Mud invasion during drilling constitutes a multiphysics problem involving miscible flow, mud cake dynamics, and anisotropic porous media. It can significantly affect near-wellbore conditions, supercharging behavior, and subsequent formation sampling performance. Existing models assume axisymmetric invasion profiles and are therefore limited to vertical wells [1]. This work presents a high‑fidelity computational fluid dynamics (CFD) framework to study mud invasion in deviated wells, with an emphasis on numerical formulation, coupling strategies, and verification. The governing equations describe transient, single‑phase miscible flow in a compressible porous medium. Flow is modeled using Darcy’s law with anisotropic permeability tensors, while mud invasion is tracked using a transport scalar formulation without diffusive flux. Mud cake evolution is represented through a filtration model [1] that introduces a time‑dependent flux boundary condition at the wellbore surface. Due to practical limitations in strongly coupling mud cake kinetics with three‑dimensional CFD solvers, a loose‑coupling strategy is adopted, prescribing mud filtrate flux obtained from a reduced one‑dimensional reference model. The numerical approach is first verified for a vertical well by benchmarking sandface pressure evolution and invasion depth against the reference solution, demonstrating close agreement. The validated model is then applied to deviated wells with inclinations up to 60°, considering both isotropic and anisotropic formations. The simulations show that well deviation increases near‑wellbore pressure and, when combined with permeability anisotropy, breaks axial symmetry of the invasion front. Non‑cylindrical, oval‑shaped invasion profiles emerge in the well cross‑section. A sensitivity study indicates that mud filtrate flux is weakly dependent on sandface pressure variations, suggesting that boundary fluxes can be accurately approximated without full three‑dimensional coupling. The proposed framework provides a robust numerical benchmark for evaluating reduced‑order mud invasion models and illustrates key computational mechanics challenges associated with anisotropic porous media, complex boundary conditions, and deviated well geometries.