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 nonlocal, different from viscous flow models that utilize numerical methods like, e.g., the so-called “peridynamic differential operator” to approximate solutions of 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 by enforcing linear consistency for the viscous stress term with the classical Navier-Stokes equations. Couette and Poiseuille flows, and incompressible fluid flow past a regular lattice of cylinders are used to verify the new formulation, 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.

我们从基本原理出发推导出牛顿粘性流的近场动力学 (PD) 模型的欧拉公式：质量和动量守恒。这个公式是非局部的，不同于粘性流模型，粘性流模型利用数值方法，例如，所谓的“近场动力学微分算子”来逼近经典 Navier-Stokes 方程的解。我们表明，假设某些平滑条件，经典连续性方程是 PD 的极限情况。粘性流动的 PD 模型通过使用经典 Navier-Stokes 方程强制粘性应力项的线性一致性来校准。Couette 和 Poiseuille 流动，以及流过规则圆柱体格的不可压缩流体用于验证低雷诺数下的新公式。