A 3D staggered Lagrangian scheme for ideal magnetohydrodynamics on unstructured meshes. (10th May 2019)

• Record Type: Journal Article
• Authors: Xu, Xiao; Gao, Zhiming; Dai, Zihuan
• Is Part Of: International journal for numerical methods in fluids. Volume 90:Number 11(2019)
• Page Start: 584
• Page End: 602
• Publication Date: 2019-05-10
• Subjects: Lagrangian magnetohydrodynamics -- staggered scheme -- unstructured meshes -- 3D; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4736
• Languages: English
• ISSNs: 0271-2091

Abstract

Summary: In this paper, we propose a 3D staggered Lagrangian scheme for the ideal magnetohydrodynamics (MHD) on unstructured meshes. All the thermal variables and the magnetic induction are defined in the cell centers while the fluid velocity is located at the nodes. The meshes are compatibly discretized to ensure the geometric conservation laws in Lagrangian computation by the classical subcell method, then the momentum equation is discretized using the subcell forces and the specific internal energy equation is obtained by the total energy conservation. Invoking the Galilean invariance, magnetic flux conservation, and the thermodynamic consistency, the expressions of subcell force as well as the cell‐centered velocity are derived. Besides, the magnetic divergence‐free constraint is fulfilled by a projection method after each time step. Various numerical tests are presented to assert the robustness and accuracy of our scheme. Abstract : A 3D pure Lagrangian scheme for the ideal MHD equations is proposed on unstructured meshes. We use a staggered discretization which the fluid velocity is located at the nodes while other variables are defined at the cell centers. We apply the classical subcell force method to MHD equations to compatibly construct the scheme and in which the artificial viscosity is based on Riemann solvers at the nodes. Besides, the magnetic divergence constraint is satisfied by projection method. The scheme is capable to handle some stringent test problems, like 2D MHD rotor test and 2D and 3D MHD blast tests, and the results of these problems are comparable to those calculated by Eulerian or ALE schemes, which validate the accuracy and robustness of our scheme.