Songdong Shao

INCOMPRESSIBLE SPH METHOD FOR SIMULATING NEWTONIAN AND NON-NEWTONIAN FLOWS WITH A FREE SURFACE

Abstract An incompressible smoothed particle hydrodynamics (SPH) method is presented to simulate Newtonian and non-Newtonian flows with free surfaces. The basic equations solved are the incompressible mass conservation and Navier–Stokes equations. The method uses prediction–correction fractional steps with the temporal velocity field integrated forward in time without enforcing incompressibility in the prediction step. The resulting deviation of particle density is then implicitly projected onto a divergence-free space to satisfy incompressibility through a pressure Poisson equation derived from an approximate pressure projection. Various SPH formulations are employed in the discretization of the relevant gradient, divergence and Laplacian terms. Free surfaces are identified by the particles whose density is below a set point. Wall boundaries are represented by particles whose positions are fixed. The SPH formulation is also extended to non-Newtonian flows and demonstrated using the Cross rheological model. The incompressible SPH method is tested by typical 2-D dam-break problems in which both water and fluid mud are considered. The computations are in good agreement with available experimental data. The different flow features between Newtonian and non-Newtonian flows after the dam-break are discussed.

Simulation of near-shore solitary wave mechanics by an incompressible SPH method

Abstract An incompressible smoothed particle hydrodynamics (SPH) method together with a large eddy simulation (LES) approach is used to simulate the near-shore solitary wave mechanics. The incompressible Navier–Stokes equations in Lagrangian form are solved using a two-step fractional method. This method first integrates the velocity field in time without enforcing incompressibility. The resulting deviation in particle density is projected onto a divergence-free space to satisfy incompressibility through a pressure Poisson equation. SPH formulations are employed for discretization of relevant gradient and divergence operators. The spatial filtering of the LES approach produces sub-particle scale stresses, which are treated by the Smagorinsky model. The cases of a solitary wave against a vertical wall and running up a plane slope are treated. The wave profiles are in good agreement with reported experimental data or analytical solutions. It is found that the assumption of hydrostatic pressure holds almost everywhere except during the last stages of wave breaking. The dynamic viscosity is also found to be a maximum near the breaking front.

SPH-LES MODEL FOR NUMERICAL INVESTIGATION OF WAVE INTERACTION WITH PARTIALLY IMMERSED BREAKWATER

The reflection and transmission characteristics of regular waves by a partially immersed curtain-type breakwater have been studied by the experiment and numerical model in the paper. Non-overtopping and overtopping of the breakwater by the incident wave were considered to compare different wave dissipation efficiencies. An incompressible Smoothed Particle Hydrodynamics (SPH) theory combined with a Large Eddy Simulation (LES) model was employed as the numerical tool. The SPH method is robust for tracking free surfaces without numerical diffusion and the LES model is capable of analyzing turbulence and eddy vortices during wave-breakwater interactions. A good agreement between computational and experimental wave profiles verifies the accuracy of the SPH-LES model. The computations also disclose that the wave energy dissipation is mainly attributed to the turbulence production and vortex shedding during the wave transmission and reflection processes.

Turbulence particle models for tracking free surfaces

Two numerical particle models, the Smoothed Particle Hydrodynamics (SPH) and Moving Particle Semi-implicit (MPS) methods, coupled with a sub-particle scale (SPS) turbulence model, are presented to simulate free surface flows. Both SPH and MPS methods have the advantages in that the governing Navier-Stokes equations are solved by Lagrangian approach and no grid is needed in the computation. Thus the free surface can be easily and accurately tracked by particles without numerical diffusion. In this paper different particle interaction models for SPH and MPS methods are summarized and compared. The robustness of two models is validated through experimental data of a dam-break flow. In addition, a series of numerical runs are carried out to investigate the order of convergence of the models with regard to the time step and particle spacing. Finally the efficiency of the incorporated SPS model is further demonstrated by the computed turbulence patterns from a breaking wave. It is shown that both SPH and MPS models provide a useful tool for simulating free surface flows.

SIMULATING COUPLED MOTION OF PROGRESSIVE WAVE AND FLOATING CURTAIN WALL BY SPH-LES MODEL

The coupled motion between progressive wave and floating curtain-wall type breakwater is simulated by an incompressible Smoothed Particle Hydrodynamics (SPH) method combined with a Large Eddy Simulation (LES) model. The Naviers-Stokes equations in Lagrangian form are solved using a two-step split method. The method first integrates the velocity field in time without enforcing incompressibility. Then the resulting deviation of particle density is projected into a divergence-free space to satisfy incompressibility. The SPH method is convenient for describing free surfaces and moving boundaries of the floating body. The LES model is capable of dealing with turbulence during the wave-breakwater interactions. The translation and rotation of the floating curtain wall is calculated through an additional rigid-body-tracking subroutine. The computed wave profiles and hydrodynamic forces by the current model are in good agreement with those reported in the literature. Finally, the wave transmission and reflection characteristics are analyzed and compared with numerical results in which the breakwater is fixed.

SPH simulation of solitary wave interaction with a curtain-type breakwater

An incompressible Smoothed Particle Hydrodynamics (SPH) method is put forward to simulate non-linear and dispersive solitary wave reflection and transmission characteristics after interacting with a partially immersed curtain-type breakwater. The Naviers-Stokes equations in Lagrangian form are solved using a two-step split method. The method first integrates the velocity field in time without enforcing incompressibility. Then the resulting deviation of particle density is projected into a divergence-free space to satisfy incompressibility by solving a pressure Poisson equation. Basic SPH formulations are employed for the discretization of relevant gradient and divergence operators in the governing equations. The curtain wall and horizontal bottom are also numerically treated by fixed wall particles and the free surface of wave is tracked by particles with a lower density as compared with inner particles. The proposed SPH model is first verified by the test of a solitary wave with different amplitudes running against a vertical wall without opening underneath. Then it is applied to simulate solitary wave interacting with a partially immersed curtain wall with different immersion depths. The characteristics of wave reflection, transmission, dissipation and impacting forces on the curtain breakwater are discussed based on computational results.

Simulation of breaking wave by SPH method coupled with k-∊ model

The paper employs a Reynolds-averaged Navier–Stokes (RANS) approach to investigate the time-dependent wave breaking processes. The numerical model is the smoothed particle hydrodynamic (SPH) method. It is a mesh-free particle approach which is capable of tracking the free surfaces of large deformation in an easy and accurate way. The widely used two-equation k-ε model is chosen as the turbulence model to couple with the incompressible SPH scheme. The numerical model is employed to reproduce cnoidal wave breaking on a slope under two different breaking conditions–spilling and plunging. The computed free surface displacements, turbulence intensities and undertow profiles are in good agreement with the experimental data and other numerical results. According to the computations, the breaking wave characteristics are presented and discussed. It is shown that the SPH method provides a useful tool to investigate the surf zone dynamics.

Source term treatment of SWEs using surface gradient upwind method

Owing to unpredictable bed topography conditions in natural shallow flows, various numerical methods have been developed to improve the treatment of source terms in the shallow water equations. The surface gradient method is an attractive approach as it includes a numerically simple approach to model flows over topographically-varied channels. To further improve the performance of this method, this study deals with the numerical improvement of the shallow-flow source terms. The so-called surface gradient upwind method (SGUM) integrates the source term treatment in the inviscid discretization scheme. A finite volume model (FVM) with the monotonic upwind scheme for conservative laws is used. The Harten–Lax–van Leer-contact approximate Riemann solver is used to reconstruct the Riemann problem in the FVM. The proposed method is validated against published analytical, numerical, and experimental data, indicating that the SGUM is robust and treats the source terms in different flow conditions well.

Evaluations of SWEs and SPH Numerical Modelling Techniques for Dam Break Flows

Abstract The standard shallow water equations (SWEs) model is often considered to provide weak solutions to the dam-break flows due to its depth-averaged shock-capturing scheme assumptions. In this study, an improved SWEs model using a recently proposed Surface Gradient Upwind Method (SGUM) is used to compute dam-break flows in the presence of a triangular hump. The SGUM allows the SWEs model to stably and accurately reproduce the highly complex shock currents caused by the dam-break event, as it improves the treatment of SWEs numerical source terms, which is particularly crucial for simulating the wet/dry front interface of the dam-break flow. Besides, an Incompressible Smoothed Particle Hydrodynamics (ISPH) modeling technique is also employed in this study to compare with the performance of the SGUM-SWEs model. The SPH method is totally mesh free and thus it can efficiently track the large free surface deformation. The ISPH approach uses a strictly incompressible two-step semi-implicit solution method. By reproducing a documented experimental dam-break flow, it has demonstrated that both model simulation results gave good agreement with the experimental data at different measurement locations. However, the ISPH simulations showed a better prediction of the dam-break peak wave building-up time, where its superiority was demonstrated. Furthermore, the ISPH model could also predict more detailed flow surface profiles across the streamwise flow direction and the velocity and pressure structures.

Wave Impact Simulations by an Improved ISPH Model

AbstractThis paper presents an improved incompressible smoothed particle hydrodynamics (ISPH) method for wave impact applications. In most conventional ISPH techniques the source term of the pressure Poisson equation (PPE) is usually treated by either a density invariant or a velocity divergence-free formulation. In this work, both the density invariant and velocity divergence free formulations are combined in a weighted average form to determine the source term. The model is then applied to two problems: (1) dam-breaking wave impact on a vertical wall and (2) solitary wave run-up and impact on a coastal structure. The computational results have indicated that the combined source term treatment can predict the wave impact pressure and force more accurately compared with using either formulation alone. It was further found that depending on the application case, the influence of the density invariant and divergence-free parts could be quite different. For the more violent wave impact case, the divergence-f...