This paper studies high-order accurate entropy stable nodal discontinuous Galerkin (DG) schemes for the ideal special relativistic magnetohydrodynamics (RMHD). It is built on the modified RMHD equations with a particular source term, which is analogous to the Powell's eight-wave formulation and can be symmetrized so that an “entropy pair” is obtained. We design an affordable “fully consistent” two-point entropy conservative flux, which is not only consistent with the physical flux, but also maintains the zero parallel magnetic component, and then construct high-order accurate semi-discrete entropy stable DG schemes based on the quadrature rules and the entropy conservative and stable fluxes. The Lax-Friedrichs flux is proven to be entropy stable when its viscosity coefficient is chosen as the speed of light, and the other two entropy stable fluxes are also derived by adding the dissipation terms to our proposed entropy conservative flux and compared to the Lax-Friedrichs flux by using numerical experiments in terms of the CPU time and accuracy. All three entropy stable numerical fluxes maintain the zero parallel magnetic component in one dimension. The resulting entropy stable DG schemes satisfy the semi-discrete “entropy inequality” for the given “entropy pair” and are integrated in time by using the high-order explicit strong stability preserving Runge-Kutta schemes to get further the fully-discrete nodal DG schemes. Extensive numerical tests are conducted to validate the accuracy and the ability to capture discontinuities of our schemes with the help of the TVB limiter. Moreover, our entropy conservative flux is compared to an existing flux through some numerical tests. The results show that the zero parallel magnetic component in the numerical flux can help to decrease the error in the parallel magnetic component in one-dimensional tests, but two entropy conservative fluxes give similar results since the error in the magnetic field divergence seems dominated in the two-dimensional tests.

本文研究理想理想的相对论磁流体动力学（RMHD）的高阶精确熵稳定节点不连续伽勒金（DG）方案。它建立在具有特定源项的修正RMHD方程的基础上，该方程类似于鲍威尔的八波公式，并且可以对称化，从而获得“熵对”。我们设计了一种价格合理的“完全一致”的两点熵保守通量，该通量不仅与物理通量一致，而且还保持零平行磁分量，然后构造基于高精确度的半离散熵稳定DG方案正交规则和熵的保守和稳定通量。选择Lax-Friedrichs通量的黏度系数作为光速时，它是熵稳定的，通过将耗散项添加到我们建议的熵保守通量中，还可以得出其他两个熵稳定通量，并通过CPU时间和精度方面的数值实验与Lax-Friedrichs通量进行比较。所有三个熵稳定的数值通量都在一个维度上保持零平行磁分量。所得的熵稳定DG方案满足给定“熵对”的半离散“熵不等式”，并通过使用高阶显式强稳定性保持Runge-Kutta方案及时积分，以进一步获得全离散节点DG计划。借助TVB限制器，进行了广泛的数值测试，以验证我们方案的准确性和捕获不连续性的能力。此外，通过一些数值测试，将我们的熵保守通量与现有通量进行比较。结果表明，在一维测试中，数值磁通中的零个平行磁分量可以帮助减小平行磁分量的误差，但是两个熵保守磁通给出了相似的结果，因为磁场散度的误差似乎占主导地位。二维测试。