  This paper presents a highly robust third-order accurate finite volume
weighted essentially non-oscillatory (WENO) method for special relativistic
hydrodynamics on unstructured triangular meshes. We rigorously prove that the
proposed method is physical-constraint-preserving (PCP), namely, always
preserves the positivity of the pressure and the rest-mass density as well as
the subluminal constraint on the fluid velocity. The method is built on a
highly efficient compact WENO reconstruction on unstructured meshes, a simple
PCP limiter, the provably PCP property of the Harten--Lax--van Leer flux, and
third-order strong-stability-preserving time discretization. Due to the
relativistic effects, the primitive variables (namely, the rest-mass density,
velocity, and pressure) are highly nonlinear implicit functions in terms of the
conservative variables, making the design and analysis of our method
nontrivial. To address the difficulties arising from the strong nonlinearity,
we adopt a novel quasilinear technique for the theoretical proof of the PCP
property. Three provable convergence-guaranteed iterative algorithms are also
introduced for the robust recovery of primitive quantities from admissible
conservative variables. We also propose a slight modification to an existing
WENO reconstruction to ensure the scaling invariance of the nonlinear weights
and thus to accommodate the homogeneity of the evolution operator, leading to
the advantages of the modified WENO reconstruction in resolving multi-scale
wave structures. Extensive numerical examples are presented to demonstrate the
robustness, expected accuracy, and high resolution of the proposed method.
