Turbulent Details Simulation for SPH Fluids via Vorticity Refinement

A major issue in Smoothed Particle Hydrodynamics (SPH) approaches is the numerical dissipation during the projection process, especially under coarse discretizations. High-frequency details, such as turbulence and vortices, are smoothed out, leading to unrealistic results. To address this issue, we introduce a Vorticity Refinement (VR) solver for SPH fluids with negligible computational overhead. In this method, the numerical dissipation of the vorticity field is recovered by the difference between the theoretical and the actual vorticity, so as to enhance turbulence details. Instead of solving the Biot-Savart integrals, a stream function, which is easier and more efficient to solve, is used to relate the vorticity field to the velocity field. We obtain turbulence effects of different intensity levels by changing an adjustable parameter. Since the vorticity field is enhanced according to the curl field, our method can not only amplify existing vortices, but also capture additional turbulence. Our VR solver is straightforward to implement and can be easily integrated into existing SPH methods

A SPH model for incompressible turbulence

A coarse-grained particle model for incompressible Navier-Stokes (NS) equation is proposed based on spatial filtering by utilizing smoothed particle hydrodynamics (SPH) approximations. This model is similar to our previous developed SPH discretization of NS equation ({\it Hu X.Y. & N.A. Adams, J. Comput. Physics}, 227: 264-278, 2007 and 228: 2082-2091, 2009) and the Lagrangian averaged NS (LANS-$\alpha$) turbulence model. Other than using smoothing approaches, this model obtains particle transport velocity by imposing constant $\sigma$ which is associated with the particle density, and is called SPH-$\sigma$ model. Numerical tests on two-dimensional decay and forced turbulences with high Reynolds number suggest that the model is able to reproduce both the inverse energy cascade and direct enstrophy cascade of the kinetic energy spectrum, the time scaling of enstrophy decay and the non-Guassian probability density function (PDF) of particle acceleration.Comment: 23 pages. 7 figure

Study on Actuator Line Modeling of Two NREL 5-MW Wind Turbine Wakes

The wind turbine wakes impact the efficiency and lifespan of the wind farm. Therefore, to improve the wind plant performance, research on wind plant control is essential. The actuator line model (ALM) is proposed to simulate the wind turbine efficiently. This research investigates the National Renewable Energy Laboratory 5 Million Watts (NREL 5-MW) wind turbine wakes with Open Field Operation and Manipulation (OpenFOAM) using ALM. Firstly, a single NREL 5-MW turbine is simulated. The comparison of the power and thrust with Fatigue, Aerodynamics, Structures, and Turbulence (FAST) shows a good agreement below the rated wind speed. The information relating to wind turbine wakes is given in detail. The top working status is proved at the wind speed of 8 m/s and the downstream distance of more than 5 rotor diameters (5D). Secondly, another case with two NREL 5-MW wind turbines aligned is also carried out, in which 7D is validated as the optimum distance between the two turbines. The result also shows that the upstream wind turbine has an obvious influence on the downstream one

GIZMO: A New Class of Accurate, Mesh-Free Hydrodynamic Simulation Methods

We present two new Lagrangian methods for hydrodynamics, in a systematic comparison with moving-mesh, SPH, and stationary (non-moving) grid methods. The new methods are designed to simultaneously capture advantages of both smoothed-particle hydrodynamics (SPH) and grid-based/adaptive mesh refinement (AMR) schemes. They are based on a kernel discretization of the volume coupled to a high-order matrix gradient estimator and a Riemann solver acting over the volume 'overlap.' We implement and test a parallel, second-order version of the method with self-gravity & cosmological integration, in the code GIZMO: this maintains exact mass, energy and momentum conservation; exhibits superior angular momentum conservation compared to all other methods we study; does not require 'artificial diffusion' terms; and allows the fluid elements to move with the flow so resolution is automatically adaptive. We consider a large suite of test problems, and find that on all problems the new methods appear competitive with moving-mesh schemes, with some advantages (particularly in angular momentum conservation), at the cost of enhanced noise. The new methods have many advantages vs. SPH: proper convergence, good capturing of fluid-mixing instabilities, dramatically reduced 'particle noise' & numerical viscosity, more accurate sub-sonic flow evolution, & sharp shock-capturing. Advantages vs. non-moving meshes include: automatic adaptivity, dramatically reduced advection errors & numerical overmixing, velocity-independent errors, accurate coupling to gravity, good angular momentum conservation and elimination of 'grid alignment' effects. We can, for example, follow hundreds of orbits of gaseous disks, while AMR and SPH methods break down in a few orbits. However, fixed meshes minimize 'grid noise.' These differences are important for a range of astrophysical problems.Comment: 57 pages, 33 figures. MNRAS. A public version of the GIZMO code, user's guide, test problem setups, and movies are available at http://www.tapir.caltech.edu/~phopkins/Site/GIZMO.htm

Numerical modelling of local scour with computational methods

Evaluating bed morphological evolution (specifically the scoured bed level) accurately using computational modelling is critical for analyses of the stability of many marine and coastal structures, such as piers, groynes, breakwaters, submarine pipelines and even telecommunication cables. This thesis considers the coupled hydrodynamic and morphodynamic modelling of the local scour around hydraulic structures, such as near a vertical pile or near a horizontal pipe. The focus in this study is on applying a fluid-structure interaction (FSI) approach to simulate the morphodynamical behaviour of the bed deformation, replacing the structural (i.e. solid mechanics) equation by the sediment continuity equation or Exner equation. Specifically, this works presents a novel method of mesh movement with anisotropic mesh adaptivity based on optimization for simulating local scour near structures with discontinuous Garlerkin (DG) discretisation methods for solving the flow field. Amongst the other goals of this work is the validation of the proposed procedure with previously performed laboratory as well as two- and three-dimensional numerical experiments. Additionally, performance is considered using an implementation of the methodology within Fluidity (http://fluidityproject.github.io/), an open-source, multi-physics, computational fluid dynamics (CFD) code, capable of handling arbitrary multi-scale unstructured tetrahedral meshes and including algorithms to perform dynamic anisotropic mesh adaptivity and mesh movement. The flexibility over mesh structure and resolution that these optimisation capabilities provide makes it potentially highly suitable for accounting the extreme bed morphological evolution close to a fixed solid structure under the action of hydrodynamics. Galerkin-based finite element methods have been used for the hydrodynamics (including discontinuous Galerkin discretisations) and morphological calculations, and automatic mesh deformation has been utilised to account for bed evolution changes while preserving the validity and quality of the mesh. Finally, the work extends the scope in regards of computational methods and considers scour modelling with pure Lagrangian and meshless methods such as smoothed particle hydrodynamics (SPH), which have also become of interest in the analysis and modelling of coastal sediment transport, particularly in scour-related processes. The SPH modelling is considered in a two-phase, flow-sediment fully Lagrangian scour simulation where the discrete-particle interaction forces between phases are resolved at the interface and continuous changes in the bed profile are obtained naturally.Open Acces

Development of the Distributed Points Method with Application to Cavitating Flow

A mesh-less method for solving incompressible, multi-phase flow problems has been developed and is discussed along with the presentation of benchmark results showing good agreement with theoretical and experimental results. Results of a systematic, parametric study of the single phase flow around a 2D circular cylinder at Reynolds numbers up to 1000 are presented and discussed. Simulation results show good agreement with experimental results. Extension of the method to deal with multiphase flow including liquid-to-vapor phase transition along with applications to cavitating flow are discussed. Insight gleaned from numerical experiments of the cavity closure problem are discussed along with recommendations for additional research. Several conclusions regarding the use of the method are made

Enhanced SPH modeling of free-surface flows with large deformations

The subject of the present thesis is the development of a numerical solver to study the violent interaction of marine flows with rigid structures. Among the many numerical models available, the Smoothed Particle Hydrodynamics (SPH) has been chosen as it proved appropriate in dealing with violent free-surface flows. Due to its Lagrangian and meshless character it can naturally handle breaking waves and fragmentation that generally are not easily treated by standard methods. On the other hand, some consolidated features of mesh-based methods, such as the solid boundary treatment, still remain unsolved issues in the SPH context. In the present work a great part of the research activity has been devoted to tackle some of the bottlenecks of the method. Firstly, an enhanced SPH model, called delta-SPH, has been proposed. In this model, a proper numerical diffusive term has been added in the continuity equation in order to remove the spurious numerical noise in the pressure field which typically affects the weakly-compressible SPH models. Then, particular attention has been paid to the development of suitable techniques for the enforcement of the boundary conditions. As for the free-surface, a specific algorithm has been designed to detect free-surface particles and to define a related level-set function with two main targets: to allow the imposition of peculiar conditions on the free-surface and to analyse and visualize more easily the simulation outcome (especially in 3D cases). Concerning the solid boundary treatment, much effort has been spent to devise new techniques for handling generic body geometries with an adequate accuracy in both 2D and 3D problems. Two different techniques have been described: in the first one the standard ghost fluid method has been extended in order to treat complex solid geometries. Both free-slip and no-slip boundary conditions have been implemented, the latter being a quite complex matter in the SPH context. The proposed boundary treatment proved to be robust and accurate in evaluating local and global loads, though it is not easy to extend to generic 3D surfaces. The second technique has been adopted for these cases. Such a technique has been developed in the context of Riemann-SPH methods and in the present work is reformulated in the context of the standard SPH scheme. The method proved to be robust in treating complex 3D solid surfaces though less accurate than the former. Finally, an algorithm to correctly initialize the SPH simulation in the case of generic geometries has been described. It forces a resettlement of the fluid particles to achieve a regular and uniform spacing even in complex configurations. This pre-processing procedure avoids the generation of spurious currents due to local defects in the particle distribution at the beginning of the simulation. The delta-SPH model has been validated against several problems concerning fluid-structure interactions. Firstly, the capability of the solver in dealing with water impacts has been tested by simulating a jet impinging on a flat plate and a dam-break flow against a vertical wall. In this cases, the accuracy in the prediction of local loads and of the pressure field have been the main focus. Then, the viscous flow around a cylinder, in both steady and unsteady conditions, has been simulated comparing the results with reference solutions. Finally, the generation and propagation of 2D gravity waves has been simulated. Several regimes of propagation have been tested and the results compared against a potential flow solver. The developed numerical solver has been applied to several cases of free-surface flows striking rigid structures and to the problem of the generation and evolution of ship generated waves. In the former case, the robustness of the solver has been challenged by simulating 2D and 3D water impacts against complex solid surfaces. The numerical outcome have been compared with analytical solutions, experimental data and other numerical results and the limits of the model have been discussed. As for the ship generated waves, the problem has been firstly studied within the 2D+t approximation, focusing on the occurrence and features of the breaking bow waves. Then, a dedicated 3D SPH parallel solver has been developed to tackle the simulation of the entire ship in constant forward motion. This simulation is quite demanding in terms of complexities of the boundary geometry and computational resources required. The wave pattern obtained has been compared against experimental data and results from other numerical methods, showing in both the cases a fair and promising agreement

Development of the Distributed Points Method with Application to Cavitating Flow

A mesh-less method for solving incompressible, multi-phase flow problems has been developed and is discussed along with the presentation of benchmark results showing good agreement with theoretical and experimental results. Results of a systematic, parametric study of the single phase flow around a 2D circular cylinder at Reynolds numbers up to 1000 are presented and discussed. Simulation results show good agreement with experimental results. Extension of the method to deal with multiphase flow including liquid-to-vapor phase transition along with applications to cavitating flow are discussed. Insight gleaned from numerical experiments of the cavity closure problem are discussed along with recommendations for additional research. Several conclusions regarding the use of the method are made