Smoothed Particle Hydrodynamics for Computational Fluid Dynamics

Smoothed particle hydrodynamics (SPH) is a simple and effective numerical method that can be used to solve a variety of challenging problems in computational mechanics. It is a Lagrangian mesh-free method ideal for solving deformation problems. In the SPH method, the state of a system is represented by a set of particles, which possesses individual material properties and interact with each other within a specific range defined as a support domain by a weight function or smoothing function. SPH features flexibility in handling complex flow fields and in including physical effects. In theory, the basic concept of the SPH method is introduced in this paper. Some detailed numerical aspects are discussed including the kernel approximation in continuous form and particle approximation in discrete form, the properties for the smoothing functions and some of the most frequently used ones in the SPH literature, the concept of support and interface domain, SPH formulations for Navier-Stokes equation, time integration, boundary treatment, particle interaction, artificial viscosity, laminar viscosity, shifting algorithm, and so on. In applications, this paper presents an improved SPH method for modeling the diffusion process of a microneedle and using smoothed particle hydrodynamics (SPH) method to simulate the 25% cross-section stenosis blood vessel model and the 75% crosssection stenosis blood vessel model. The obtained numerical results are in close agreement with available theoretical and experimental results in the literature. As an emerging transdermal drug delivery device, microneedles demonstrate some superior potential and advantages over traditional metallic needles-on-syringes in skin injection and vaccine [1]. However, very few research papers are available. This project uses a high order continuous method, the spectral element method (SEM), and a low order discrete method, the Smoothed Particle Hydrodynamics (SPH), to investigate this new drug delivery system. The incompressible Navier-Stokes equations were solved with SEM under appropriate initial and slip boundary conditions for the transport of medicine inside microneedles of rectangular and circular cross-sections. In addition, Darcy-Brinkman equations and a concentration equation were solved with SEM under appropriate initial and boundary conditions for the infiltration of medicine solution through porous media of the dermis tissue once a microneedle enters the skin. Meanwhile, the Lagrangian form of the Navier-Stokes equations were solved with the weighted interpolation approach via numerical integrations without inverting any matrices. Results from the mesh-based SEM and the mesh-free SPH simulations revealed technical details about the processes of delivery of medicine particles through microneedles and diffusion in the skin tissue, and the medicine concentration changes with space and time. The overall effect of medicine delivery under initial concentration and conditions were simulated and the effect of drug delivery were assessed. The formation of thrombus is a complicated process. The existing literature rarely has a model for high-fidelity simulation of the effects and hazards of blood clots on blood flow. In this model, high-fidelity simulations are performed for complex human internal environments. The result of this simulation indicates high pressure area in blood vessel wall which matches the real condition of the vessel experiment

An SPH multi-fluid model based on quasi-buoyancy for interface stabilization up to high density ratios and realistic wave speed ratios

We introduce a Smoothed Particle Hydrodynamics (SPH) concept for the stabilization of the interface between two fluids. It is demonstrated that the change in the pressure gradient across the interface leads to a force imbalance. This force imbalance is attributed to the particle approximation implicit to SPH. To stabilize the interface a pressure gradient correction is proposed. In this approach the multi-fluid pressure gradients are related to the (gravitational and fluid) accelerations. This leads to a quasi-buoyancy correction for hydrostatic (stratified) flows, which is extended to non-hydrostatic flows. The result is a simple density correction which involves no parameters or coefficients. This correction is included as an extra term in the SPH momentum equation. The new concept for the stabilization of the interface is explored in five case studies and compared with other multi-fluid models. The first case is the stagnant flow in a tank: the interface remains stable up to density ratios of 1:1000 (typical for water and air) in combination with artificial wave speed ratios up to 1:4. The second and third cases are the Rayleigh-Taylor instability and the rising bubble, where a reasonable agreement between SPH and level-set models is achieved. The fourth case is an air flow across a water surface up to density ratios of 1:100, artificial wave speeds for water higher than that of air, and high air velocities. The fifth case is about the propagation of internal gravity waves up to density ratios of 1:100 and artificial wave speed ratios of 1:2. It is demonstrated that the quasi-buoyancy model may be used to stabilize the interface between two fluids up to high density ratios, with real (low) viscosities and more realistic wave speed ratios than achieved by other WCSPH multi-fluid models. Real wave speed ratios can be achieved, as long as the fluid velocities are not very high. Although the wave speeds may be artificial in many cases, correct and realistic wave speed ratios are essential in the modelling of heat transfer between two fluids (e.g. in engineering applications such as gas turbines)

MLPG_R method for modelling 2D flows of two immiscible fluids

This is a first attempt to develop the Meshless Local Petrov-Galerkin method with Rankine source solution (MLPG_R method) to simulate multiphase flows. In this paper, we do not only further develop the MLPG_R method to model two-phase flows but also propose two new techniques to tackle the associated challenges. The first technique is to form an equation for pressure on the explicitly identified interface between different phases by considering the continuity of the pressure and the discontinuity of the pressure gradient (i.e. the ratio of pressure gradient to fluid density), the latter reflecting the fact that the normal velocity is continuous across the interface. The second technique is about solving the algebraic equation for pressure, which gives reasonable solution not only for the cases with low density ratio but also for the cases with very high density ratio, such as more than 1000. The numerical tests show that the results of the newly developed two-phase MLPG_R method agree well with analytical solutions and experimental data in the cases studied. The numerical results also demonstrate that the newly developed method has a second-order convergent rate in the cases for sloshing motion with small amplitudes

SPH-ALE Scheme for Weakly Compressible Viscous Flow with a Posteriori Stabilization

[Abstract] A highly accurate SPH method with a new stabilization paradigm has been introduced by the authors in a recent paper aimed to solve Euler equations for ideal gases. We present here the extension of the method to viscous incompressible flow. Incompressibility is tackled assuming a weakly compressible approach. The method adopts the SPH-ALE framework and improves accuracy by taking high-order variable reconstruction of the Riemann states at the midpoints between interacting particles. The moving least squares technique is used to estimate the derivatives required for the Taylor approximations for convective fluxes, and also provides the derivatives needed to discretize the viscous flux terms. Stability is preserved by implementing the a posteriori Multi-dimensional Optimal Order Detection (MOOD) method procedure thus avoiding the utilization of any slope/flux limiter or artificial viscosity. The capabilities of the method are illustrated by solving one- and two-dimensional Riemann problems and benchmark cases. The proposed methodology shows improvements in accuracy in the Riemann problems and does not require any parameter calibration. In addition, the method is extended to the solution of viscous flow and results are validated with the analytical Taylor–Green, Couette and Poiseuille flows, and lid-driven cavity test cases.This research was funded by Ministerio de Ciencia, Innovación y Universidades of the Spanish Government Grant #RTI2018-093366-B-I00, by the Consellería de Educación e Ordenación Universitaria of the Xunta de Galicia (grant#ED431C 2018/41)Xunta de Galicia; ED431C 2018/4

Developments of numerical methods for linear and nonlinear fluid-solid interaction dynamics with applications

This paper presents a review on some developments of numerical methods for linear and nonlinear fluid-solid interaction (FSI) problems with their applications in engineering. The discussion covers the four types of numerical methods: 1) mixed finite element (FE)-substructure-subdomain model to deal with linear FSI in a finite domain, such as sloshing, acoustic-structure interactions, pressure waves in fluids, earthquake responses of chemical vessels, dam-water couplings, etc.; 2) mixed FE-boundary element (BE) model to solve linear FSI with infinite domains, for example, VLFS subject to airplane landing impacts, ship dynamic response caused by cannon / missile fire impacts, etc.; 3) mixed FE-finite difference (FD) / volume (FV) model for nonlinear FSI problems with no separations between fluids and solids and breaking waves; 4) mixed FE-smooth particle (SP) method to simulate nonlinear FSI problems with f-s separations as well as breaking waves. The partitioned iteration approach is suggested in base of available fluid and solid codes to separately solve their governing equations in a time step, and then through reaching its convergence in coupling iteration to forward until the problem solved. The selected application examples include air-liquid-shell three phases interactions, LNG ship-water sloshing; acoustic analysis of air-building interaction system excited by human foot impacts; transient dynamic response of an airplane-VLFS-water interaction system excited by airplane landing impacts; turbulence flow-body interactions; structure dropping down on the water surface with breaking waves, etc. The numerical results are compared with the available experiment or numerical data to demonstrate the accuracy of the discussed approaches and their values for engineering applications. Based on FSI analysis, linear and nonlinear wave energy harvesting devices are listed to use the resonance in a linear system and the periodical solution in a nonlinear system, such as flutter, to effectively harvest wave energy. There are 231 references are given in the paper, which provides very useful resources for readers to further investigate their interesting approaches

A two-phase consistent particle method for wave impact problems with entrapped air pockets

Ph.DDOCTOR OF PHILOSOPH

Improved multiphase smoothed particle hydrodynamics

Smoothed Particle Hydrodynamics (SPH) is a relatively new meshless numerical approach which has attracted significant attention in the last 15 years. Compared with the conventional mesh-dependent computational fluid dynamics (CFD) methods, the SPH approach exhibits unique advantages in modeling multiphase fluid flows and associated transport phenomena due to its capabilities of handling complex material surface behavior as well as modeling complicated physics in a relatively simple manner. On the other hand, as SPH is still a developing CFD tool, it is vital to investigate its attributes, namely, advantages or potential limitations in modeling different multiphase flow problems to further understand and then improve this technique. Toward this end, this work aims to design a computational code using SPH method for the simulation of multiphase flows. In this work, we present numerical solutions for flow over an airfoil and square obstacle using both weakly compressible and incompressible SPH method with an improved solid boundary treatment approach, referred to as Multiple Boundary Tangents (MBT) method. It is shown that the MBT boundary treatment technique is very effective for tackling boundaries of complex shapes. Also, we have proposed the usage of the repulsive component of the Leonard Jones Potential (LJP) in the advection equation to repair particle fracture occurring in SPH method due to the tendency of SPH particles to follow the stream line trajectory. This approach is named as the artificial particle displacement method. Furthermore, the proposed method is totalized for the multiphase uid systems and implemented accordingly. The presented model is validated by solving Laplace's law, and square bubble deformation without surface tension whereby it is shown that the implemented SPH discretization does not produce any artificial surface tension. Then, the problem descriptions and solutions for two important hydrodynamic instabilities namely, Kelvin-Helmholtz and Rayleigh-Taylor instabilities, are provided along with their brief analytical linear stability analysis to describe the accuracy and the limitation of the numerical scheme. The long time evolution for both cases are investigated and the comparison between the simulation results and existence theories are provided in details. Finally, we have presented a model to study the deformation of a droplet suspended in a quiescent fluid subjected to the combined effects of surface tension and electric field forces. The electrostatics phenomena are coupled to hydrodynamics through the solution of a set of Maxwell equations. The relevant Maxwell equations and associated interface conditions are simplified relying on the assumptions of the so called leaky dielectric model. All governing equations and the relevant jump and boundary conditions are discretized in space using the SPH method with improved interface and boundary treatments. Numerical results are validated by two highly credential analytical results which are frequently cited in the literature