A diffuse interface method for complex three-dimensional free surface flows

An MLSPH algorithm for free surface flows in engineering applications

In this paper we will present an algorithm to perform free surface flow simulations with the lattice Boltzmann method on adaptive grids. This reduces the required computational time by more than a factor of three for simulations with large volumes of fluid. To achieve this, the simulation of large fluid regions is performed with coarser grid resolutions. We have developed a set of rules to dynamically adapt the coarse regions to the movement of the free surface, while ensuring the consistency of all grids. Furthermore, the free surface treatment is combined with a Smagorinsky turbulence model and a technique for adaptive time steps to ensure stable simulations. The method is validated by comparing the position of the free surface with an uncoarsened simulation. It yields speedup factors of up to 3.85 for a simulation with a resolution of 4803 cells and three coarser grid levels, and thus enables efficient and stable simulations of free surface flows, e.g. for highly detailed physically based animations of fluids.

Fully three-dimensional Reynolds-averaged Navier–Stokes modeling for solving free surface flows around coastal drainage gates

Three-dimensional dynamic gas–liquid flow simulations that accurately track the phase interface are numerically challenging. This article presents a numerical study of the performance of the level-set phase–interface tracking method when combined with extremely high order (7th to 11th) weighted essentially non-oscillatory (WENO) advection schemes for gas–liquid free surface flows. Comparisons between simulation results and prior benchmark results suggest that such a combination of methods can be satisfactorily applied to the level-set and Navier-Stokes equations for free surface flow simulations when volume conservation is enforced at every time step, and minor numerical oscillations are suppressed through use of an artificial viscosity term. In particular, simulations of solid body rotation, the unsteady flow following an ideal dam break, tank sloshing, and the rise of a single bubble all agree with analytical or experimental results to within ± 3.12% when the level-set method is combined with an 11th order WENO scheme. Furthermore, use of an 11th order WENO advection scheme actually has a computational cost advantage because, for the same accuracy, it can be used on a coarser grid when compared with a more-common second-order advection scheme; computational savings of up to 87% are possible.

Since free surface flows are seen in nature phenomena and artificial systems, the analysis for these flows has been more important in mechanical engineering. However, theoretical analyses are almost impossible because the boundary conditions are nonlinear equations in analyzing the free surface flows. Thus, numerical analyses are needed. Finite element method (FEM) which can be used for unstructured grid can easily treat boundary conditions. Thus, FEM is used in many technological fields. In this thesis, free surface flow problems were analyzed using the finite element method. In solving these problems, an arbitrary Lagrangian-Eulerian (ALE) kinematical description of the fluid domain was adopted, in which the nodal point can be displaced independently of the fluid motion. The ALE method was introduced into the Generalized Simplified Marker and Cell (GSMAC) method. Damping out the alternating errors was examined in this scheme.

Unsteady viscoelastic free surface flows are common in many industrial processes and a variety of numerical techniques have been employed to simulate these flows. The majority of constitutive models employed are based on differential equations to define the extra stress tensor. However, for some complex fluids, for instance, Boger fluids, integral models are more adequate to approximate the nonlinear behaviour of these fluids. This work deals with the numerical solution of the integral constitutive model KBKZ-PSM for two-dimensional unsteady free surface flows. The proposed numerical method is a numerical technique that employs finite differences to simulate moving free surface flows that interact with solid walls. The main features of the method are: numerical solution of the momentum and mass equations by an implicit method; the pressure condition on the free surface is implicitly coupled with the Poisson equation for obtaining the pressure field from mass conservation; a novel scheme for defining the past times t is employed; the Finger tensor is calculated by the deformation fields method and is advanced in time by the modified Euler method. This new technique is verified by solving shear and uniaxial elongational flows. Moreover, an analytic solution for channel flows is obtained that is used in the verification and convergence analysis of the proposed methodology. For free surface flows, the assessment of convergence lies on the mesh refinement on the simulation of a jet impinging on a flat surface and the extrudade swell problem. Finally, the new method is applied to investigate the jet buckling phenomenon and extrudate swell of KBKZ-PSM fluids.

Modelling free-surface flow has very important applications in many engineering areas such as oil transportation and offshore structures. Current research focuses on the modelling of free surface flow in a tank by solving the Navier-Stokes equation. An unstructured finite volume method is used to discretize the governing equations. The free surface is tracked by dynamically adapting the mesh and making it always surface conforming. A mesh-smoothing scheme based on the spring analogy is also implemented to ensure mesh quality throughout the computaiton. Studies are performed on the sloshing response of a liquid in an elastic container subjected to various excitation frequencies. Further investigations are also carried out on the critical frequency that leads to large deformation of the tank walls. Another numerical simulation involves the free-surface flow past as submerged obstacle placed in the tank to show the flow separation and vortices. All these cases demonstrate the capability of this numerical method in modelling complicated practical problems.

Free surface flow over square bars at different Reynolds numbers

The concept of “feedback” is introduced into potential free surface flow to derive a new and simple iterative method termed the residual pressure feedback method that is used for computing free surface profile. The residual pressure that vanishes when the convergence is achieved is fed back in order to adjust the residual pressure at the free surface and the free surface elevation continuously during the process of iteration. The use of the proposed method is demonstrated through a typical example of flow under sluice gates. The calculated results agree satisfactorily with those obtained from other methods and experimental data. This method features a simple iterative process, an easy-to-formulate computer code, and rapid convergence. Unlike some iterative methods, it is not necessary to greatly modify the computer program when the method is used to calculate different examples.

A three-dimensional non-hydrostatic coupled model for free surface – Subsurface variable – Density flows

The Finite Volume Particle Method (FVPM) is a meshless method that incorporates features of both Smoothed Particle Hydrodynamics and the Finite Volume Method. Here, two new formulations are presented which enhance its performance in simulation of free surface flows. One is a method for determining the velocity of the free surface, making use of a partial Riemann problem to analyse the flow between the particle barycentre and the geometric free surface. The second is a well-balanced formulation for gravity forces that enables hydrostatic equilibrium to be preserved exactly. Results are presented for hydrostatic, 1D impact, dambreak and deep-water standing wave test cases. Computations display convergence and good agreement with experimental data. The new methods recover exact hydrostatic equilibrium, improve robustness and reduce acoustic pressure fluctuations in dambreak flows, and reduce dissipation.

To simulate free surface flows, various numerical methods can be used. One of these numerical schemes is Smoothed particle hydrodynamics which, as a Lagrangian method, has been considered by many of researchers to model violent free surface deformation. In the present article, an effort has been made to find how solitary wave generation can be simulated using SPH method, more accurately. WCSPH formulation was utilized, different time stepping algorithms were considered and the effects of density filter and smoothing length on simulated solitary wave, and wave breaking were studied. The obtained results were compared with other solutions existing in the literature. Based on the numerical findings, it is concluded that predictor-corrector scheme in conjunction with moving least square (MLS) density filter can give more accurate results. It was also indicated that number of time steps in which density filter must be performed, plays an important role in achieving favorable results.

A 3D Free Surface Flow and Transport Model on Different High Performance Computation Architectures

Chapter 6 - Free Surface and Buoyancy Driven Flows

Numerical solution of the Giesekus model for incompressible free surface flows without solvent viscosity