Comparative evaluation of matrix-free implicit viscosity solvers for GPU-accelerated SPH simulation of highly viscous fluids

The demand for accurate and efficient simulation of highly viscous fluids is growing across engineering domains such as energy systems, advanced manufacturing, and multi-phase transport. Applications including crude oil pipeline flow, extrusion-based additive manufacturing, and non-Newtonian material modeling frequently involve fluids with extreme viscosity or shear-dependent behavior. In such cases, implicit viscosity solvers are often favored over traditional explicit SPH solvers, which are hindered by stringent time step constraints that lead to high computational costs in large-scale simulations. In this study, we enhance existing matrix-free implicit viscosity solvers and evaluate their effectiveness within a GPU-accelerated smoothed particle hydrodynamics (SPH) framework. To improve computational efficiency under complex boundary conditions, we reformulate the coefficient matrix to satisfy symmetry, enabling more efficient implicit computation. A wide range of benchmark cases is considered, including steady and transient flows, single- and multi-phase Newtonian fluids, and diverse non-Newtonian rheologies. We also compare solver performances such as convergence behavior, accuracy, and computing time under multiple boundary condition implementations. The results demonstrate clear trends in solver robustness and efficiency across flow regimes, offering practical insights into the deployment of matrix-free implicit solvers in high-fidelity SPH simulations of highly viscous fluids.