Peridynamic differential operator-based Eulerian particle method for 2D internal flows

Abstract

This paper proposes a non-local Eulerian particle method for two-dimensional internal flows. To balance computational accuracy and efficiency, the governing Navier–Stokes equations for this specific problem are recast in their integral form using a second-order peridynamic differential operator (PDDO). The particle method is then derived by applying a symmetric and uniform particle distribution to the solution of such an integral equation, yielding a readily accessible discretized algorithm. To stabilize and accelerate the proposed method, a pressure correction and a strategy of particle refinement are introduced with only a marginal loss of accuracy. The main procedure of the proposed method is detailed, as well as some other computational issues, such as time step and boundary conditions. Finally, several benchmark numerical examples, including Couette flow, shear-driven cavity, and internal flow around a cylinder, are carried out using the proposed method, demonstrating the level of its efficiency, accuracy, and capabilities.