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

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.

ISPH with a Geometric Multigrid Preconditioning Solver using Background Cells in GPU environment

“…As shown in section 2.3, matrix equation from the PPE needs to be solved in the ISPH method. This procedure is time-consuming and requires a large amount of memory, so we developed a background cell-based geometric multigrid preconditioner following previous studies [7][8][9].…”

“…There are many examples of application of multigrid methods to numerical methods that use grids or meshes, such as the finite difference method (FDM) [4] and the finite element method (FEM) [6]. However, there are few examples of application of the multigrid method to particle methods [7][8][9], and none to the SPH method used in this study. In this study, we develop a multigrid preconditioning solver for the linear equations of the ISPH method.…”

“…In this study, we develop a multigrid preconditioning solver for the linear equations of the ISPH method. Specifically, following previous studies [8,9], we develop a geometric multigrid preconditioning solver that constructs an auxiliary grid based on the background cell used to search for neighboring particles. Then, we compare the number of iterations between the no-preconditioning CG method and the multigrid preconditioning CG method using a dam-breaking problem for incompressible fluids and confirm the effectiveness of the multigrid preconditioning method.…”

The Mathematics of Smoothed Particle Hydrodynamics (SPH) Consistency

“…For example, consistent Shepard interpolation scheme can be combined with the implicit viscosity solver introduced by Weiler et al [25] to model complex physical effects in highly viscous fluids, such as rope coiling and melting. Very recent progress in improving the physical consistency of highly viscous, free surface flow calculations has been reported by Kondo et al [26]. Unlike incompressible fluids, with the exception perhaps of turbulent flows, compressible fluid flows are likely to develop small-scale structures.…”

“…Such improvements are not only useful for animation purposes, but also for other science and engineering applications. Improved simulations of highly-viscous free-surface flows were recently reported by Kondo et al [26]. A completely different scheme based on a piecewise high-order Moving-Least-Squares WENO reconstruction and the use of Riemann solvers was presented by Avesani et al [27].…”