Academic Journal
High-Order Well-Balanced Methods for the Euler Equations of Gas Dynamics with Gravitational Forces and the Ripa Model: High-order well-balanced methods for the Euler equations of gas dynamics with gravitational forces and the Ripa model
| Τίτλος: | High-Order Well-Balanced Methods for the Euler Equations of Gas Dynamics with Gravitational Forces and the Ripa Model: High-order well-balanced methods for the Euler equations of gas dynamics with gravitational forces and the Ripa model |
|---|---|
| Συγγραφείς: | I. Gómez-Bueno, M. J. Castro, C. Parés |
| Πηγή: | RIUMA. Repositorio Institucional de la Universidad de Málaga Universidad de Málaga |
| Στοιχεία εκδότη: | Springer Science and Business Media LLC, 2025. |
| Έτος έκδοσης: | 2025 |
| Θεματικοί όροι: | Hydrology, hydrography, oceanography, finite volume methods, Método de los volúmenes finitos, Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations, reconstruction operators, Gas dynamics (general theory), Ecuaciones Euler, Compressible Euler equations, compressible Euler equations, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, High-order methods, Finite volume methods for initial value and initial-boundary value problems involving PDEs, Reconstruction operators, Finite-volume methods, Dinámica de gases, Finite volume methods for boundary value problems involving PDEs, Finite volume methods applied to problems in fluid mechanics, Euler equations, PDEs in connection with geophysics, high-order methods, Análisis matemático, well-balanced methods, Ripa model, Well-balanced methods, Análisis numérico |
| Περιγραφή: | Different well-balanced high-order finite-volume numerical methods for the one-dimensional compressible Euler equations of gas dynamics with gravitational force and for the Ripa model have been proposed in the literature. Most of them preserve either a given family of hydrostatic stationary solutions exactly or all of them approximately. The goal of this paper is to design a general methodology to obtain high-order finite-volume numerical methods for a class of one-dimensional hyperbolic systems of balance laws that preserve approximately all the hydrostatic equilibria and exactly a given family of them. Many fluid models for which the velocity is an eigenvalue of the system belong to this class, the Euler equations and the Ripa model among them. The methods proposed here are based on the design of well-balanced reconstruction operators that require the exact or the approximate computation of local hydrostatic equilibria. To check the efficiency and the well-balancedness of the methods, a number of numerical tests have been performed: the numerical results confirm the theoretical ones. |
| Τύπος εγγράφου: | Article |
| Περιγραφή αρχείου: | application/xml |
| Γλώσσα: | English |
| ISSN: | 1573-7691 0885-7474 |
| DOI: | 10.1007/s10915-024-02781-1 |
| Σύνδεσμος πρόσβασης: | https://hdl.handle.net/10630/37656 https://zbmath.org/7983279 https://doi.org/10.1007/s10915-024-02781-1 |
| Rights: | CC BY |
| Αριθμός Καταχώρησης: | edsair.doi.dedup.....4a9f97bb38362f9ae5effe6d8b99cf02 |
| Βάση Δεδομένων: | OpenAIRE |
| ISSN: | 15737691 08857474 |
|---|---|
| DOI: | 10.1007/s10915-024-02781-1 |