TY - JOUR
T1 - A Gegenbauer-Galerkin spectral scheme for three-dimensional incompressible Hall-magnetohydrodynamics system
AU - Guo, Shimin
AU - Jiang, Han
AU - Zhou, Pengrui
AU - Mei, Liquan
N1 - Publisher Copyright:
© 2026 Elsevier B.V.
PY - 2026/6
Y1 - 2026/6
N2 - This study is devoted to designing an efficient finite difference/spectral scheme for three-dimensional incompressible Hall-MHD system on infinite domain, which combines a novel Gegenbauer-Galerkin spectral method for spatial approximation, the non-zero auxiliary variable for dealing with the nonlinear parts, the Lagrange multiplier approach for magnetic field equation, the second-order projection method for momentum equations, and the time-stepping-varying Crank-Nicolson scheme for temporal discretization. The proposed fully-discrete scheme simultaneously reaches several desired properties including global approximation on infinite domain, linearity, divergence-free constraint of magnetic field in the weak sense, second-order temporal accuracy, decoupling structure in the Stokes solver, and unconditional energy stability. Comprehensive numerical examples are presented to demonstrate the stability, accuracy, and efficiency of the proposed scheme. As the applications, the null points of magnetic field are simulated by the proposed scheme within the framework of Hall-MHD.
AB - This study is devoted to designing an efficient finite difference/spectral scheme for three-dimensional incompressible Hall-MHD system on infinite domain, which combines a novel Gegenbauer-Galerkin spectral method for spatial approximation, the non-zero auxiliary variable for dealing with the nonlinear parts, the Lagrange multiplier approach for magnetic field equation, the second-order projection method for momentum equations, and the time-stepping-varying Crank-Nicolson scheme for temporal discretization. The proposed fully-discrete scheme simultaneously reaches several desired properties including global approximation on infinite domain, linearity, divergence-free constraint of magnetic field in the weak sense, second-order temporal accuracy, decoupling structure in the Stokes solver, and unconditional energy stability. Comprehensive numerical examples are presented to demonstrate the stability, accuracy, and efficiency of the proposed scheme. As the applications, the null points of magnetic field are simulated by the proposed scheme within the framework of Hall-MHD.
KW - Energy stability
KW - Gegenbauer function
KW - Hall-MHD
KW - Spectral approximation
KW - Time-splitting
UR - https://www.scopus.com/pages/publications/105032101463
U2 - 10.1016/j.cpc.2026.110103
DO - 10.1016/j.cpc.2026.110103
M3 - 文章
AN - SCOPUS:105032101463
SN - 0010-4655
VL - 323
JO - Computer Physics Communications
JF - Computer Physics Communications
M1 - 110103
ER -