A High-Order WENO Finite Difference Scheme for the Equations of Ideal Magnetohydrodynamics

E-CUSP scheme for the equations of ideal magnetohydrodynamics with high order WENO Scheme

“…The contact discontinuity and shock wave are captured very well. These numerical results agree well with those of Jiang and Wu [4] and show that the present scheme can deal well with MHD high Mach number flow.…”

“…The Kelvin-Helmholtz instability is considered as an important mechanism for momentum transfer at Earth's magnetopause boundary, which separates the solar wind flow from the Earth's magnetosphere [59,4]. In order to compare the results, the computational conditions are taken as the same used in [4,19].…”

“…Depending on the direction and the magnitude of the magnetic field, these wave speeds may coincide. Thus the MHD equations form a non-strictly hyperbolic system [1][2][3][4][5].…”

“…HLL (Harten-Lax-van Leer)-type schemes are developed by Janhunen [9], Honkkila and Janhunen [10], Gurski [11], Li [12], Miyoshi and Kusano [13] and Balsara et al [14]. Flux vector splitting methods are developed by MacCormack [15] and Jiang and Wu [4]. The equations of magnetohydrodynamics are not homogeneous of degree one with respect to the state vector and hence cannot directly perform flux vector splitting.…”

2D MHD simulation of the emergence and merging of coherent structures

“…In our simulations, we solved these equations on a computer as an initial-and boundary-value problem. We used a high-order accurate (5th-order in space and 4th-order in time) upwind scheme [Jiang and Wu, 1999], which can handle shocks, discontinuities and large gradients without introducing spurious oscillations and at the same time can provide high-order accurate solution in the smooth region. The code is constructed in conservative form so that the total mass, total energy, total magnetic fluxes and total momenta are conserved.…”