Enhanced cut-cell material point method for viscous incompressible flow past a cylinder : development and validation

Abstract

The material point method (MPM) is widely used for free-surface flows, but its performance for viscous incompressible flow past a cylinder has not been systematically assessed. This problem poses several challenges for MPM, including robust boundary treatment, precise discretization of the viscous term, and reliable evaluation of hydrodynamic forces. This work develops an enhanced cut-cell MPM tailored for viscous incompressible flow past a cylinder. A fractional-step explicit-implicit algorithm is employed, with an explicit stage for the intermediate velocity and an implicit stage for incompressible pressure and final velocity. Irregular boundaries on orthogonal grids are represented using a cut-cell method, while the viscous term is discretized via particle viscous stresses rather than grid stresses, improving accuracy near walls and curved boundaries. A simple grid-based wall-boundary scheme is adopted to prescribe velocities on the background grid. In addition, a mixed particle-grid algorithm is developed for inlet and outlet boundaries, and a boundary-particle method is proposed to accurately compute hydrodynamic forces on immersed bodies. The model is first validated against dam-break flow over an irregular bed and lid-driven semi-circular cavity flow, confirming its accuracy for complex geometries. It is then applied to viscous flow past a circular cylinder for Reynolds numbers from 10 to 1000, showing close agreement with experimental data and established numerical solutions. Finally, a comparative analysis with Smoothed Particle Hydrodynamics (SPH) and the Finite Volume Method (FVM) demonstrates that the proposed cut-cell MPM effectively combines the strengths of particle-based and mesh-based methods for viscous incompressible flows.