In this article, we propose high-order finite-difference entropy stable schemes for the two-fluid relativistic plasma flow equations. This is achieved by exploiting the structure of the equations, which consists of three independent flux components. The first two components describe the ion and electron flows, which are modeled using the relativistic hydrodynamics equation. The third component is Maxwell's equations, which are linear systems. The coupling of the ion and electron flows, and electromagnetic fields is via source terms only. Furthermore, we also show that the source terms do not affect the entropy evolution. To design semi-discrete entropy stable schemes, we extend the RHD entropy stable schemes in Bhoriya et al. to three dimensions. This is then coupled with entropy stable discretization of the Maxwell's equations. Finally, we use SSP-RK schemes to discretize in time. We also propose ARK-IMEX schemes to treat the stiff source terms; the resulting nonlinear set of algebraic equations is local (at each discretization point). These equations are solved using the Newton's Method, which results in an efficient method. The proposed schemes are then tested using various test problems to demonstrate their stability, accuracy and efficiency.

翻译：本文针对两流体相对论等离子体流动方程，提出了高阶有限差熵稳定格式。该格式通过利用方程的结构实现，该结构包含三个独立的通量分量：前两个分量描述离子流和电子流，采用相对论流体动力学方程建模；第三个分量为麦克斯韦方程组，属于线性系统。离子流、电子流与电磁场仅通过源项耦合。此外，我们进一步证明源项不影响熵演化。为设计半离散熵稳定格式，我们将Bhoriya等人的RHD熵稳定格式推广至三维空间，并与麦克斯韦方程组的熵稳定离散格式耦合。时间离散采用SSP-RK格式，针对刚性源项提出ARK-IMEX格式；所得非线性代数方程组具有局部性（在每个离散点处），通过牛顿法高效求解。通过多个数值算例对所提格式的稳定性、精度和效率进行验证。