Year: 2025
Type: article
Abstract: In this work, third-order semi-implicit schemes on staggered meshes for the shallow water and Saint-Venant-Exner systems are presented. They are based on a third-order extension of the technique introduced in Casulli & Cheng [15]. The stability conditions for these schemes depend on the velocity and not on the celerity, allowing us to reduce computational efforts, especially in subcritical flow simulations, which is the regime we are mainly interested in. The main novelty consists in the third-order approximation of the pressure gradient term in the momentum equation through appropriate polynomial reconstructions. Concretely, CWENO conservative reconstruction is considered for the water thickness h and a centered fourth-degree polynomial is adopted interpolating the cell averages of the free surface $$\eta $$ η . For time discretization, a third-order IMEX scheme is applied. In addition, a novel time-dependent semi-analytical solution for Saint-Venant-Exner system is introduced and compared with the numerical ones. Several tests are performed, including accuracy tests showing third-order accuracy, well-balance tests, and simulations of slow bedload processes for large time.
Source: Journal of Scientific Computing
Institutions: Universidad de Sevilla, University of Catania
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", European Commission, Ministero dell’Istruzione, dell’Università e della Ricerca, Università di Catania, Junta de Andalucía, Gruppo Nazionale per il Calcolo Scientifico, European Regional Development Fund, Agencia Estatal de Investigación
Awards: G1270778082, G1326039963, G1511544777, G1622782223, G2084764210, G2582585287, G3314809433, G3480869486, G4490508387, G4575922874, G465505792, G4772130973, G490430286, G5245466801, G5402479840, G5465607307, G5488169599, G5636153502, G5796505130, G617794351, G7084143925, G7103356121, G792356639, G7951113301, G8082311658, G8295278529, G8409961469, G881421601, G8820152341, G972786147, G990108450
OpenAlex ID: W4415474695