs Scheme for Visual Simulation of Shallow Water
Many game applications require fluid flow visualization of shallow water, especially dam-break flow. A Shallow Water Equation (SWE) is a mathematical model of shallow water flow which can be used to compute the flow depth and velocity. We propose a stable algorithm for visualization of dam-break fl...
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| Format: | Article |
| Language: | English |
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Politeknik Elektronika Negeri Surabaya
2020-06-01
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| Series: | Emitter: International Journal of Engineering Technology |
| Subjects: | |
| Online Access: | https://emitter.pens.ac.id/index.php/emitter/article/view/479 |
| _version_ | 1818880889044598784 |
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| author | Bandung Arry Sanjoyo Mochamad Hariadi Mauridhi Hery Purnomo |
| author_facet | Bandung Arry Sanjoyo Mochamad Hariadi Mauridhi Hery Purnomo |
| author_sort | Bandung Arry Sanjoyo |
| collection | DOAJ |
| description | Many game applications require fluid flow visualization of shallow water, especially dam-break flow. A Shallow Water Equation (SWE) is a mathematical model of shallow water flow which can be used to compute the flow depth and velocity. We propose a stable algorithm for visualization of dam-break flow on flat and flat with bumps topography. We choose Lax-Friedrichs scheme as the numerical method for solving the SWE. Then, we investigate the consistency, stability, and convergence of the scheme. Finally, we transform the strategy into a visualization algorithm of SWE and analyze the complexity. The results of this paper are: 1) the Lax-Friedrichs scheme that is consistent and conditionally stable; furthermore, if the stability condition is satisfied, the scheme is convergent; 2) an algorithm to visualize flow depth and velocity which has complexity O(N) in each time iteration. We have applied the algorithm to flat and flat with bumps topography. According to visualization results, the numerical solution is very close to analytical solution in the case of flat topography. In the case of flat with bumps topography, the algorithm can visualize the dam-break flow and after a long time the numerical solution is very close to the analytical steady-state solution. Hence the proposed visualization algorithm is suitable for game applications containing flat with bumps environments. |
| first_indexed | 2024-12-19T14:53:08Z |
| format | Article |
| id | doaj.art-f21cb0cc1b5e4bb8a7003b9b6d8bdbe5 |
| institution | Directory Open Access Journal |
| issn | 2355-391X 2443-1168 |
| language | English |
| last_indexed | 2024-12-19T14:53:08Z |
| publishDate | 2020-06-01 |
| publisher | Politeknik Elektronika Negeri Surabaya |
| record_format | Article |
| series | Emitter: International Journal of Engineering Technology |
| spelling | doaj.art-f21cb0cc1b5e4bb8a7003b9b6d8bdbe52022-12-21T20:16:47ZengPoliteknik Elektronika Negeri SurabayaEmitter: International Journal of Engineering Technology2355-391X2443-11682020-06-018110.24003/emitter.v8i1.479479Stable Algorithm Based On Lax-Friedrichs Scheme for Visual Simulation of Shallow WaterBandung Arry Sanjoyo0Mochamad Hariadi1Mauridhi Hery Purnomo2Institut Teknologi Sepuluh NopemberInstitut Teknologi Sepuluh NopemberInstitut Teknologi Sepuluh NopemberMany game applications require fluid flow visualization of shallow water, especially dam-break flow. A Shallow Water Equation (SWE) is a mathematical model of shallow water flow which can be used to compute the flow depth and velocity. We propose a stable algorithm for visualization of dam-break flow on flat and flat with bumps topography. We choose Lax-Friedrichs scheme as the numerical method for solving the SWE. Then, we investigate the consistency, stability, and convergence of the scheme. Finally, we transform the strategy into a visualization algorithm of SWE and analyze the complexity. The results of this paper are: 1) the Lax-Friedrichs scheme that is consistent and conditionally stable; furthermore, if the stability condition is satisfied, the scheme is convergent; 2) an algorithm to visualize flow depth and velocity which has complexity O(N) in each time iteration. We have applied the algorithm to flat and flat with bumps topography. According to visualization results, the numerical solution is very close to analytical solution in the case of flat topography. In the case of flat with bumps topography, the algorithm can visualize the dam-break flow and after a long time the numerical solution is very close to the analytical steady-state solution. Hence the proposed visualization algorithm is suitable for game applications containing flat with bumps environments.https://emitter.pens.ac.id/index.php/emitter/article/view/479shallow water equationsdam-break flowLax-Friedrichs schemeflow visualization |
| spellingShingle | Bandung Arry Sanjoyo Mochamad Hariadi Mauridhi Hery Purnomo Stable Algorithm Based On Lax-Friedrichs Scheme for Visual Simulation of Shallow Water Emitter: International Journal of Engineering Technology shallow water equations dam-break flow Lax-Friedrichs scheme flow visualization |
| title | Stable Algorithm Based On Lax-Friedrichs Scheme for Visual Simulation of Shallow Water |
| title_full | Stable Algorithm Based On Lax-Friedrichs Scheme for Visual Simulation of Shallow Water |
| title_fullStr | Stable Algorithm Based On Lax-Friedrichs Scheme for Visual Simulation of Shallow Water |
| title_full_unstemmed | Stable Algorithm Based On Lax-Friedrichs Scheme for Visual Simulation of Shallow Water |
| title_short | Stable Algorithm Based On Lax-Friedrichs Scheme for Visual Simulation of Shallow Water |
| title_sort | stable algorithm based on lax friedrichs scheme for visual simulation of shallow water |
| topic | shallow water equations dam-break flow Lax-Friedrichs scheme flow visualization |
| url | https://emitter.pens.ac.id/index.php/emitter/article/view/479 |
| work_keys_str_mv | AT bandungarrysanjoyo stablealgorithmbasedonlaxfriedrichsschemeforvisualsimulationofshallowwater AT mochamadhariadi stablealgorithmbasedonlaxfriedrichsschemeforvisualsimulationofshallowwater AT mauridhiherypurnomo stablealgorithmbasedonlaxfriedrichsschemeforvisualsimulationofshallowwater |