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In this work we present IMRPhenomTP, a time domain phenomenological model forthe dominant $l=2$, $m=|2|$ modes of coalescing black hole binary systems andits extension to describe general precessing systems within the "twisting up"approximation. The underlying non-precessing model is calibrated to the newrelease of Numerical Relativity simulations of the SXS Collaboration and itsaccuracy is comparable to the state-of-the-art non-precessing dominant modemodels as IMRPhenomX and SEOBNRv4. The precessing extension allows forflexibility choosing the Euler angles of the time-dependent rotation betweenthe co-precessing and the inertial reference systems, including the single spinNNLO and the double spin MSA PN descriptions present in other models, numericalintegration of the orbit averaged spin evolution equations, different choicesfor the evolution of the orbital angular momentum norm and a simpleapproximation to the ringdown behaviour.

IMRPhenomTP: A phenomenological time domain model for dominant quadrupole gravitational wave signal of coalescing binary black holes