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The ideal gas equation of state (EOS) with a constant adiabatic index is apoor approximation for most relativistic astrophysical flows, although it iscommonly used in relativistic hydrodynamics. The paper develops high-orderaccurate physical-constraints-preserving (PCP) central discontinuous Galerkin(DG) methods for the one- and two-dimensional special relativistic hydrodynamic(RHD) equations with a general EOS. It is built on the theoretical analysis ofthe admissible states for the RHD and the PCP limiting procedure enforcing theadmissibility of central DG solutions. The convexity, scaling and orthogonalinvariance, and Lax-Friedrichs splitting property of the admissible state setare first proved with the aid of its equivalent form, and then the high-ordercentral DG methods with the PCP limiting procedure and strong stabilitypreserving time discretization are proved to preserve the positivity of thedensity, pressure, and specific internal energy, and the bound of the fluidvelocity, maintain the high-order accuracy, and be $L^1$-stable. The accuracy,robustness, and effectiveness of the proposed methods are demonstrated byseveral 1D and 2D numerical examples involving large Lorentz factor, strongdiscontinuities, or low density or pressure etc.

Physical-constraints-preserving central discontinuous Galerkin methods for special relativistic hydrodynamics with a general equation of state