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arXiv 0810.1838astro-phgr-qc
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超越理想的MHD:朝向相对论性天体物理等离子体的更真实的模拟

Beyond ideal MHD: towards a more realistic modeling of relativistic astrophysical plasmas

Carlos Palenzuela, Luis Lehner, Oscar Reula, Luciano Rezzolla

摘要:

许多天体物理过程,包括磁场和准定常过程很好地描述时,假设流体作为一个完美的导体。对于这些系统,理想的磁流体动力学(MHD)的描述有效地捕捉动态和一些行之有效的技术存在其数值解。然而,有几个天体物理过程涉及磁场,这是高度动态的,电阻效应可以发挥重要作用。这种非理想MHD流的数值建模明显更具挑战性,因为预计电阻率在整个流中会发生几个数量级的变化,并且方程具有双曲-抛物线性质或具有刚性项的双曲。在这里,我们提出了一种新的方法来解决这些相对论性电阻MHD方程利用隐式显式(IMEX)龙格库塔方法的属性。通过检查一些测试,我们说明了我们的方法在各种条件下的准确性,并强调其鲁棒性相比,替代方法,如Strang-splitting。最重要的是,我们表明,我们的方法可以处理,在一个统一的框架内,这些地区的流动是流体压力为主(如在紧凑的对象的内部),而不是磁压力为主(如在其磁层)

英文摘要:

Many astrophysical processes involving magnetic fields and quasi-stationary processes are well described when assuming the fluid as a perfect conductor. For these systems, the ideal-magnetohydrodynamics (MHD) description captures the dynamics effectively and a number of well-tested techniques exist for its numerical solution. Yet, there are several astrophysical processes involving magnetic fields which are highly dynamical and for which resistive effects can play an important role. The numerical modeling of such non-ideal MHD flows is significantly more challenging as the resistivity is expected to change of several orders of magnitude across the flow and the equations are then either of hyperbolic-parabolic nature or hyperbolic with stiff terms. We here present a novel approach for the solution of these relativistic resistive MHD equations exploiting the properties of implicit-explicit (IMEX) Runge Kutta methods. By examining a number of tests we illustrate the accuracy of our approach under a variety of conditions and highlight its robustness when compared with alternative methods, such as the Strang-splitting. Most importantly, we show that our approach allows one to treat, within a unified framework, both those regions of the flow which are fluid-pressure dominated (such as in the interior of compact objects) and those which are instead magnetic-pressure dominated (such as in their magnetospheres)

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