Improved well-balanced AWENO schemes with hydrostatic reconstruction for the Euler equations under gravitational fields

Qingcheng Fu, Zhen Gao, Yaguang Gu, Peng Li and Bao-Shan Wang

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 221, issue C, 260-280

Abstract: The Euler equations under gravitational fields allow the hydrostatic equilibrium states, which requires that the numerical scheme of the system should also have this characteristic. In our previous work, a well-balanced finite difference conservative AWENO scheme has been constructed to preserve the isothermal equilibrium state accurately (Fu et al., Appl. Numer. Math., 180:1-15, 2022). However, the scheme fails to maintain more complicated hydrostatic equilibrium states, such as the isentropic equilibrium state. In this study, the improved well-balanced AWENO schemes with hydrostatic reconstruction are designed to maintain the general equilibrium states numerically. The key technologies to achieve the well-balanced property are rewriting the source term into an appropriate form based on the equilibrium equation, acting on the conserved variables with an affine-invariant WENO or linearized WENO interpolation operator, employing hydrostatic reconstruction methods to create auxiliary conserved variables, and modifying the numerical flux with auxiliary conserved variables and higher-order conserved terms based on pressure. The proposed well-balanced schemes maintain the equilibrium solution near the machine precision and capture small perturbations of the equilibrium state without spurious oscillations even at the coarse mesh. Furthermore, they can be applicable to the general hydrostatic equilibrium more than the isothermal equilibrium state. Several numerical experiments are tested to show that the developed well-balanced schemes perform well in maintaining equilibrium states and capturing small perturbations.

Keywords: Well-balanced; AWENO scheme; Affine-invariant WENO operator; Euler equations with gravity; Hydrostatic reconstruction (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475424000788
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:221:y:2024:i:c:p:260-280

DOI: 10.1016/j.matcom.2024.03.007

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().