Spectral Ewald Acceleration of Stokesian Dynamics for polydisperse suspensions

In this work we develop the Spectral Ewald Accelerated Stokesian Dynamics (SEASD), a novel computational method for dynamic simulations of polydisperse colloidal suspensions with full hydrodynamic interactions. SEASD is based on the framework of Stokesian Dynamics (SD) with extension to compressible solvents, and uses the Spectral Ewald (SE) method [Lindbo & Tornberg, J. Comput. Phys. 229 (2010) 8994] for the wave-space mobility computation. To meet the performance requirement of dynamic simulations, we use Graphic Processing Units (GPU) to evaluate the suspension mobility, and achieve an order of magnitude speedup compared to a CPU implementation. For further speedup, we develop a novel far-field block-diagonal preconditioner to reduce the far-field evaluations in the iterative solver, and SEASD-nf, a polydisperse extension of the mean-field Brownian approximation of Banchio & Brady [J. Chem. Phys. 118 (2003) 10323]. We extensively discuss implementation and parameter selection strategies in SEASD, and demonstrate the spectral accuracy in the mobility evaluation and the overall $\mathcal{O}(N\log N)$ computation scaling. We present three computational examples to further validate SEASD and SEASD-nf in monodisperse and bidisperse suspensions: the short-time transport properties, the equilibrium osmotic pressure and viscoelastic moduli, and the steady shear Brownian rheology. Our validation results show that the agreement between SEASD and SEASD-nf is satisfactory over a wide range of parameters, and also provide significant insight into the dynamics of polydisperse colloidal suspensions.Comment: 39 pages, 21 figure

Hybrid smoothed particle hydrodynamics

We present a new algorithm for enforcing incompressibility for Smoothed Particle Hydrodynamics (SPH) by preserving uniform density across the domain. We propose a hybrid method that uses a Poisson solve on a coarse grid to enforce a divergence free velocity field, followed by a local density correction of the particles. This avoids typical grid artifacts and maintains the Lagrangian nature of SPH by directly transferring pressures onto particles. Our method can be easily integrated with existing SPH techniques such as the incompressible PCISPH method as well as weakly compressible SPH by adding an additional force term. We show that this hybrid method accelerates convergence towards uniform density and permits a significantly larger time step compared to earlier approaches while producing similar results. We demonstrate our approach in a variety of scenarios with significant pressure gradients such as splashing liquids

A comparison between weakly-compressible smoothed particle hydrodynamics (WCSPH) and moving particle semi-implicit (MPS) methods for 3d dam-break flows

Lagrangian particle-based methods have opened new perspectives for the investigation of complex problems with large free-surface deformation. Some well-known particle-based methods adopted to solve non-linear hydrodynamics problems are the smoothed particle hydrodynamics (SPH) and the moving particle semi-implicit (MPS). Both methods modeled the continuum by a system of Lagrangian particles (points) but adopting distinct approaches for the numerical operators, pressure calculation, and boundary conditions. Despite the ability of the particle-based methods in modeling highly nonlinear hydrodynamics, some shortcomings, such as unstable pressure computation and high computational cost remains. In order to assess the performance of these two methods, the weaklycompressible SPH (WCSPH) parallel solver, DualSPHysics, and an in-house incompressible MPS solver are adopted in this work. Two test cases consisting of threedimensional (3D) dam-break problems are simulated, and wave heights, pressures and forces are compared with available experimental data. The influence of the artificial viscosity on the accuracy of WCSPH is investigated. Computational times of both solvers are also compared. Finally, the relative benefits of the methods for solving free-surface problems are discussed, therefore providing directions of their applicability.Comment: 26 pages, 12 figure

Local uniform stencil (LUST) boundary condition for arbitrary 3-D boundaries in parallel smoothed particle hydrodynamics (SPH) models

This paper presents the development of a new boundary treatment for free-surface hydrodynamics using the smoothed particle hydrodynamics (SPH) method accelerated with a graphics processing unit (GPU). The new solid boundary formulation uses a local uniform stencil (LUST) of fictitious particles that surround and move with each fluid particle and are only activated when they are located inside a boundary. This addresses the issues currently affecting boundary conditions in SPH, namely the accuracy, robustness and applicability while being amenable to easy parallelization such as on a GPU. In 3-D, the methodology uses triangles to represent the geometry with a ray tracing procedure to identify when the LUST particles are activated. A new correction is proposed to the popular density diffusion term treatment to correct for pressure errors at the boundary. The methodology is applicable to complex arbitrary geometries without the need of special treatments for corners and curvature is presented. The paper presents the results from 2-D and 3-D Poiseuille flows showing convergence rates typical for weakly compressible SPH. Still water in a complex 3-D geometry with a pyramid demonstrates the robustness of the technique with excellent agreement for the pressure distributions. The method is finally applied to the SPHERIC benchmark of a dry-bed dam-break impacting an obstacle showing satisfactory agreement and convergence for a violent flow.EPSRC, Reino Unido | Ref. EP/L014890/1Ministry of Education, Universities and Research, Italia | Ref. RBSI14R1GPXunta de Galicia | Ref. ED431C 2017/64Ministerio de Economía y Competividad | Ref. ENE2016-75074-C2-1-

Local uniform stencil (LUST) boundary condition for arbitrary 3-D boundaries in parallel smoothed particle hydrodynamics (SPH) models

Abstract This paper presents the development of a new boundary treatment for free-surface hydrodynamics using the smoothed particle hydrodynamics (SPH) method accelerated with a graphics processing unit (GPU). The new solid boundary formulation uses a local uniform stencil (LUST) of fictitious particles that surround and move with each fluid particle and are only activated when they are located inside a boundary. This addresses the issues currently affecting boundary conditions in SPH, namely the accuracy, robustness and applicability while being amenable to easy parallelization such as on a GPU. In 3-D, the methodology uses triangles to represent the geometry with a ray tracing procedure to identify when the LUST particles are activated. A new correction is proposed to the popular density diffusion term treatment to correct for pressure errors at the boundary. The methodology is applicable to complex arbitrary geometries without the need of special treatments for corners and curvature is presented. The paper presents the results from 2-D and 3-D Poiseuille flows showing convergence rates typical for weakly compressible SPH. Still water in a complex 3-D geometry with a pyramid demonstrates the robustness of the technique with excellent agreement for the pressure distributions. The method is finally applied to the SPHERIC benchmark of a dry-bed dam-break impacting an obstacle showing satisfactory agreement and convergence for a violent flow

Numerical study of fluid-structure interaction with macro-scale particle methods

The problems of fluid-structure interaction (FSI) are often encountered in different industries as well as the nature. The macro-scale particle methods are advantageous in the FSI simulations, which include smoothed particle hydrodynamics (SPH), macro-scale pseudo- particle modelling (MaPPM), and so forth. Compared with the grid-based numerical techniques, particle methods could provide the flow and/or deformation details without complex tracking of interfaces. The progress of FSI simulation of multiphase flows with rigid particles is presented, and some major findings about heterogeneous structures are stressed. Meanwhile, weakly compressible outflow from elastic tube is investigated, and some preliminary results of flow details are presented. The possible development of macro-scale particle methods in the FSI simulation is prospected finally

A general pressure equation based method for incompressible two-phase flows

We present a fully-explicit, iteration-free, weakly-compressible method to simulate immiscible incompressible two-phase flows. To update pressure, we circumvent the computationally expensive Poisson equation and use the general pressure equation. In addition, the volume-of-fluid approach is used for interface capturing under the operator-split methodology. Our method is fully-explicit and stable with simple local spatial discretization, and hence, it is easy to implement. Several two- and three-dimensional canonical two-phase flows are simulated. The qualitative and quantitative results prove that our method is capable of accurately handling problems involving a range of density and viscosity ratios and surface tension effects

Fluid Simulation by the Smoothed Particle Hydrodynamics Method: A Survey.

This paper presents a survey of Smoothed Particle Hydrodynamics (SPH) and its use in computational fluid dynamics. As a truly mesh-free particle method based upon the Lagrangian formulation, SPH has been applied to a variety of different areas in science, computer graphics and engineering. It has been established as a popular technique for fluid based simulations, and has been extended to successfully simulate various phenomena such as multi-phase flows, rigid and elastic solids, and fluid features such as air bubbles and foam. Various aspects of the method will be discussed: Similarities, advantages and disadvantages in comparison to Eulerian methods; Fundamentals of the SPH method; The use of SPH in fluid simulation; The current trends in SPH. The paper ends with some concluding remarks about the use of SPH in fluid simulations, including some of the more apparent problems, and a discussion on prospects for future work