RT Journal Article
T1 High-order well-balanced methods for the Euler equations of gas dynamics with gravitational forces and the Ripa model
A1 Gómez Bueno, Irene
A1 Castro-Díaz, Manuel Jesús
A1 Parés-Madroñal, Carlos María
K1 Ecuaciones Euler
K1 Método de los volúmenes finitos
K1 Análisis numérico
K1 Análisis matemático
K1 Dinámica de gases
AB 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.
PB Springer Nature
YR 2025
FD 2025
LK https://hdl.handle.net/10630/37656
UL https://hdl.handle.net/10630/37656
LA eng
NO Gómez-Bueno, I., Castro, M.J. & Parés, C. High-Order Well-Balanced Methods for the Euler Equations of Gas Dynamics with Gravitational Forces and the Ripa Model. J Sci Comput 102, 77 (2025). https://doi.org/10.1007/s10915-024-02781-1
NO Funding for open access charge: Universidad de Málaga/CBUA. This research has been partially supported by Spanish projects RTI2018-096064-B-C1 and PID2022-137637NB-C21 funded by MCIN/AEI/10.13039/501100011033 and FSE+. I. Gómez-Bueno was also supported by a Grant from “El Ministerio de Ciencia, Innovación y Universidades”, Spain (FPU2019/01541) funded by MCIN/AEI/10.13039/ 501100011033 and “ESF Investing in your future”.
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 20 ene 2026