General equations for conservative yet dissipative (entropy producing) extended magnetohydrodynamics are derived from two-fluid theory. Keeping all terms generates unusual cross-effects, such as thermophoresis and a current viscosity that mixes with the usual velocity viscosity. While the Poisson bracket of the ideal version of this model have already been discovered, we determine its metriplectic counterpart that describes the dissipation. This is done using a new and general thermodynamic point of view for deriving dissipative brackets, a means of derivation that is natural for understanding and creating dissipative brackets. Finally the formalism is used to study dissipation in the Lagrangian variable picture where, in the context of extended magnetohydrodynamics, nonlocal dissipative brackets naturally emerge.
Resistive dissipative magnetohydrodynamics from the Boltzmann-Vlasov equation
从Boltzmann-Vlasov方程出发，利用矩量法导出了相对论性、电阻性、二阶耗散磁流体力学的运动方程。因此，我们将之前的工作[Phys. Rev. D 98，076009（2018）]扩展到有限电导率的情况，其中我们只考虑了非电阻极限。这需要在运动方程中保持与电场$E^μ$成比例的项，并且由于电场与耗散量的耦合而导致新的输运系数。我们还表明，电荷扩散电流的纳维尔-斯托克斯极限对应于欧姆定律，而电导率系数和电荷扩散系数则与一种类型的维德曼-弗朗茨定律相关。
Here we derive the relativistic resistive dissipative second-order magnetohydrodynamic evolution equations using the Boltzmann equation, thus extending our work from the previous paper \href{https://link.springer.com/article/10.1007/JHEP03(2021)216}{JHEP 03 (2021) 216} where we considered the non-resistive limit. We solve the Boltzmann equation for a system of particles and antiparticles using the relaxation time approximation and the Chapman-Enskog like gradient expansion for the off-equilibrium distribution function, truncating beyond second-order. In the first order, the bulk and shear stre…
We study charge diffusion in relativistic resistive second-order dissipative magnetohydrodynamics. In this theory, charge diffusion is not simply given by the standard Navier-Stokes form of Ohm's law, but by an evolution equation which ensures causality and stability. This, in turn, leads to transient effects in the charge diffusion current, the nature of which depends on the particular values of the electrical conductivity and the charge-diffusion relaxation time. The ensuing equations of motion are of so-called stiff character, which requires special care when solving them numerically. To th…
We derive the relativistic non-resistive, viscous second-order magnetohydrodynamic equations for the dissipative quantities using the relaxation time approximation. The Boltzmann equation is solved for a system of particles and antiparticles using Chapman-Enskog like gradient expansion of the single-particle distribution function truncated at second order. In the first order, the transport coefficients are independent of the magnetic field. In the second-order, new transport coefficients that couple magnetic field and the dissipative quantities appear which are different from those obtained in…
Here we study the wave propagation and stability of general relativistic non-resistive dissipative second-order magnetohydrodynamic equations in curved space-time. We solve the Boltzmann equation for a system of particles and antiparticles using the relaxation time approximation and the Chapman-Enskog-like gradient expansion for the off-equilibrium distribution function, truncating beyond second-order in curved space-time in electromagnetic fields. Unlike holographic calculation~\cite{Baier:2007ix}, we show that the viscous evolution equations do not explicitly depend on the curvature of space…
Characterization of Numerical Dissipation in Simulations of Magnetohydrodynamic Turbulence
Center for Applied Physics and Technology, HEDPS and SKLNPT, School of Physics, Peking University（北京大学物理学院，应用物理与技术中心，HEDPS和SKLNPT）；Frontiers Science Center for Nano-optoelectronics, Peking University（北京大学纳米光电前沿科学中心）
Conservative regularization of compressible flow and ideal magnetohydrodynamics
理想系统如MHD和欧拉流可能发展出涡量奇点（w =旋度v）。粘度和电阻率是耗散正则化。我们提出了一个最小的，局部的，保守的，非线性的，分散的可压缩流和理想的MHD正则化，在类比的KdV正则化的一维霍普夫方程。这项工作显着扩展了不可压缩欧拉和理想MHD的早期工作。它涉及到一个与密度ρ的平方根成反比的截止λ，这类似于一个位置相关的平均自由程。正则化的“twirl”项是- lambda w x curl w。这一项在有涡量的高速流动中可能是重要的，并在克努森数动力学方程的展开中出现。在理想磁流体力学中，旋度项的磁类比-（B ×旋度B）/（ρ μ_0），作为洛伦兹力出现。我们的正则化保留了理想系统的对称性，并与适当的边界条件，意味着相关的守恒律。能量和拟能服从于由初始数据确定的先验界限。一个哈密顿和泊松括号制定和用于推广的本构关系，有界高阶矩的w和旋度w。一个'漩涡'的速度场被证明运输w/rho和B/rho，推广开尔文-亥姆霍兹和阿尔文定理。定常正则化方程用于模拟旋转涡，MHD箍缩，平面涡面，通道流，平面流和传播的球形和圆柱形涡;解决方案比相应的欧拉更规则。所提出的正则化可以方便地模拟流体/MHD方程，并提供了一致的统计力学的涡/电流丝在3D中，而不会爆破拟能。流体和等离子体系统的详细分析的影响进行了讨论。
