  The merger of supermassive black holes (SMBHs) produces mHz gravitational
waves (GW), which are potentially detectable by future Laser Interferometer
Space Antenna (LISA). Such binary systems are usually embedded in an accretion
disk environment at the centre of the active galactic nucleus (AGN). Recent
studies suggest the plasma environment imposes measurable imprints on the GW
signal if the mass ratio of the binary is around q $ \sim10^{-4}-10^{-3}$. The
effect of the gaseous environment on the GW signal is strongly dependent on the
disk's parameters, therefore it is believed that future low-frequency GW
detections will provide us with precious information about the physics of AGN
accretion disks. We investigate this effect by measuring the viscous torque via
modelling the evolution of magnetized tori around the primary massive black
hole. Using GRMHD HARM-COOL code, we perform 2D and 3D simulations of
weakly-magnetized thin accretion disks, with a possible truncation and
transition to advection-dominated accretion flow (ADAF). We study the angular
momentum transport and turbulence generated by magnetorotational instability
(MRI). We quantify the disk's effective alpha viscosity and its evolution over
time. We apply our numerical results to quantify the relativistic viscous
torque on a hypothetical low-mass secondary black hole via a 1D analytical
approach, and we estimate the GW phase shift due to the gas environment.
