Abstract
For viscosity-dominated flows, the viscous effect plays a much more important role. Since the viscosity term in SPH-governing (Smoothed Particle Hydrodynamics) equations involves the discretization of a second-order derivative, its treatment could be much more challenging than that of a first-order derivative, such as the pressure gradient. The present paper summarizes a series of improved methods for modeling the second-order viscosity force term. By using a benchmark patch test, the numerical accuracy and efficiency of different approaches are evaluated under both uniform and non-uniform particle configurations. Then these viscosity force models are used to compute a documented lid-driven cavity flow and its interaction with a cylinder, from which the most recommended viscosity term formulation has been identified.
Highlights
Free surface flow simulations have always generated substantial theoretical and practical interests
In order to demonstrate the effect of four methods of viscosity term calculation, this section presents two numerical tests on the viscous flow modeling, which are based on the benchmarks of the lid-driven flow and its interaction with an inside cylinder
This work introduced a series of approaches to discretize the viscosity term and its main contributions lie in the following two aspects: firstly, by comparing with the formulations used to discretize the Laplacian of pressure Poisson equation (PPE), four benchmark calculation methods on the viscosity term were proposed; secondly, a comprehensive analysis on the different viscosity force models was carried out through vigorous benchmark tests, and the most accurate model was identified
Summary
Free surface flow simulations have always generated substantial theoretical and practical interests. Bontozoglou [1] used the spectral spatial discretization method for the laminar film flow along a periodic wall. Scholle et al [2] used the Finite Element Method (FEM) and complex variable method for modeling the film over corrugated surfaces. Marner et al [3] developed a potential-velocity formulation of the Navier-Stokes (N-S) equations by using the least square FEM approach. Marner et al [4] proposed a generalized complex-valued first integral of the N-S equations for the unsteady Couette flows in a corrugated channel system. The Smoothed Particle Hydrodynamics (SPH) method is equipped with the unique advantage of tracking the free surfaces with much larger deformation even leading to violent breaking
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