Sequential Cavity Method for Computing Free Energy and Surface Pressure

The gravity-driven free surface flow problems for which both the solid and free surface boundaries are highly curved are very difficult to solve. A computational scheme using a variable domain and a fixed domain natural element method (NEM) is developed in the present study for the computation of the free surface profile, velocity and pressure distributions, and the flow rate of a 2D gravity fluid flow through a conduit and under a radial gate. The problem involves two highly curved unknown free surfaces and arbitrary curved-shaped boundaries. These features make the problem more complicated than flow under a sluice gate or over a weir. The fluid is assumed to be inviscid and incompressible and the results obtained are confirmed by conducting a hydraulic model test. The results are in agreement with other flow solutions for free surface profiles and pressure distributions.

A liquid sloshing experimental rig driven by a wave-maker is designed and built to study liquid sloshing problems in a rectangular liquid tank with perforated baffle. A series of experiments are conducted in this experimental rig to estimate the free surface fluctuation and pressure distribution by changing external excitation frequency of the shaking table. An in-house CFD code is also used in this study to simulate the liquid sloshing in three-dimensional (3D) rectangular tank with perforated baffle. Good agreements of free surface elevation and pressure between the numerical results and the experimental data are obtained and presented. Spectral analysis of the time history of free surface elevation is conducted by using the fast Fourier transformation.

The basic principle and numerical technique for simulating two three-dimensional bubbles near a free surface are studied in detail by using boundary element method. The singularities of influence coefficient matrix are eliminated using coordinate transformation and so-called 4π rule. The solid angle for the open surface is treated in direct method based on its definition. Several kinds of configurations for the bubbles and free surface have been investigated. The pressure contours during the evolution of bubbles are ob- tained in our model and can better illuminate the mechanism underlying the motions of bubbles and free surface. The bub- ble dynamics and their interactions have close relation with the standoff distances, buoyancy parameters and initial sizes of bubbles. Completely different bubble shapes, free surface motions, jetting patterns and pressure distributions under dif- ferent parameters can be observed in our model, as demon- strated in our calculation results.

Water impact phenomenon in the case of a circular cylinder is an important issue in offshore industry where cross members may be in the splash zone of the incident wave. An analytical method as well as a numerical solution are employed to study the water entry problem of a circular section. The procedure for derivation of the analytical formulas is demonstrated step by step. The volume of fluid (VOF) simulation of the water entry problem is also performed to offer comparison of the results of the linearized analytical solution with a fully nonlinear and viscous fluid flow solution. To achieve this, the FLOW-3D code is utilized. Some consideration has also been given to the points of intersection of the free surface and the body, where the singularities exist in the free surface deformation and velocities, as predicted by the linear theory. These singularities appear to be avoided in the real fluid by the formation of jets which quickly break up into sprays under the action of surface tension. Slamming force, free surface profile, impact force, pressure distribution and evolution of intersection points are also presented and comparisons of the obtained results against the results of previous studies illustrate favorable agreements.

Water entry is a fluid–structure interaction process closely related to the ocean environment. Repeated water entries take place when ships are sailing in an ocean environment, e.g., ocean currents, which greatly affect the ship's safety and stability in navigation. In this paper, we adopt a smoothed particle hydrodynamics method to numerically study the water entry of a bow-flare ship body section under ocean currents. We simulate the process of water entry under different current velocities and analyze in detail the fluid field regarding the free surface evolution, the velocity and pressure distributions, and the body's forces and motions. It is revealed that the ocean current can induce multidirectional fluid impacts, and a stagnation point with zero velocity occurs at the upstream side. Asymmetric fluid fields including the evolution of the free surface and the velocity and pressure distributions around the body can also be found. In addition, discrepancies are caused in the formation time and the range of the high-pressure region. These fluid field changes greatly affect the ship body's dynamic responses. However, the effects of the ocean current are mainly reflected in the direction of the current flow and are relatively small in the direction perpendicular to the flow.

Seawall is a most commonly used structure in coastal areas to protect the landscape and coastal facilities. The studies of interactions between the tsunami-like solitary waves and the seawalls are relatively rare in the literature. In this study, a three-dimensional numerical model based on OpenFOAM® was developed to investigate the tsunami-like solitary waves propagating over a rectangular seawall. The Navier–Stokes equations for two-phase incompressible flow, combining with methods of [Formula: see text] for turbulence closure and Volume of Fluid (VOF) for tracking the free surface, were solved. Laboratory experiments were performed to measure some of the hydrodynamic feature associated with solitary waves. The model was then validated by the laboratory data, and good agreements were found for free surface, velocity and dynamic pressure around the seawall. Finally, a series of numerical experiments were conducted to analyze the evolution of both wave and flow fields, the overtopping discharge as well as wave pressure (force) around the seawall, special attention is given to the effects of seawall crest width. Our findings will help to improve the understanding in the occurrences of tsunami-induced damages in the vicinity of seawall such as wave impact and local scouring.

Many biomolecules undergo conformational changes associated with allostery or ligand binding. Observing these changes in computer simulations is difficult if their timescales are long. These calculations can be accelerated by observing the transition on an auxiliary free energy surface with a simpler Hamiltonian and connecting this free energy surface to the target free energy surface with free energy calculations. Here, we show that the free energy legs of the cycle can be replaced with energy representation (ER) density functional approximations. We compute: (1) The conformational free energy changes for alanine dipeptide transitioning from the right-handed free energy basin to the left-handed basin and (2) the free energy difference between the open and closed conformations of β-cyclodextrin, a "host" molecule that serves as a model for molecular recognition in host-guest binding. β-cyclodextrin contains 147 atoms compared to 22 atoms for alanine dipeptide, making β-cyclodextrin a large molecule for which to compute solvation free energies by free energy perturbation or integration methods and the largest system for which the ER method has been compared to exact free energy methods. The ER method replaced the 28 simulations to compute each coupling free energy with two endpoint simulations, reducing the computational time for the alanine dipeptide calculation by about 70% and for the β-cyclodextrin by > 95%. The method works even when the distribution of conformations on the auxiliary free energy surface differs substantially from that on the target free energy surface, although some degree of overlap between the two surfaces is required. © 2016 Wiley Periodicals, Inc.

In this work a novel meshless technique for mold filling simulation is presented. The governing equation for this kind of problem is named Hele-Shaw and it is derivated applying some simplifications on the 3D conservation equations. This approach is also commonly called 21/2D, referring to limitations of the mold geometry to narrow and weakly curved channels. Since products manufactured by injection molding in real life, as for example buckets, automobiles bumpers and cell phone casings, are not expected to be planar, in this work the mold cavity is modeled by point set surfaces. Thus, no computational effort referring to either mesh generation or mesh maintenance is required for the numerical solution of the governing equations. The developed technique for simulating the free surface position, velocity and pressure distribution in the injection molding process using this 21/2D approach is presented and discussed. The details of our framework, which is based on Smoothed Particle Hydrodynamics Method and a Meshless Volume of Fluid Method is also presented.

Adiabatic free energy dynamics (AFED) was introduced by Rosso et al. [J. Chem. Phys. 2002, 116, 4389] for computing free energy profiles quickly and accurately using a dynamical adiabatic separation between a set of collective variables or reaction coordinates and the remaining degrees of freedom of a system. This approach has been shown to lead to a significant gain in efficiency versus traditional methods such as umbrella sampling, thermodynamic integration, and free energy perturbation for generating one-dimensional free energy profiles. More importantly, AFED is able to generate multidimensional free energy surfaces efficiently via full sweeps of the surface that rapidly map out the locations of the free energy minima. The most significant drawback to the AFED approach is the need to transform the coordinates into a generalized coordinate system that explicitly contains the collective variables of interest. Recently, Maragliano and Vanden-Eijnden built upon the AFED approach by introducing a set of extended phase-space variables, to which the adiabatic decoupling and high temperature are applied [Chem. Phys. Lett. 2006, 426, 168]. In this scheme, which the authors termed "temperature accelerated molecular dynamics" or TAMD, the need for explicit coordinate transformations is circumvented. The ability of AFED and TAMD to generate free energy surfaces efficiently depends on the thermostatting mechanism employed, since both approaches are inherently nonequilibrium due to the adiabatic decoupling. Indeed, Maragliano and Vanden-Eijnden did not report any direct generation of free energy surfaces within the overdamped Langevin dynamics employed by these authors. Here, we show that by formulating TAMD in a manner that is closer to the original AFED approach, including the generalized Gaussian moment thermostat (GGMT) and multiple time-scale integration, multidimensional free energy surfaces for complex systems can be generated directly from the probability distribution function of the extended phase-space variables. The new TAMD formulation, which we term driven AFED or d-AFED, is applied to compare the conformational preferences of small peptides both in gas phase and in solution for three force fields. The results show that d-AFED/TAMD accurately and efficiently generates free energy surfaces in two collective variables useful for characterizing the conformations, namely, the radius of gyration, R(G), and number of hydrogen bonds, N(H).

Abstract. The sensitivity of the dynamics of the Mediterranean Sea to atmospheric pressure and free surface elevation formulation using NEMO (Nucleus for European Modelling of the Ocean) was evaluated. Four different experiments were carried out in the Mediterranean Sea using filtered or explicit free surface numerical schemes and accounting for the effect of atmospheric pressure in addition to wind and buoyancy fluxes. Model results were evaluated by coherency and power spectrum analysis with tide gauge data. We found that atmospheric pressure plays an important role for periods shorter than 100 days. The free surface formulation is important to obtain the correct ocean response for periods shorter than 30 days. At frequencies higher than 15 days−1 the Mediterranean basin's response to atmospheric pressure was not coherent and the performance of the model strongly depended on the specific area considered. A large-amplitude seasonal oscillation observed in the experiments using a filtered free surface was not evident in the corresponding explicit free surface formulation case, which was due to a phase shift between mass fluxes in the Gibraltar Strait and at the surface. The configuration with time splitting and atmospheric pressure always performed best; the differences were enhanced at very high frequencies.

Using exact computations we study the classical hard-core monomer-dimer models on m x n plane lattice strips with free boundaries. For an arbitrary number v of monomers (or vacancies), we found a logarithmic correction term in the finite-size correction of the free energy per lattice site. The coefficient of the logarithmic correction term depends on the number of monomers present (v) and the parity of the width n of the lattice strip: the coefficient equals to v when n is odd, and v/2 when n is even. The results are generalizations of the previous results for a single monomer in an otherwise fully packed lattice of dimers. We also study the finite-size correction in the low dimer density limit, where the number of dimers d is fixed. In this case the coefficient of the logarithmic correction term equals to d, for both odd and even n.

A finite-element algorithm for computing free-surface flows driven by arbitrary body forces is presented. The algorithm is primarily designed for the microfluidic parameter range where (i) the Reynolds number is small and (ii) force-driven pressure and flow fields compete with the surface tension for the shape of a stationary free surface. The free surface shape is represented by the boundaries of finite elements that move according to the stress applied by the adjacent fluid. Additionally, the surface tends to minimize its free energy and by that adapts its curvature to balance the normal stress at the surface. The numerical approach consists of the iteration of two alternating steps: The solution of a fluidic problem in a prescribed domain with slip boundary conditions at the free surface and a consecutive update of the domain driven by the previously determined pressure and velocity fields. For a Stokes problem the first step is linear, whereas the second step involves the nonlinear free-surface boundary condition. This algorithm is justified both by physical and mathematical arguments. It is tested in two dimensions for two cases that can be solved analytically. The magnitude of the errors is discussed in dependence on the approximation order of the finite elements and on a step-width parameter of the algorithm. Moreover, the algorithm is shown to be robust in the sense that convergence is reached also from initial forms that strongly deviate from the final shape. The presented algorithm does not require a remeshing of the used grid at the boundary. This advantage is achieved by a built-in mechanism that causes a smooth change from the behavior of a free surface to that of a rubber blanket if the boundary mesh becomes irregular. As a side effect, the element sides building up the free surface in two dimensions all approach equal lengths. The presented variational derivation of the boundary condition corroborates the numerical finding that a second-order approximation of the velocity also necessitates a second-order approximation for the free surface discretization.

A comparison study of water impact and water exit models

ABSTRACTIn this paper, a domain-topology-based, two-phase, incompressible flow model is proposed to simulate transient flow variations associated with the gate opening motions of water conservancy projects, such as hydropower stations with plain and radial gates. The research source code is written in the OpenFOAM platform and incorporates the interDyMFoam solver. Two benchmark experiments were performed in the laboratory to validate the numerical results. The water level, pressure, flow pattern and development of vortices were recorded for comparison with numerical solutions. The results show that the relative error associated with the weir flow time was less than 5.00%. Moreover, good agreement was obtained between the time history curves of the free surface elevation and pressure based on numerical and experiment results. The detailed flow pattern reflects the simulation capability of the model, which can be used to numerically investigate the generation mechanisms of vertical vortices around gate grooves. The proposed model can be applied to further investigate flow variations in real hydraulic engineering applications.

An eigenfunction expansion is used to calculate a solution for wave movement in an axisymmetric tank of liquid that is accelerated horizontally by an earthquake. Fluid motion is assumed to be irrotational and incompressible, and tank boundaries are assumed to be rigid. A major portion of the solution is obtained from the numerical solution of an integral equation eigenvalue problem. A comparison between solutions calculated for a cylindrical tank and a conical tank, both filled with equal volumes of liquid, shows that solutions for free surface displacements and pressure forces are similar in magnitude and behavior, but that moments created by the fluid pressure differ considerably.