Session: 12-08-01: Peridynamic Modeling of Materials’ Behavior

Paper Number: 100184

100184 - the Fast Convolution-Based Method for the Peridynamic Form of Navier Stokes Equations 

Modeling of complex fluids requires, often, the use of homogenization techniques to reduce the complexity of the system and be able to compute numerical solutions in reasonable times. Homogenization can naturally lead to a nonlocal model [1]. To use such techniques to analyze the flow of complex fluids, in [2] was presented a nonlocal version of the Navier-Stokes equations. The meshfree method, based on the one-point Gaussian integration method (modified to account for volumes of nodes only partially covered by the nonlocal horizon of an arbitrary node) was used in [2]. This method, which we will refer to as the “direct quadrature method” (DQM), scales as O(NM), where N is the total number of nodes in the discretization grid and M is the total number of nodes inside the nonlocal region of each node. Especially in 3D, this approach is expensive because M can easily be in the hundreds or thousands.

To overcome this problem, we have recently introduced a “fast convolution-based method” (FCBM) for peridynamic (PD) models of diffusion and fracture [3], [4]. In this talk, we present an extension of the FCBM to the PD reformulation of the Navier-Stokes equations. We use the new numerical model to simulate fluid flow and show how the convolution-based model compares, in terms of computing time and memory requirements, with the DQM on the same problem. Comparisons with classical local models and experimental data are also shown. We find that the new computational method for the PD form of the Navier-Stokes equations is an effective method to accurately predict the physical behavior of fluids.

Acknowledgments: This work has been supported in part by the US National Science Foundation Grant No. 1953346. This work was completed utilizing the Holland Computing Center of the University of Nebraska, which receives support from the Nebraska Research Initiative.

References:

[1] S. A. Silling. Origin and effect of nonlocality in a composite. Journal of Mechanics of Materials and Structures, 9(2):245–258, 2014.

[2] J.  Zhao, A. Larios, and F. Bobaru. Construction of a peridynamic model for viscous flow. Journal of Computational Physics (in review), 2022.

[3] S. Jafarzadeh, L. Wang, A. Larios, and F. Bobaru. A fast convolution-based method for peridynamic transient diffusion in arbitrary domains. Computer Methods in Applied Mechanics and Engineering, 375, 113633, 2021.

[4] S. Jafarzadeh, F. Mousavi, A. Larios, and F. Bobaru. A general and fast convolution-based method for peridynamics: Applications to elasticity and brittle fracture. Computer Methods in Applied Mechanics and Engineering, 392, 114666, 2022.

Presenting Author: Chad Alexander University of Nebraska-Lincoln

Presenting Author Biography: I am a senior mechanical engineering student at the University of Nebraska-Lincoln. I joined Dr. Florin Bobaru's research group in the summer of 2022 to help conduct research in computational mechanics. I am interested primarily in fluid mechanics and decided to tailor my research to non-local (peridynamic) approaches to solve problems in computational fluid dynamics.

Authors:

Chad Alexander University of Nebraska-Lincoln
Florin Bobaru University of Nebraska-Lincoln