scholarly journals NUMERICAL MODELLING OF KINEMATICS AND DYNAMICS OF SPILLING AND PLUNGING BREAKERS IN SHALLOW WATERS

2018 ◽  
pp. 4
Author(s):  
Mayilvahanan Alagan Chella ◽  
Hans Bihs
Keyword(s):  
Free Surface ◽  
Wave Breaking ◽  
Two Phase Flow ◽  
Staggered Grid ◽  
Shallow Waters ◽  
Phase Flow ◽  
Two Phase ◽  
Linear Interaction ◽  
Water Interaction ◽  
Non Linear

Wave breaking is a complex two-phase flow process that strongly influences the air-water interaction. A number of physical processes are involved in the exchange of mass, momentum and energy between air and water interaction during the wave breaking process. In shallow waters, waves undergo different transformation processes such as shoaling, refraction, diffraction and breaking due to their non-linear interaction with the seabed. Thus, the associated hydrodynamics are rather complicated to understand when compared to wave breaking in deep water (Lin, 2008). In the present numerical study, a two phase flow CFD model REEF3D (Bihs et al. 2016) is used to model and investigate the hydrodynamics of spilling and plunging breakers over a slope. An accurate modeling of the wave breaking process is still highly demanding due to the strong non-linear air-water interaction and turbulent production at the free surface. The numerical wave tank is based on the incompressible Reynolds Averaged Navier-Stokes (RANS) equations together with the level set method for free surface and the k-ω model for turbulence (Alagan Chella et al. 2015). The model uses the 5th-order Weighted Essentially Non- Oscillatory (WENO) scheme for the convective discretization and the 3rd-order TVD Runge Kutta Scheme for the time discretization. A staggered grid method is employed in the model in order to achieve a stronger coupling between the pressure and velocity. The model is fully parallelized with the domain decomposition method and MPI (Message passing interface).

Magma dynamics using FD-PDE: a new, PETSc-based, finite-difference staggered-grid framework for solving partial differential equations

2020 ◽  
Author(s):  
Adina E. Pusok ◽  
Dave A. May ◽  
Richard F. Katz
Keyword(s):  
Free Surface ◽  
Partial Differential Equations ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Differential Operators ◽  
Two Phase Flow ◽  
Flow Dynamics ◽  
Staggered Grid ◽  
Phase Flow ◽  
Two Phase

<p>All divergent plate boundaries are associated with magmatism, yet its role in their dynamics and deformation is not known. The RIFT-O-MAT project seeks to understand how magmatism promotes and shapes rifts in continental and oceanic lithosphere by using models that build upon the two-phase flow theory of magma/rock interaction. Numerical models of magma segregation from partially molten rocks are usually based on a system of equations for conservation of mass, momentum and energy. One key challenge of these problems is to compute a mass-conservative flow field that is suitable for advecting thermochemically active material that feeds back on the flow. This feedback tends to destabilise the coupled mechanics+thermochemical solver. </p><p>Staggered grid finite-volume/difference methods are: mimetic (i.e., discrete differential operators mimic the properties of the continuous differential operators); conservative by construction; inf-sup stable and "light weight" (small stencil) thus they are well suited to address these problems. We present a new framework for finite difference staggered grids for solving partial differential equations (FD-PDE) that allows testable and extensible code for single-/two-phase flow magma dynamics. We build the framework using PETSc (Balay et al., 2019) and make use of the new features for staggered grids, such as DMStag. The aim is to separate the user input from the discretization of governing equations, allow for extensible development, and implement a robust framework for testing. Any customized applications can be created easily, without interfering with previous work or tests.</p><p>Here, we present benchmark and performance results with our new FD-PDE framework. In particular, we focus on preliminary results of a two-phase flow mid-ocean ridge (MOR) model with a free surface and extensional boundary conditions. We compare flow calculations with previous work on MORs that either employed two-phase flow dynamics with kinematic boundary conditions (i.e., corner flow, Spiegelman and McKenzie, 1987), or single-phase flow dynamics with free surface (i.e., Behn and Ito, 2008). In the latter case, the effect of magma is parameterised according to a priori expectations of its role. </p><p> </p><p>Balay et al. (2019), PETSc Users Manual, ANL-95/11 - Revision 3.12, 2019.</p><p>Spiegelman and McKenzie (1987), EPSL, 83 (1-4), 137-152.</p><p>Behn and Ito (2008), Geochem. Geophys. Geosyst., 9, Q08O10.</p>

CFD Simulations of Breaking Stokes Waves

2019 ◽  
Author(s):  
Takanori Hino ◽  
Harushi Ikenoue ◽  
Youhei Takagi
Keyword(s):  
Free Surface ◽  
Wave Breaking ◽  
Single Phase ◽  
Two Phase Flow ◽  
Surface Boundary ◽  
Phase Flow ◽  
Two Phase ◽  
Flow Models ◽  
Phase Approach ◽  
Stokes Waves

Abstract Free surface flow simulations using CFD (Computational Fluid Dynamics) can be categorized into two approaches in terms of free surface modeling. One is a two-phase flow model which solves both water and air. The other is a single-phase approach in which only the water region is solved with free surface boundary conditions. Breaking waves have been simulated by many researchers using CFD techniques with two-phase flow models in the most cases. In ship flow CFD applications, however, a single-phase approach is often used since this is considered to be more effective and efficient. However, when a single-phase method is applied to flows with bow wave breaking of a blunt ship, it is observed in some cases that numerical solutions fail to reproduce wave breaking well. This may be due to the differences of the air-water interface treatment between two-phase and single-phase approaches. To investigate these differences, breaking of Stokes waves is simulated by using both single-phase and two-phase flow models. The comparisons of single-phase and two-phase approaches are made in wave profiles, pressure and vorticity distributions. The velocity distributions near the free surface boundaries are also compared. Through these comparisons, impact of free surface boundary conditions in a single-phase approach to wave breaking phenomena is discussed.

Free surface models of partially molten rock with visco-elasto–plastic rheology: numerical solutions using a staggered-grid finite-difference discretisation 

2021 ◽  
Author(s):  
Yuan Li ◽  
Adina Pusok ◽  
Dave May ◽  
Richard Katz
Keyword(s):  
Free Surface ◽  
Finite Difference ◽  
Phase Field ◽  
Numerical Solutions ◽  
Two Phase Flow ◽  
Staggered Grid ◽  
Phase Flow ◽  
Two Phase ◽  
Rock Interaction ◽  
Pde Framework

<p>It is broadly accepted that magmatism plays a key dynamic role in continental and oceanic rifting. However, these dynamics remain poorly studied, largely due to the difficulty of consistently modelling liquid/solid interaction across the lithosphere. The RIFT-O-MAT project seeks to quantify the role of magma in rifting by using models that build upon the two-phase flow theory of magma/rock interaction. A key challenge is to extend the theory to account for the non-linear rheological behaviour of the host rocks, and investigate processes such as diking, faulting and their interaction. Here we present our progress in consistent numerical modelling of poro-viscoelastic–plastic modelling of deformation with a free surface.</p><p>Failure of rocks (plasticity) is an essential ingredient in geodynamics models because Earth materials cannot sustain unbounded stresses. However, plasticity represents a non-trivial problem even for single-phase flow formulations (Spiegelman et al. 2016). The elastic deformation of rocks can also affect the propagation of internal failure. Furthermore, deformation and plastic failure drives topographic change, which imposes a significant static stress field. Robustly solving a discretised model that includes this physics presents severe challenges, and many questions remain as to effective solvers for these strongly nonlinear systems. </p><p>We present a new finite difference staggered grid framework for solving partial differential equations (FD-PDE) for single-/two-phase flow magma dynamics (Pusok et al., 2020). Staggered grid finite-difference methods are mimetic, conservative, inf-sup stable and with small stencil — thus they are well suited to address these problems. The FD-PDE framework uses PETSc (Balay et al., 2020) and aims to separate the user input from the discretization of governing equations. The core goals for the FD-PDE framework is to allow for extensible development and implement a framework for rigorous code validation. Here, we present simplified model problems using the FD-PDE framework for two-phase flow visco-elasto-plastic models designed to characterise the solution quality and assess both the discretisation and solver robustness. We also present results obtained using the phase-field method (Sun and Beckermann, 2007) for representing the free surface. Verification of the phase-field approach will be shown via simplified problems previously examined in the geodynamics community (Crameri et al, 2012).</p><p>Balay et al. (2020), PETSc Users Manual, ANL-95/11 - Revision 3.13.</p><p>Pusok et al. (2020) https://doi.org/10.5194/egusphere-egu2020-18690 </p><p>Spiegelman et al. (2016) https://doi.org/10.1002/2015GC006228</p><p>Sun and Beckermann (2007) https://doi.org/10.1016/j.jcp.2006.05.025</p><p>Crameri et al. (2012) https://doi.org/10.1111/j.1365-246X.2012.05388.x</p><div> <div><span></span><div></div> </div> <div></div> </div><div> <div><span></span><div></div> </div> <div></div> </div>

Gradient-Augmented Level Set Two-Phase Flow Method With Pretreated Reinitialization for Three-Dimensional Violent Sloshing

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Jianjian Xin ◽  
Fulong Shi ◽  
Qiu Jin ◽  
Lin Ma
Keyword(s):  
Free Surface ◽  
Level Set ◽  
Two Phase Flow ◽  
Three Dimensional ◽  
Surface Shape ◽  
Phase Flow ◽  
Two Phase ◽  
Correction Technique ◽  
Highly Nonlinear ◽  
Violent Sloshing

Abstract A three-dimensional (3D) gradient-augmented level set (GALS) two-phase flow model with a pretreated reinitialization procedure is developed to simulate violent sloshing in a cuboid tank. Based on a two-dimensional (2D) GALS method, 3D Hermite, and 3D Lagrange polynomial schemes are derived to interpolate the level set function and the velocity field at arbitrary positions over a cell, respectively. A reinitialization procedure is performed on a 3D narrow band to treat the strongly distorted interface and improve computational efficiency. In addition, an identification-correction technique is proposed and incorporated into the reinitialization procedure to treat the tiny droplet which can distort the free surface shape, even lead to computation failure. To validate the accuracy of the present GALS method and the effectiveness of the proposed identification-correction technique, a 3D velocity advection case is first simulated. The present method is validated to have better mass conservation property than the classical level set and original GALS methods. Also, distorted and thin interfaces are well captured on all grid resolutions by the present GALS method. Then, sloshing under coupled surge and sway excitation, sloshing under rotational excitation are simulated. Good agreements are obtained when the present wave and pressure results are compared with the experimental and numerical results. In addition, the highly nonlinear free surface is observed, and the relationship between the excitation frequency and the impulsive pressure is investigated.

scholarly journals Study on the internal two-phase flow of the inverted-umbrella aerator

2019 ◽  
Vol 11 (8) ◽  
pp. 168781401987173 ◽  
Author(s):  
Liang Dong ◽  
Jiawei Liu ◽  
Houlin Liu ◽  
Cui Dai ◽  
Dmitry Vladimirovich Gradov
Keyword(s):  
Free Surface ◽  
Velocity Distribution ◽  
Surface Deformation ◽  
Two Phase Flow ◽  
Back Surface ◽  
High Speed Photography ◽  
Aeration Tank ◽  
Phase Flow ◽  
Two Phase ◽  
Radial Profiles

In order to reveal the gas–liquid two-phase flow pattern of inverted-umbrella aerator, the high-speed photography technology, particle image velocimetry, and Volume of Fluid model are employed to capture the free-surface dynamics and velocity distribution. The Computational Fluid Dynamics simulations are validated by experimental data and the results are in good agreement with experiment. The simulation results of flow field, streamline distribution, velocity distribution, free-surface deformation, and turbulence kinetic energy are analyzed at in time and at radial profiles sampled at several vertical positions. Back surface of each blade revealed the area of low-pressure, which can drag air into water directly from surface and thus enhance liquid aeration and oxygenation capacity. Lifting capacity of the inverted-umbrella aerator is enough to get the liquid at the bottom of the aeration tank accelerated toward liquid surface generating the hydraulic jump. As a result, liquid phase splashes capture portions of air promoting aeration of the solution. A clear circulation whirlpool is formed during the process. The circulation whirlpool starts at the bottom of the impeller moving upward along the plate until the outer edge of the impeller, which is close to the free surface. The circulation whirlpool indicates that the inverted-umbrella aerator plays a significant role in shallow aeration. The turbulence intensity created by the impeller gradually reduces with depth. The position ( z = 0.65 H) is the watershed in the tank. The oxygen mass transfer mainly occurs in the layer above watershed.

A Two-Phase Flow Model with VOF for Free Surface Flow Problems

2012 ◽  
Vol 232 ◽  
pp. 279-283 ◽  
Author(s):  
Wei Zhang ◽  
You Hong Tang ◽  
Cheng Bi Zhao ◽  
Cheng Zhang
Keyword(s):  
Free Surface ◽  
Flow Model ◽  
Two Phase Flow ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Phase Model ◽  
Phase Flow ◽  
Two Phase ◽  
Flow Problems ◽  
Fluid Sloshing

A numerical model based on the two-phase flow model for incompressible viscous fluid with a complex free surface has been developed in this study. The two-step projection method is employed to solve the Navier–Stokes equations in the numerical solutions, and finite difference method on a staggered grid is used throughout the computation. The two-order accurate volume of fluid (VOF) method is used to track the distorted and broken free surfaces. The two-phase model is first validated by simulating the dam break over a dry bed, in which the numerical results and experimental data agree well. Then 2-D fluid sloshing in a horizontally excited rectangular tank at different excitation frequencies is simulated using this two-phase model. The results of this study show that the two-phase flow model with VOF method is a potential tool for the simulation of nonlinear fluid sloshing. These studies demonstrate the capability of the two-phase model to simulate free surface flow problems with considering air movement effects.

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