Date of this Version
Journal of Computational Physics 468 (2022) 111509
We derive the Eulerian formulation for a peridynamic (PD) model of Newtonian viscous flow starting from fundamental principles: conservation of mass and momentum. This formulation is different from models for viscous flow that utilize the so-called “peridynamic differential operator” with the classical Navier- Stokes equations. We show that the classical continuity equation is a limiting case of the PD one, assuming certain smoothness conditions. The PD model for viscous flow is calibrated to the classical Navier-Stokes equations by enforcing linear consistency for the viscous stress term. Couette and Poiseuille flows, and incompressible fluid flow past a regular lattice of cylinders are used to verify the new formulation, at least at low Reynolds numbers. The constructive approach in deriving the model allows for a seamless coupling with peridynamic models for corrosion or fracture for simulating complex fluid-structure interaction problems in which solid degradation takes place, such as in erosion-corrosion, hydraulic fracture, etc. Moreover, the new formulation sheds light on the relationships between local and nonlocal models.