Locally divergence-free well-balanced path-conservative central-upwind schemes for rotating shallow water MHD

Chertock，Alina1; Kurganov，Alexander2; Redle，Michael3,4; Zeitlin，Vladimir5,6

2024-12-01

10.1016/j.jcp.2024.113300

Journal of Computational Physics   影响因子和分区

0021-9991

1090-2716

We develop a new second-order flux globalization based path-conservative central-upwind (PCCU) scheme for rotating shallow water magnetohydrodynamic equations. The new scheme is designed not only to maintain the divergence-free constraint of the magnetic field at the discrete level but also to satisfy the well-balanced (WB) property by exactly preserving some physically relevant steady states of the underlying system. The locally divergence-free constraint of the magnetic field is enforced by following the method recently introduced in Chertock et al. (2024) [19]: we consider a Godunov-Powell modified version of the studied system, introduce additional equations by spatially differentiating the magnetic field equations, and modify the reconstruction procedures for magnetic field variables. The WB property is ensured by implementing a flux globalization approach within the PCCU scheme, leading to a method capable of preserving both still- and moving-water equilibria exactly. In addition to provably achieving both the WB and divergence-free properties, the new method is implemented on an unstaggered grid and does not require any (approximate) Riemann problem solvers. The performance of the proposed method is demonstrated in several numerical experiments that confirms robustness, a high resolution of obtained results, and a lack of spurious oscillations.

Divergence-free constraints Flux globalization based well-balanced scheme Nonconservative hyperbolic systems of nonlinear PDEs Path-conservative central-upwind scheme Rotating shallow water magnetohydrodynamics

SCI

英语

通讯

PHYSICS

2-s2.0-85200145896

Scopus

1.Department of Mathematics and Center for Research in Scientific Computing,North Carolina State University,Raleigh,27695,United States
2.Department of Mathematics,Shenzhen International Center for Mathematics,Guangdong Provincial Key Laboratory of Computational Science and Material Design,Southern University of Science and Technology,Shenzhen,518055,China
3.Applied and Computational Mathematics,RWTH Aachen University,Aachen,52062,Germany
4.Department of Mathematics,North Carolina State University,Raleigh,27695,United States
5.Laboratoire de Météorologie Dynamique,Sorbonne Université (SU),Ecole Normale Supérieure (ENS),CNRS,Paris,75231,France
6.Shenzhen International Center for Mathematics,Southern University of Science and Technology,Shenzhen,518055,China

Chertock，Alina,Kurganov，Alexander,Redle，Michael,et al. Locally divergence-free well-balanced path-conservative central-upwind schemes for rotating shallow water MHD[J]. Journal of Computational Physics,2024,518.

Chertock，Alina,Kurganov，Alexander,Redle，Michael,&Zeitlin，Vladimir.(2024).Locally divergence-free well-balanced path-conservative central-upwind schemes for rotating shallow water MHD.Journal of Computational Physics,518.

Chertock，Alina,et al."Locally divergence-free well-balanced path-conservative central-upwind schemes for rotating shallow water MHD".Journal of Computational Physics 518(2024).