A New Scheme To Solve The Two-Fluid Cosmic-Ray Magnetohydrodynamic Equations

10th International Conference on Numerical Modeling of Space Plasma Flows: ASTRONUM-2015

Kudoh, Yuki^1 ; Hanawa, Tomoyuki^2

Graduate School of Science, Chiba University, Yayoi-cho 1-33, Inage-ku, Chiba

263-8522, Japan^1

Center for Frontier Science, Chiba University, Yayoi-cho 1-33, Inage-ku, Chiba

263-8522, Japan^2

关键词: Adiabatic indices;    Dynamical effects;    Magnetohydrodynamic equations;    Numerical solution;    Rankine-Hugoniot relations;    Riemann solutions;    Shock-tube problem;    Spurious oscillations;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/719/1/012021/pdf
DOI  :  10.1088/1742-6596/719/1/012021

来源: IOP

【 摘 要 】

We examine the two-fluid cosmic-ray magnetohydrodynamic (CR MHD) equations to take account of the dynamical effects of cosmic rays (CRs) in the simplest form. For simplicity we assume that the pressure of the CRs is proportional to the energy density, Pcr= (γcr- 1)Ecr, where γcrdenotes the adiabatic index of CRs. We find the fully conservative form of the CR MHD equations and derive the Rankine-Hugoniot relation for a shock. One component of the CR MHD equations describes conservation of total number of CRs where the number density is defined as ρcr= Pcr1/γcr. We also find the Riemann solution, which provides us approximate Riemann fluxes fluxes for numerical solutions. We have also identified origin of spurious oscillation originating from the pressure balance mode across which the CR pressure has a jump while the total pressure is continuous. We propose the two step method to solve the CR MHD equations. We use 1D shock tube problems to compare our method with others.