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

Fu，Qingcheng1,2; Gao，Zhen1; Gu，Yaguang3; Li，Peng4; Wang，Bao Shan1

2024-07-01

10.1016/j.matcom.2024.03.007

Mathematics and Computers in Simulation   影响因子和分区

0378-4754

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.

Affine-invariant WENO operator AWENO scheme Euler equations with gravity Hydrostatic reconstruction Well-balanced

SCI ; EI

英语

其他

20241115738438

Gravitational effects ; Hydraulics ; Isotherms ; Numerical methods

Fluid Flow, General:631.1 ; Hydraulics:632.1 ; Mathematics:921 ; Numerical Methods:921.6 ; Gravitation, Relativity and String Theory:931.5

ENGINEERING

2-s2.0-85187220164

Scopus

1.School of Mathematical Sciences,Ocean University of China,Qingdao,China
2.Department of Mathematics,Southern University of Science and Technology,Shenzhen,China
3.School of Mathematics,South China University of Technology,Guangzhou,China
4.Department of Engineering Mechanics/Innovation Center for Wind Engineering and Wind Energy Technology of Hebei Province,Shijiazhuang Tiedao University,Shijiazhuang,China

Fu，Qingcheng,Gao，Zhen,Gu，Yaguang,et al. Improved well-balanced AWENO schemes with hydrostatic reconstruction for the Euler equations under gravitational fields[J]. Mathematics and Computers in Simulation,2024,221:260-280.

Fu，Qingcheng,Gao，Zhen,Gu，Yaguang,Li，Peng,&Wang，Bao Shan.(2024).Improved well-balanced AWENO schemes with hydrostatic reconstruction for the Euler equations under gravitational fields.Mathematics and Computers in Simulation,221,260-280.

Fu，Qingcheng,et al."Improved well-balanced AWENO schemes with hydrostatic reconstruction for the Euler equations under gravitational fields".Mathematics and Computers in Simulation 221(2024):260-280.