The SPH technique applied to free surface flows

This paper deals with an application of the SPH (Smooth Particle Hydrodynamics) technique to treat free surface problems. The SPH technique was originally conceived and developed for treating astrophysical problems and belongs to the class of “meshless” methods that dispense with the requirement of a computational grid. Instead, a cloud of particles is used to represent the continuum, the contact interaction between them is introduced with their subsequent trajectory being computed in the Lagrangian sense. The design and implementation of the method for transport equations and the Euler inviscid equations is fairly well-documented. Applications to the treatment of free surface flows is however more recent. In this work, the computation of three-dimensional free surface flows with the method is presented. The introduction of Riemann solvers to model the breakup of the initial surface discontinuities between particles is a novel feature of this work. For purposes of illustration, a three-dimensional simulation of the Vaiont dam disaster that occurred in 1963 in northern Italy is presented. This is a case where complicated three-dimensional geometries are involved and was chosen to show-off the versatility of the technique. The results are in general agreement with the qualitative observations and reconstruction of the event as reported by experts. The SPH technique is found to be very promising and powerful for application to free surface flows. In particular, the stage is being reached where for hydraulic problems; it may be used as a powerful simulation tool to delineate high-risk zones downstream of a possible dam failure where geometries of almost arbitrary complexity are involved. At the present time, significant progress is being achieved in developing the technique for application in different domains.     

Algebraic factorizations for 3D non-hydrostatic free surface flows

The high amount of computer resources required to simulate complex free surface flows has prompted for developing fractional step schemes capable of reducing the computational effort. These schemes are borrowed from a wider family of methods originally devised for the incompressible Navier-Stokes equations. An alternative approach is to perform an algebraic splitting on the coefficient matrix of the linear system resulting from the discretized problem, ending up with the successive solution of sub-problems of smaller size. The resulting schemes are shown in different cases to be the algebraic counterpart of the standard fractional step formulations. This algebraic procedure was again originally devised in the context of incompressible Navier-Stokes system, but we believe it is far more general: in this paper it is indeed extended to the more involved 3D free surface flow model. The inexact block factorization technique is applied to the coefficient matrix arising from the problem at hand and two significant choices for the approximation are discussed and numerically tested.     

A new corrective scheme for SPH

A new corrective scheme for Smoothed Particle Hydrodynamics (SPH) is introduced which greatly improves its accuracy, particularly in regions of particle deficiency or when particles are irregularly distributed. The scheme is based on the Taylor expansion of the SPH kernel estimates. The corrective equations are derived up to the second derivative in an arbitrary number of dimensions. Test applications for the new scheme include the interpolation of functions and the numerical solution of the heat equation in one and two dimensions.     

JOSEPHINE: A parallel SPH code for free-surface flows

JOSEPHINE is a parallel Smoothed Particle Hydrodynamics program, designed to solve unsteady free-surface flows. The adopted numerical scheme is efficient and has been validated on a first case, where a liquid drop is stretched over the time. Boundary conditions can also be modelled, as it is demonstrated in a second case: the collapse of a water column. Results show good agreement with both reference numerical solutions and experiments. The use of parallelism allows significant reduction of the computational time, even more with large number of particles. JOSEPHINE has been written so that any untrained developers can handle it easily and implement new features.Program summaryProgram title: JOSEPHINECatalogue identifier: AELV_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AELV_v1_0.htmlProgram obtainable from: CPC Program Library, Queen?s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 5139No. of bytes in distributed program, including test data, etc.: 22 833Distribution format: tar.gzProgramming language: Fortran 90 and OpenMPIComputer: All shared or distributed memory parallel processors, tested on a Xeon W3520, 2.67 GHz.Operating system: Any system with a Fortran 90 compiler and MPI, tested on Debian Linux.Has the code been vectorised or parallelised?: The code has been parallelised but has not been explicitly vectorised.RAM: Dependent upon the number of particles.Classification: 4.12Nature of problem: JOSEPHINE is designed to solve unsteady incompressible flows with a free-surface and large deformations.Solution method: JOSEPHINE is an implementation of Smoothed Particle Hydrodynamics. SPH is a Lagrangian mesh free particle method, thus, no explicit tracking procedure is required to catch the free surface. Incompressibility is satisfied using a weakly compressible model. Boundary conditions at walls are enforced by means of the ghost particles technique. The free-surface dynamic and kinematic conditions are applied implicitly.Running time: 15 mn on 4 processors for the dam-break case with 5000 particles, dependent upon the real duration (2 s here).     

A SVD-GFD scheme for computing 3D incompressible viscous fluid flows

A generalized finite difference (GFD) scheme for the simulation of three-dimensional (3D) incompressible viscous fluid flows in primitive variables is described in this paper. Numerical discretization is carried out on a hybrid Cartesian cum meshfree grid, with derivative approximation on non-Cartesian grids being carried out by a singular value decomposition (SVD) based GFD procedure. The Navier-Stokes equations are integrated by a time-splitting pressure correction scheme with second-order Crank-Nicolson and second-order discretization of time and spatial derivatives respectively. Axisymmetric and asymmetric 3D flows past a sphere with Reynolds numbers of up to 300 are simulated and compared with the results of Johnson and Patel [Johnson TA, Patel VC. Flow past a sphere up to a Reynolds number of 300. J Fluid Mech 1999;378:19-70] and others. Flows past toroidal rings are also simulated to illustrate the ability of the scheme to deal with more complex body geometry. The current method can also deal with flow past 3D bodies with sharp edges and corners, which is shown by a simple 3D case.     

A finite element overlapping scheme for turbomachinery flows on parallel platforms

Two- and three-dimensional turbomachinery flows in stationary and rotating compressor cascades are studied by using a one-level inexact explicit Schwarz method, and a cubic eddy viscosity turbulence closure. The message passing paradigm is used for the parallel implementation of the domain decomposition algorithm, allowing the solver portability on different parallel platforms. A convergence accelerator is proposed, based on a condensed cycle structure that merges the additive Schwarz iterations with the fixed point non-linear ones. The use of a stable finite element formulation on higher-order elements Q2-Q1 is addressed as a mean for retaining non-oscillatory and accurate solutions. Furthermore, the elementwise quadratic approximation is used to enable the exact implementation of higher-order integrals arising in the anisotropic turbulence closure adopted. Numerical campaigns are carried out on IBM SP2 and SP3, and CRAY T3E architectures, in order to demonstrate the portability. The accompanying performance improvement is assessed. Finally, the predicting capabilities are discussed with reference to challenging turbomachinery test cases: a transitional linear compressor cascade, and an isolated compressor rotor designed for non-free vortex operation. Convergence speed-up in such configurations is discussed.     

Evaluation of a bounded high order upwind scheme for 3D incompressible free surface flow computations

In the context of normalized variable formulation (NVF) of Leonard and total variation diminishing (TVD) constraints of Harten, this paper presents an extension of a previous work by the authors for solving unsteady incompressible flow problems. The main contributions of the paper are threefold. First, it presents the results of the development and implementation of a bounded high order upwind adaptative QUICKEST scheme in the 3D robust code (Freeflow), for the numerical solution of the full incompressible Navier–Stokes equations. Second, it reports numerical simulation results for 1D shock tube problem, 2D impinging jet and 2D/3D broken dam flows. Furthermore, these results are compared with existing analytical and experimental data. And third, it presents the application of the numerical method for solving 3D free surface flow problems.     

A new shape preserving parallel thinning algorithm for 3D digital images

This paper is concerned with a new parallel thinning algorithm for three-dimensional digital images that preserves the topology and maintains their shape. We introduce an approach of selecting shape points and outer-layer used for erosion during each iteration. The approach produces good skeleton for different types of corners. The concept of using two image versions in thinning is introduced and its necessity in parallel thinning is justified. The robustness of the algorithm under pseudo-random noise as well as rotation with respect to shape properties is studied and the results are found to be satisfactory.     

A numerical method for the simulation of free surface flows with surface tension

A numerical model for the simulation of three-dimensional liquid–gas flows with free surfaces and surface tension is presented. The incompressible Navier–Stokes equations are assumed to hold in the liquid domain, while the gas pressure is assumed to be constant in each connected component of the gas domain and to follow the ideal gas law. The surface tension effects are imposed as a normal force on the interface.

An implicit splitting scheme is used to decouple the physical phenomena. Given the curvature of the liquid–gas interface, the method described in [Caboussat A, Picasso M, Rappaz J. Numerical simulation of free surface incompressible liquid flows surrounded by compressible gas. J Comput Phys 2005;203(2):626–49] is used to track the liquid domain and compute the velocity and pressure in the liquid and the pressure in the gas domain. Then the surface tension effects are added. A variational method for the computation of the curvature is presented by smoothing the characteristic function of the liquid domain and using a finite element unstructured mesh.

The model is validated and numerical results in two and three space dimensions are presented for bubbles and/or droplets flows.     

A new energy-based method for 3D motion estimation of incompressible PIV flows

Motion estimation has many applications in fluid analysis, and a lot of work has been carried out using Particle Image Velocimetry (PIV) to capture and measure the flow motion from sequences of 2D images. Recent technological advances allow capturing 3D PIV sequences of moving particles. In the context of 3D flow motion, the assumption of incompressibility is an important physical property that is satisfied by a large class of problems and experiments. Standard motion estimation techniques in computer vision do not take into account the physical constraints of the flow, which is a very interesting and challenging problem. In this paper, we propose a new variational motion estimation technique which includes the incompressibility of the flow as a constraint to the minimization problem. We analyze, from a theoretical point of view, the influence of this constraint and we design a new numerical algorithm for motion estimation which enforces it. The performance of the proposed technique is evaluated from numerical experiments on synthetic and real data.     

A framework for parallel computational physics algorithms on multi-core: SPH in parallel

In this paper, a simulation framework that enables distributed numerical computing in multi-core shared-memory environments is presented. Using multiple threads allows a single memory image to be shared concurrently across cores but potentially introduces race conditions. Race conditions can be avoided by ensuring each core operates on an isolated memory block. This is usually achieved by running a different operating system process on each core, such as multiple MPI processes. However, we show that in many computational physics problems, memory isolation can also be enforced within a single process by leveraging spatial sub-division of the physical domain. A new spatial sub-division algorithm is presented that ensures threads operate on different memory blocks, allowing for in-place updates of state, with no message passing or creation of local variables during time stepping. Additionally, the developed framework controls task distribution dynamically ensuring an events based load balance. Results from fluid mechanics analysis using Smoothed Particle Hydrodynamics (SPH) are presented demonstrating linear performance with number of cores.     

基于SPH的三维流体模拟

流体模拟是计算机图形学和虚拟现实技术的一个研究热点和难点,针对目前的流体模拟真实感不够强,不能描述流体表面破碎的缺陷,根据流体的物理模型,采用基于光滑粒子动力学（SPH）的方法实现了三维流体的模拟。算法的核心思想就是将流体视为一系列“粒子”的集合,粒子的物理量及其空间导数是通过搜索光滑半径内与其相互作用的粒子的物理量进行插值得到。此举可以简化拉氏流体力学偏微分方程组求解过程。与传统的流体模拟方法相比,采用SPH算法所得到的模拟结果不仅可以比较真实地模拟流体流动的效果,而且还能实现流体表面的剧烈变形,甚至表面破碎（如浪花飞溅效果）。试验结果表明采用的算法在流体自由表面描述的逼真度上具有十分明显的优势。     

A 3D finite element model for free-surface flows

The present work deals with the validation of 3D finite element model for free-surface flows. The model uses the non-hydrostatic pressure and the eddy viscosities from the conventional linear turbulence model are modified to account for the secondary effects generated by strong channel curvature in the natural rivers with meandering open channels. The unsteady Reynolds-averaged Navier–Stokes equations are solved on the unstructured grid using the Raviart–Thomas finite element for the horizontal velocity components, and the common P1 linear finite element in the vertical direction. To provide the accurate resolution at the bed and the free-surface, the governing equations are solved in the multi-layers system (the vertical plane of the domain is subdivided into fixed thickness layers). The up-to-date k–ε turbulence solver is implemented for computing eddy coefficients, the Eulerian–Lagrangian–Galerkin (ELG) temporal scheme is performed for enhancing numerical time integration to guarantee high degree of mass conservation while the CFL restriction is eliminated. The present paper reports on successful validation of the numerical model through available benchmark tests with increasing complexity, using the high quality and high spatial resolution three-dimensional data set collected from experiments.     

A fixed-grid model for simulation of a moving body in free surface flows

A two-dimensional computer model is developed to simulate free surface flow interaction with a moving body. The model is based on the cut-cell technique in a fixed-grid system. In this model, a body is approximated by the partial cell treatment (PCT), in which an irregular body is represented by the volumetric fraction of solid in Cartesian cells. The body motion is tracked by Lagrangian method whereas the fluid motion around the body is solved by Eulerian method. The concept of “locally relative stationary (LRS)” is introduced in this study. In the LRS method, a source term is added locally to the conventional continuity equation on body surfaces to take account of body motions, which subsequently affects the computational results of fluid pressure and flow velocity around the body. The LRS method is incorporated into an earlier Reynolds averaged Navier-Stokes (RANS) equations model developed by Lin and Liu [A numerical study of breaking waves in the surf zone. J Fluid Mech 1998;359:239-64]. The new model is capable of simulating generic turbulent free surface flows and their interaction with a moving body or multiple moving bodies. A series of numerical experiments have been conducted to verify the accuracy of the model for simulation of moving body interaction with a free surface flow. These tests include the generation of a solitary wave with the prescribed wave paddle movements, water exit and water impact and entry of a horizontal circular cylinder, fluid sloshing in a horizontally excited tank, and the acceleration/deceleration of an elliptical cylinder near a water surface. Excellent agreements are obtained when numerical results are compared to available analytical, experimental, and other numerical results. The model is a simple-to-implement computational tool for simulating a moving body in turbulent free surface flows.     

Numerical simulation of two-phase free surface flows

Free surface flows are of most interest in many engineering or mathematical problems and many methods have been developed for their numerical resolution in various fields of the physics or the engineering. In this work, the volume-of-fluid method is used for the numerical simulation of two-phase free surface flows involving an incompressible liquid and a compressible gas and taking into account the surface tension effects. The incompressible Navier-Stokes equations are assumed to hold in the liquid domain, while the dynamical effects in the ideal gas are disregarded. A time splitting scheme is used together with a two-grids method for the space discretization. An original algorithm is introduced to track the bubbles of gas trapped in the liquid. Numerical results are presented in the frame of mold filling and bubbles and droplets flows. Some theoretical results concerning free boundary problems are also summarized.     

Coupling of free surface and groundwater flows

In this paper we present some preliminary results about the coupling of shallow water equations for free surface flows and Darcy equation for groundwater flows. A suitable set of interface conditions is discussed: the Beavers and Joseph formula for the bottom stress is used. An iterative algorithm to solve the coupled problem is proposed and some numerical results are presented.     

A novel parallel approach for 3D seismological problems

The large spatial scale associated with the modelling of strong ground motion in three dimensions requires enormous computational resources. For this reason, the simulation of soil shaking requires high-performance computing. The aim of this work is to present a new parallel approach for these kind of problems based on domain decomposition technique. The main idea is to subdivide the original problem into local ones. It allows to investigate large-scale problems that cannot be solved by a serial code. The performance of our parallel algorithm has been examined analysing computational times, speed-up and efficiency. Results of this approach are shown and discussed.     

A Parallel Voting Scheme for Aspect Recovery

Recently,a qualitative approach was proposed for 3-D shape recovery based on a hybrid object representation^[1].In this approach,aspect recovery is the most important stage which binds regions in the image into meaningful aspects to support 3-D primitive recovery.There is no known polynomial time algorithm to solve this problem.the previous approach dealt with this problem by using a heuristic method based on the conditional probability.Unlike the previous method,this paper presents a novel parallel voting scheme to conquer the problem for efficiency.For this purpose,the previous global aspect representation is replaced with a distributed representation of aspects.Based on this representation,a three-layer parallel voting network for aspect recovery is proposed.For evaluating likelihood,a continuous Hopfield net is employed so that all aspect coverings in decreasing order of likelihood can be enumerated.The paper describes this method in detail and demonstrates its usefulness with simulation.     

A generalized scheme for mapping parallel algorithms

A generalized mapping strategy that uses a combination of graph theory, mathematical programming, and heuristics is proposed. The authors use the knowledge from the given algorithm and the architecture to guide the mapping. The approach begins with a graphical representation of the parallel algorithm (problem graph) and the parallel computer (host graph). Using these representations, the authors generate a new graphical representation (extended host graph) on which the problem graph is mapped. An accurate characterization of the communication overhead is used in the objective functions to evaluate the optimality of the mapping. An efficient mapping scheme is developed which uses two levels of optimization procedures. The objective functions include minimizing the communication overhead and minimizing the total execution time which includes both computation and communication times. The mapping scheme is tested by simulation and further confirmed by mapping a real world application onto actual distributed environments