A new central-upwind scheme for solving the shallow water equations | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 1، دوره 6، شماره 3، 2025، صفحه 193-203 اصل مقاله (713.09 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2023.22640.1182 | ||
| نویسنده | ||
| Rooholah Abedian* | ||
| School of Engineering Science, College of Engineering, University of Tehran, Iran | ||
| چکیده | ||
| We have conducted a study where we applied one-dimensional central-upwind methods to estimate solutions of the Saint-Venant (SV) system. Our approach carefully considers the source terms associated with bottom topography. Within the context of the SV system, there are steady-state solutions that arise when the non-zero gradients of flux are exactly balanced by the corresponding source terms. Maintaining this delicate equilibrium with numerical approaches presents a challenging problem. Finding slight variations in these states proves to be extremely difficult in the field of computing. To address this, we propose an extension of semi-discrete central schemes, commonly employed in hyperbolic conservation law systems, to encompass balance laws (BL). In our approach, we specifically focus on discretizing the source term with great care and attention. To verify the superior accuracy, precise preservation of the $C$-property, and outstanding resolution of our approach, we perform comprehensive one-dimensional simulations on both continuous and discontinuous solutions. | ||
| کلیدواژهها | ||
| Saint-Venant system؛ Central-upwind methods؛ Balance laws؛ Hyperbolic conservation laws | ||
| مراجع | ||
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