An Integrated High-Resolution 3D CFD Framework for Viscous Fingering in Porous Media: Relative Permeability, Extend Directional Velocity Weighting and GPU-Accelerated Solution

Viscous fingering develops when a higher mobility fluid displaces a lower mobility fluid in porous media, creating preferential pathways that accelerate breakthrough and reduce sweep efficiency. This instability affects enhanced oil recovery, groundwater remediation, underground gas storage, and geological carbon storage. Predicting its three-dimensional evolution remains difficult because phase mobility, nonlinear pathway interactions, numerical directional bias, and computational cost must be addressed together. Reservoir simulators represent relative permeability, fractional flow, and residual saturation, but often smear individual fingerings. High-resolution miscible and pore-scale methods resolve detailed morphology, yet are not naturally formulated for reservoir-style saturation-dependent mobility or large continuum domains. Multidirectional transport treatments and GPU sparse solvers address numerical limitations, but these capabilities have generally been developed separately. We therefore develop a pressure-based high-resolution 3D CFD framework integrating Corey-type relative permeability, fractional-flow phase partitioning, clipped effective saturation, D3Q27-inspired directional link-velocity weighting, and GPU-based implement solution. The calculations concern homogeneous, viscosity-dominated liquid displacement; capillary pressure, gravity, and Forchheimer inertia are excluded. The framework was assessed against one-dimensional Buckley–Leverett solutions and benchmarked against Habermann’s miscible quarter five-spot experiments for macroscopic mobility-ratio trends. It reproduced saturation-profile classes, the compact-to-dendritic transition, and declining sweep efficiency with increasing mobility ratio. Three-dimensional calculations revealed tubular pathways, bypass, coalescence, and pressure-field shielding. Mesh, realization, and connectivity comparisons showed that directional treatment affects the resolved morphology, while GPU pressure-solver tests demonstrated acceleration. The framework provides a unified computational route from reservoir-relevant mobility closure to quantitative three-dimensional morphology, connectivity-sensitivity assessment, pressure-field interpretation, and accelerated sparse solution for viscosity-dominated porous-media displacement.