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

Abstract

a b s t r a c tAn E-CUSP (energy-convective upwind and split pressure) scheme is developed to solve the equations of magnetohydrodynamics. Fifth order WENO reconstructions are employed to calculate the fluxes in order to achieve high order spacial accuracy. A characteristic speed of sound by averaging the fast wave speed and the acoustic speed of sound is suggested to evaluate the Mach number, which will yield robust and accurate solutions. The numerical experiments have demonstrated the accuracy and the capability of the new scheme to capture complex interactions of multiple shocks and vortices.

Hybridized SLAU2–HLLI and hybridized AUSMPW$$+$$–HLLI Riemann solvers for accurate, robust, and efficient magnetohydrodynamics (MHD) simulations, part I: one-dimensional MHD

“…The divergence-free requirement for the magnetic field ( •B = 0) is automatically satisfied, as long as B x = const. [52]. Then, Equation (1a) is solved with a 1D finite-volume code, and can be written in the delta form as:…”

“…Only a few FVS-based Riemann solvers for MHD have been presented in the literature. These include E-CUSP [52] and AUSMPW+ [53,54]. While E-CUSP will not accurately capture a stationary contact discontinuity in MHD, AUSMPW+ will capture such a discontinuity.…”

“…We confine the present work to one dimension (1D) because multi-dimensional treatments of MHD inevitably call for a divergence-free constraint on the magnetic field ( •B = 0) [71][72][73][74][75][76][77][78][79]. There are several methods to guarantee this divergence-free property, and the employed method differs from one literature to another (for instance, Han et al [53] proposed AUSMPW+ for MHD and coupled it with Dedner's method [73], whereas E-CUSP for MHD [52] was developed and tested with a constraint transport method by Balsara and Spicer [72]). In this work, such influences of the choice of divergence-treatment method is excluded from our 1D MHD discussion (the multidimensional performance, such as robustness against the carbuncle phenomenon, is deferred to the future work).…”

A High-Order Finite Difference WENO Scheme for Ideal Magnetohydrodynamics on Curvilinear Meshes

“…which has the same form as (52). Note that whereas the consistency condition (53) on ρu is used to obtain B * α in the HLLC solver, here the RH condition across S α is applied to ρu and B for determining ρu * α and B * α , and a consistency condition similar to (53) Note that this is consistent with the fact that densities are identical across rotational discontinuities, which is assumed in deriving the estimates of S * L and S * R in (59).…”

行星际太阳风暴的数值模拟研究

“…Shen 等 [111] 注意到在 MHD 的特征系统中, 对应于 Alfvén 波的特征值对通 量没有影响, 也就是说用任何值代替对应的特征值, 通量不变, 这使得基于 Roe 近似的黎曼解具有不确定 性. 另一种低耗散高阶格式 [111,112] 将对流迎风压力分 裂的 WENO 格式和约束输运算法结合起来, 不需要 繁复的求解特征系统, 这些低耗散的格式预计可以 用于未来低粘性的太阳风数值研究中.…”