Finite Integration Method with Chebyshev Expansion for Shallow Water Equations over Variable Topography
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| Xuất bản năm: | Mathematics vol. 13, no. 15 (2025), p. 2492-2522 |
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MDPI AG
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| Truy cập trực tuyến: | Citation/Abstract Full Text + Graphics Full Text - PDF |
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| 100 | 1 | |a Ampol, Duangpan |u Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand; ampol.d@chula.ac.th (A.D.); 6370023023@alumni.chula.ac.th (L.A.) | |
| 245 | 1 | |a Finite Integration Method with Chebyshev Expansion for Shallow Water Equations over Variable Topography | |
| 260 | |b MDPI AG |c 2025 | ||
| 513 | |a Journal Article | ||
| 520 | 3 | |a The shallow water equations (SWEs) model fluid flow in rivers, coasts, and tsunamis. Their nonlinearity challenges analytical solutions. We present a numerical algorithm combining the finite integration method with Chebyshev polynomial expansion (FIM-CPE) to solve one- and two-dimensional SWEs. The method transforms partial differential equations into integral equations, approximates spatial terms via Chebyshev polynomials, and uses forward differences for time discretization. Validated on stationary lakes, dam breaks, and Gaussian pulses, the scheme achieved errors below <inline-formula>10−12</inline-formula> for water height and velocity, while conserving mass with volume deviations under <inline-formula>10−5</inline-formula>. Comparisons showed superior shock-capturing versus finite difference methods. For two-dimensional cases, it accurately resolved wave interactions over complex topographies. Though limited to wet beds and small-scale two-dimensional problems, the method provides a robust simulation tool. | |
| 653 | |a Finite volume method | ||
| 653 | |a Velocity | ||
| 653 | |a Partial differential equations | ||
| 653 | |a Shallow water equations | ||
| 653 | |a Topography | ||
| 653 | |a Finite difference method | ||
| 653 | |a Integral equations | ||
| 653 | |a Numerical analysis | ||
| 653 | |a Polynomials | ||
| 653 | |a Fluid flow | ||
| 653 | |a Water | ||
| 653 | |a Chebyshev approximation | ||
| 653 | |a Exact solutions | ||
| 653 | |a Approximation | ||
| 653 | |a Wave interaction | ||
| 700 | 1 | |a Ratinan, Boonklurb |u Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand; ampol.d@chula.ac.th (A.D.); 6370023023@alumni.chula.ac.th (L.A.) | |
| 700 | 1 | |a Apisornpanich Lalita |u Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand; ampol.d@chula.ac.th (A.D.); 6370023023@alumni.chula.ac.th (L.A.) | |
| 700 | 1 | |a Phiraphat, Sutthimat |u Department of Mathematics, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand | |
| 773 | 0 | |t Mathematics |g vol. 13, no. 15 (2025), p. 2492-2522 | |
| 786 | 0 | |d ProQuest |t Engineering Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3239074859/abstract/embedded/75I98GEZK8WCJMPQ?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text + Graphics |u https://www.proquest.com/docview/3239074859/fulltextwithgraphics/embedded/75I98GEZK8WCJMPQ?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text - PDF |u https://www.proquest.com/docview/3239074859/fulltextPDF/embedded/75I98GEZK8WCJMPQ?source=fedsrch |