HFQPOs and discoseismic mode excitation in eccentric, relativistic discs. I. Hydrodynamical simulations

High-frequency quasi-periodic oscillations (HFQPOs) observed in the emission of black hole X-ray binary systems promise insight into strongly curved spacetime. `Discoseismic' modes with frequencies set by the intrinsic properties of the central black hole, in particular `trapped inertial waves' (r-modes), offer an attractive explanation for HFQPOs. To produce an observable signature, however, such oscillations must be excited to sufficiently large amplitudes. Turbulence driven by the magnetorotational instability (MRI) does not appear to provide the necessary amplification, but r-modes may still be excited via interaction with accretion disc warps or eccentricities. We present global, hydrodynamic simulations of relativistic accretion discs, which demonstrate for the first time the excitation of trapped inertial waves by an imposed eccentricity in the flow. While the r-modes' saturated state depends on the vertical boundary conditions used in our unstratified, cylindrical framework, their excitation is unambiguous in all runs with eccentricity >0.005 near the ISCO. These simulations provide a proof of concept, demonstrating the robustness of the trapped inertial wave excitation mechanism in a non-magnetized context. We explore the competition between this excitation, and damping by MHD turbulence and radial inflow in a companion paper.