Divergence-free condition in transport simulation

AbstractIn this work, two adaptations of the particle method allowing one to reduce the numerical errors induced by the non-zero divergence of flow fields in the numerical simulations of particle transport are presented. The first adaptation is based on the renormalization method allowing one to use an irregular distribution of particles induced by the non-zero divergence of flow fields. The second adaptation consists in applying a correction on the weight of the particles by using the relation between the divergence of flow fields and the particles' volume evolution. This adaptation may be considered as a relaxation method. The accuracy of both methods is evaluated by simulating the transport of an inert tracer by the flow of a jet in crossflow whose concentration fields were measured experimentally. The comparison between the numerical and experimental results shows clearly that the two adaptations of the particle method correct efficiently the effect of a non-zero divergence velocity field on the computed concentration

A New Interface Identification Technique Based on Absolute Density Gradient for Violent Flows

An identification technique for sharp interface and penetrated isolated particles is developed for simulating two-dimensional, incompressible and immiscible two-phase flows using meshless particle methods in this paper. This technique is based on the numerically computed density gradient of fluid particles and is suitable for capturing large interface deformation and even topological changes such as merging and breaking up of phases. A number of assumed particle configurations will be examined using the technique, including these with different level of randomness of particle distribution. The tests will show that the new technique can correctly identify almost all the interface and isolated particles, and also show that it is better than other existing popular methods tested

Improved SPH simulation of spilled oil contained by flexible floating boom under wave-current coupling condition

A multi-phase Smoothed Particle Hydrodynamics (SPH) method is developed to model the failure process of a flexible oil boom. An algorithm is proposed based on the dynamic boundary particles (DBPs) for preventing the particle disorders during the multi-fluid particle movement around the solid boundary. The improved multi-phase SPH model is firstly validated by the experimental data of a wedge falling into a two-layer oil-water fluid. Then a numerical wave-current flume is established with an active absorbing piston-type wave generator and a circulating current system. The model reliability is validated against the measured vertical profiles of velocity. Simulation of the flexible floating boom movement is implemented by introducing a Rigid Module and Flexible Connector (RMFC) multi-body system. The model is finally applied to the simulation of movement of a flexible floating boom in containing industrial gear oil under the combined waves and currents. Good agreements are obtained between the SPH modeling results and the experimental data in terms of the ambient wave-current field, hydrodynamic responses of the floating body and evolution process of the oil slick for the flexible boom. The hydrodynamic responses and containment performances of the flexible floating boom are also compared with those of the rigid one. It is found from both the experimental and numerical results that two vortices of the water phase exist in the front and rear of the boom skirt and the size of the front vortex decreases with an increase of the current velocity while the wake vortex is reversed. It is also found that the skirt of the flexible boom has a larger magnitude of the swaying and rolling than the rigid one and the maximum quantity of the escaped oil of a flexible boom within one wave cycle is about 5% more than a rigid one under the present test conditions

Multi-phase fluid flow simulation by using peridynamic differential operator

The problems of multi-phase fluid flows are often encountered in engineering. In this study, a non-local numerical model of multi-phase fluid flows in the Lagrangian description is developed. Based on the peridynamic theory, a peridynamic differential operator is proposed which can convert any arbitrary order of differentials into their integral form without calculating the peridynamic parameters. Therefore, the Navier-Stokes equations including the surface tension forces are reformulated into their integral form. Subsequently, an updated Lagrangian algorithm for solving the multi-phase fluid flow problems is proposed. Besides, the particle shifting technology and moving least square algorithm are also adopted to avoid the possible tension instability. Finally, several benchmark multi-phase fluid flow problems such as two-phase hydrostatic problem, two-phase Poiseuille flow, and 2D square droplet deformation are solved to validate the proposed non-local model. It can be concluded from the current study that the peridynamic differential operator can be applied as an alternative method for multi-phase fluid flow simulation

An SPH model for multiphase flows with complex interfaces and large density differences

10.1016/j.jcp.2014.11.037Journal of Computational Physics283169-18

Verification and Validation of Numerical Modelling Approaches Pertinent to Stomach Modelling

The digestive system is vital to the human body. Over many decades, scientists have been investigating the food breakdown mechanisms inside the stomach through in vivo human and animal studies and in vitro experiments. Due to recent improvements in computing speed and algorithm development, computational modelling has become a viable option to investigate in-body processes. Such in silico models are more easily controlled to investigate individual variables, do not require invasive physical experiments, and can provide valuable insights into the local physics of gastric flow. There is a huge potential for numerical approaches in stomach modelling as they can provide a comprehensive understanding of the complex flow and chemistry in the stomach. However, to make sure the numerical methods are accurate and reliable, rigorous verification and validation are essential as part of model development. A significant focus of this thesis was on verifying and validating the numerical modelling approaches pertinent to stomach modellin

Meshless Local Petrov-Galerkin method with Rankine source solution for two-dimensional two-phase flow modelling

A Lagrangian particle multiphase model based on the Meshless Local Petrov-Galerkin method with Rankine source solution (MLPG_R) is proposed to simulate 2D flows of two immiscible fluids. The model is applicable to fluids with a wide range of density ratio from 1.01 to 1000, capable of dealing with violent flow situations (e.g. breaking waves) and maintaining the sharp discontinuity of properties of the fluids at the interface. In order to extend the MLPG_R method to model multiphase flows, an innovative phase coupling is proposed using an equation for pressure at the interface particle through two stages. In the first stage, the formulation is based on ensuring the continuity of the pressure and the ratio of the pressure derivative in the normal direction of the interface to the fluid density across the interface. Gravity current, natural sloshing of two layered liquids and air-water violent sloshing are successfully simulated and compared with either experimental data or analytical solution demonstrating a second order convergent rate. The second stage involves the extension of the method to account for interface tension and large viscosity. This is achieved by adding additional terms in the original pressure formulation considering jumps for both the pressure and the ratio of pressure derivatives in either the normal or tangential direction to fluid density at the interface. The method ensures both velocity continuity even with highly viscous fluids and interface stress balance in the presence of interface tension. Simulation of square-droplet deformation illustrates sharp pressure drop at the interface and relieved spurious currents that are known to be associated with predictions by other existing models. The capillary wave case also demonstrates the necessity of maintaining the jump in the ratio of pressure gradient to fluid density and the bubble rising case further validates the model as compared with the benchmark numerical results. Apart from being the first application of the MLPG_R method to multiphase flows the proposed model also contains two highly effective and robust techniques whose applicability is not restricted to the MLPG_R method. One is based on use of the absolute density gradient for identifying the interface and isolated particles which is essential to ensure that interface conditions are applied at the correct locations in violent flows. The effectiveness of the technique has been examined by a number of particle configurations, including those with different levels of randomness of particle distribution. The other is about solving the discretised pressure equation, by splitting the one set equations into two sets corresponding to two phases and solving them separately but coupled by the interface particles. This technique efficiently gives reasonable solutions not only for the cases with low density ratio but also for the ones with very high density ratio