Numerical investigation of the interactions between solitary waves and pile breakwaters using BGK-based methods

AbstractThe interactions between a solitary wave, which can be used to model a leading tsunami wave, and a pile breakwater made of circular cylinders are numerically investigated. We use the depth-averaged shallow water equations, which are solved by the finite volume method based on the Bhatnagar–Gross–Krook (BGK) model. The numerical results are compared with the experimental data, which yields very good agreement between them when the ratio of wave height to water depth is small (<0.25). As this ratio exceeds the value of 0.25, the larger the ratio is, the bigger deviation of numerical results from experimental data is observed, the possible reasons for this observation are discussed. Both numerical and experimental results indicate that the transmission of the solitary wave decreases and the reflection of the wave increases with reducing gaps between the adjacent cylinders, and that both transmission and reflection coefficients are not very sensitive to the variation in wave height

A Junction and Drop-Shaft Boundary Conditions for Modeling Free Surface, Pressurized, and Mixed Free Surface-Pressurized Transient Flows

A junction and drop-shaft boundary conditions (BCs) for one-dimensional modeling of transient flows in single-phase conditions (pure liquid) are formulated, implemented and their accuracy are evaluated using two Computational Fluid Dynamics (CFD) models. The BCs are formulated for the case when mixed flows are simulated using two sets of govern- ing equations, the Saint Venant equations for the free surface regions and the compressible water hammer equations for the pressurized regions. The proposed BCs handle all possible flow regimes and their combinations. The flow in each pipe can range from free surface to pressurized flow and the water depth at the junction or drop-shaft can take on all possible levels. The BCs are applied to the following three cases: a three-way merging flow, a three- way dividing flow and a drop-shaft connected to a single-horizontal pipe subjected to a rapid variation of the water surface level in the drop-shaft. The flow regime for the first two cases range from free surface to pressurized flows, while for the third case, the flow regime is pure pressurized flow. For the third case, laboratory results as well as CFD results were used for evaluating its accuracy. The results suggest that the junction and drop-shaft boundary conditions can be used for modeling transient free surface, pressurized, and mixed flow conditions with good accuracy

Blockage detection in networks : The area reconstruction method

In this note we present a reconstructive algorithm for solving the cross-sectional pipe area from boundary measurements in a tree network with one inaccessible end. This is equivalent to reconstructing the first order perturbation to a wave equation on a quantum graph from boundary measurements at all network ends except one. The method presented here is based on a time reversal boundary control method originally presented by Sondhi and Gopinath for one dimensional problems and later by Oksanen to higher dimensional manifolds. The algorithm is local, so is applicable to complicated networks if we are interested only in a part isomorphic to a tree. Moreover the numerical implementation requires only one matrix inversion or least squares minimization per discretization point in the physical network. We present a theoretical solution existence proof, a step-by-step algorithm, and a numerical implementation applied to two numerical experiments.Peer reviewe

Weakly Nonlinear Analysis of Shallow Mixing Layers with Variable Friction

Methods of linear and weakly nonlinear stability theory are widely used for the analysis of shallow mixing layers. It is known that bottom friction in shallow water, where the horizontal length scale is significantly larger the flow depth, plays an important role for the development of instability.In the present paper we perform linear and weakly nonlinear stability analysis of shallow mixing layers with variable friction coefficient. One important case of a situation where friction force varies in the transverse direction is related to shallow flows during floods where water flows through partially vegetated area or in compound and composite channels

A numerical study of temporal shallow mixing layers using BGK-based schemes

A numerical study of the temporal shallow mixing layers is performed. The depth-averaged shallow water equations are solved by the finite volume method based on the Bhatnagar–Gross–Krook (BGK) equation. The filtering operation is applied to the governing equations and the well-known Smagorinsky model for the subgrid-scale (SGS) stress is employed in order to present a large eddy simulation (LES). The roll-up and pairing processes are clearly shown and the corresponding kinetic energy spectra are calculated. The effects of the Froude number and the bottom friction are numerically investigated. It is shown that the growth rate of the mixing layer decreases as the Froude number increases, which is very similar to the compressible mixing layers when considering the effects of the Mach number. The numerical results also indicate that the increase in bottom friction can enhance the stability of the flows, which is physically reasonable and consistent with the theoretical and experimental findings

Onset and Development of Instabilities in Shallow Shear Flows

Large scale coherent structures are prominent in free surface flows including estuaries, oceans, lakes and rivers. The structures are in the form of vortices with vertical axis which extend from the bed to the water surface and possess diameters that are far larger than the water depth. Understanding of such coherent structures is important for the mixing and transport of mass (e.g., pollutants and sediments), momentum and energy in surface water flows. The life of the structures involves birth, growth with downstream distance for part of the flow domain followed by decay and ultimately full disappearance. The mechanisms leading to birth and growth are believed to involve flow instabilities which, because of the near twodimensionality of the flow, evolve under the constraint of enstrophy and energy cascade. The energy and enstrophy constraint – a result of the suppression of vortex stretching due to the vertical confinement by the bed and free surface – promotes growth via vortex merging. On the other hand, the bottom friction, which represents the effect of the background three-dimensional turbulence on the large scale quasi-two dimensional turbulence, suppresses the large scale instabilities, limits their growth and causes them to eventually disappear with distance downstream. In this paper, the role of linear, weakly nonlinear and nonlinear hydrodynamic stability theories in illuminating the mechanisms of formation, growth and then decay of large scale structures in free shear flows is explained. For illustration purpose, the shallow mixing layer is used

A robust two-equation model for transient-mixed flows

A finite-volume model was built upon earlier work with the aim of simulating free surface flows, pressurized flows and their simultaneous occurrence (mixed flows) in single-liquid and two-phase flow conditions (entrapment and release of air pockets). The model presented herein is based on a two-governing equation model. Three main contributions are presented herein, namely (1) the ability of the proposed model to simulate mixed flows without restriction of the flow type in the free surface region (e. g. supercritical flow), (2) extension of our single-phase flow model for simulating the entrapment and release of air pockets and (3) formulation of an approach for handling numerical instabilities that may occur during numerical pressurization of the flow. The model presented herein is robust and simulates any transient-mixed flow condition for realistic pressure wave celerities