A physically consistent particle method for high-viscous free-surface flow calculation

Masahiro Kondo,Junichi Matsumoto,Issei Masaie,Takahiro Fujiwara

doi:10.1007/s40571-021-00408-y

Abstract

Particle methods for high-viscous free-surface flows are of great use to capture flow behaviors which are intermediate between solid and liquid. In general, it is important for numerical methods to satisfy the fundamental laws of physics such as the conservation laws of mass and momentum and the thermodynamic laws. Especially, the angular momentum conservation is necessary to calculate rotational motion of high-viscous objects. However, most of the particle methods do not satisfy the physical laws in their spatially discretized system. The angular momentum conservation law is broken mostly because of the viscosity models, which may result in physically strange behavior when high-viscous free-surface flow is calculated. In this study, a physically consistent particle method for high-viscous free-surface flows is developed. The present method was verified, and its performance was shown with calculating flow in a rotating circular pipe, high-viscous Taylor–Couette flow, and offset collision of a high-viscous object.

Highlights

Particle methods are the numerical methods which have an advantage in handling large deformations of free surface flow
The typical ones are the weakly compressible Smoothed Particle Hydrodynamics (SPH) method developed by Monaghan [1] and the strictly incompressible Moving Particle Semi-implicit (MPS) method developed by Koshizuka and Oka [2]
0.10 (m) 2.0 × 1 03 (Pa s) 1.0 × 106 (Pa) 2.0 × 10−3 (s) had positive distribution and σθr had negative distribution (Fig. 3a). These non-zero different distributions indicate that unphysical stress against the angular momentum conservation law may emerge when the difference-based viscosity model is adopted

Summary

Introduction

Particle methods are the numerical methods which have an advantage in handling large deformations of free surface flow. For high-viscous fluid calculation using particle methods, numerical stability against high viscosity and physical consistency such as conservation of angular momentum are important The former is effectively achieved by implicit velocity calculation with respect to viscosity term. From the viewpoint of numerical stability against high viscosity and the physical consistency such as angular momentum conservation, the high viscosity fluid calculation of Weiler et al [16] is currently advantageous Their model is not clearly related to an analytical mechanical framework. The second term on the right-hand side in Eq (10) is a discretized version of the shear viscosity term This type of difference-based Laplacian model [2, 9, 18, 41,42,43] does not conserve angular momentum and unphysically hinders rotational motion. This is because the large pressure load is not expected in this study and the explicit calculation is numerically efficient in such cases

Flow in a rotating circular pipe

Time integration

High‐viscous Taylor–Couette flow i

Offset collision of a high‐viscous object

Conclusion