A Localized Current-Sheet Magnetic-Diffusion and Heating Prescription for Ideal-GRMHD Simulations of M87*-like Accretion Flows

Ideal-GRMHD calculations provide the bulk accretion flows used in black-hole emission models. A localized dissipation prescription can add a resolved map of current-sheet activity while retaining that dynamical reference. We implement such a prescription in Athena++, using a smooth threshold on the dimensionless current proxy α J to select the magnetic-diffusion coefficient. The constrained-transport update is coupled to a conservative energy-flux correction. Gas heating follows from primitive recovery; q Ohm=ηJ squared is recorded as a diagnostic, without a second energy source. Static Fourier and traveling Alfvén tests measure the evolved thermal gain, and an open-boundary Schwarzschild test closes the Killing-energy ledger. The relative total-energy residual is below 2 times10-15 in these tests. A two-resolution Harris matrix gives localized rate exponents 0.510 plus or minus0.027 and 0.488 plus or minus0.028, consistent with 1/2 over the specified early interval. The η=10-3 rate exceeds the same-resolution ideal control by a factor of 5.96. In matched axisymmetric M87*-like runs, localized diffusion changes the early mean magnetic flux, accretion rate, and normalized flux by less than 0.02%, with a radial-density distance of 0.005%. During the late active phase, a common-restart on/off comparison keeps these mean shifts below 1.6%, within the intrinsic temporal variability, and gives a density distance of 0.29%. Uniform diffusion at the tested coefficient reduces the raw flux and accretion rate by 85% and 99.8%. These comparisons establish a spatially selective diffusion prescription with explicit energy accounting and a quantified, small bulk-flow response.