A free surface updating methodology for marker function-based Eulerian free surface capturing techniques on unstructured meshes

AbstractA model adopting the surface capturing method is developed for the simulation of dam-break flows by solving the Navier-Stokes equations of weakly compressible and variable density flows in open channels. Due to the characteristics of weakly compressible flow equations, a compressibility parameter describing the compressibility of fluid is determined to obtain the time-accurate flow fields in both liquid and gas regions simultaneously. Accordingly, the location of free surface can be captured as a discontinuity of the density field for dam-break flow simulations. The numerical algorithm in the proposed method is based on the framework of the finite volume method for discretization in space. To deal with the discontinuity property of fluid density near the free surface, the TVD-MUSCL scheme is adopted to overcome numerical oscillations and dissipation. For discretization in time, the explicit 4-stage Runge-Kutta scheme is employed in the model. Finally, several typical dam-break flow problems in open channel are simulated to demonstrate the validation and applicability of the proposed model.

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3D numerical modelling of scour around a jacket structure with dynamic free surface capturing

Ocean Engineering ◽

10.1016/j.oceaneng.2020.107104 ◽

2020 ◽

Vol 200 ◽

pp. 107104

Author(s):

Nadeem Ahmad ◽

Arun Kamath ◽

Hans Bihs

Keyword(s):

Free Surface ◽

Numerical Modelling ◽

3D Numerical Modelling ◽

Free Surface Capturing

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A Stern Slamming Analysis Using Three-Dimensional CFD Simulation

Volume 5: Materials Technology; CFD and VIV ◽

10.1115/omae2008-57805 ◽

2008 ◽

Cited By ~ 3

Author(s):

Kunho Kim ◽

Yung S. Shin ◽

Suqin Wang

Keyword(s):

Free Surface ◽

Cfd Simulation ◽

Two Phase Flow ◽

Three Dimensional ◽

Phase Flow ◽

Loading Conditions ◽

Two Phase ◽

Pressure Coefficients ◽

Free Surface Capturing ◽

Design Pressure

A stern slamming analysis based on three-dimensional computational fluid dynamics (CFD) simulation is presented with an application to a liquefied natural gas (LNG) carrier with twin skegs. This study includes; seakeeping analysis, statistical analysis for relative motions and velocities, three-dimensional slamming simulation by a CFD software, and structural assessment for plates and stiffeners. The stern areas are divided into panels in which relative velocity/motion and pressure coefficients are to be calculated. Seakeeping calculations are carried out in full load and ballast loading conditions at ship speeds of 0 and 5 knots. A series of equivalent 20-year return sea states in a wave scatter diagram are selected for environmental conditions. Extreme velocities are then evaluated from the loading conditions and the speeds considered with reference to the probability of slamming occurrence. Slamming simulations are carried out in a three-dimensional domain with a CFD software to calculate pressure coefficients. Two-phase flow with water and air is to be adopted in conjunction with free surface capturing method. Viscous laminar flow is assumed in simulation. Slamming design pressure is calculated by the pressure coefficients and the extreme velocities. Based on computed design pressure, an ultimate strength analysis is performed for the determination of required plate thickness. Also, required stiffener dimensions are determined by analytic formulas. As mentioned above, this approach has been applied to an LNG carrier with twin skegs. In the application, two-phase flow with water and air was adopted in conjunction with the volume-of-fluid method for free surface capturing. Mixed hexahedral and tetrahedral grids were employed. The computational case was determined from simulations of global ship motion. Maximum slamming pressure was found near the end of a skeg. Large pressure also can be observed in the stern overhang area. Generally slamming pressure decreases away from the stern.

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A level-set aided single-phase model for the numerical simulation of free-surface flow on unstructured meshes

Computers & Fluids ◽

10.1016/j.compfluid.2016.09.014 ◽

2016 ◽

Vol 140 ◽

pp. 97-110 ◽

Cited By ~ 4

Author(s):

Eugenio Schillaci ◽

Lluís Jofre ◽

Néstor Balcázar ◽

Oriol Lehmkuhl ◽

Assensi Oliva

Keyword(s):

Numerical Simulation ◽

Free Surface ◽

Level Set ◽

Single Phase ◽

Free Surface Flow ◽

Unstructured Meshes ◽

Surface Flow ◽

Phase Model

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Numerical Study of Advection Schemes for Interface Capturing in a Volume of Fluid Method on Unstructured Meshes

ASME-JSME-KSME 2011 Joint Fluids Engineering Conference: Volume 1, Symposia – Parts A, B, C, and D ◽

10.1115/ajk2011-04029 ◽

2011 ◽

Author(s):

Hua Shan ◽

Sung-Eun Kim

Keyword(s):

Free Surface ◽

Volume Fraction ◽

Numerical Study ◽

Volume Of Fluid ◽

Unstructured Meshes ◽

Higher Order ◽

Numerical Dispersion ◽

Numerical Dissipation ◽

Interface Capturing ◽

Advection Schemes

In solving naval hydrodynamics problems using computational fluid dynamics (CFD), the moving free surface between air and water introduces extra difficulties to numerical methods, since the material property jumps across the interface and the time-dependent free surface position becomes part of the solution. Engineering applications often require a flexible and robust solver for incompressible multi-phase viscous flows with the capability of capturing the interface. In the volume of fluid (VOF) method, the interface is captured by directly solving the convection transport equation of volume fraction. In this case, the numerical dissipation of the advection scheme smears the sharp interface and the numerical dispersion causes unphysical oscillations near the interface. Utilizing the guidance of boundedness criteria, many limited higher-order non-liner advection schemes have been developed in an attempt to balance numerical dissipation and dispersion. Though it is well-known that these non-linear advection schemes can lead to solutions combining boundednesss and accuracy, users are often overwhelmed by the wide variety of available schemes. Also, these schemes are developed with the assumption of a uniform Cartesian-type mesh. Thus, a thorough investigation and comparison of the performance of these interface-capturing advection schemes are necessary, especially for naval hydrodynamics problems solved on unstructured meshes. In this study, a systematic comparison and evaluation of several existing and new bounded, higher-order advection schemes has been conducted within the framework of NavyFOAM, which is developed based on OpenFOAM — an object orientated C++ toolbox for the customization and extension of numerical solvers for continuum mechanics problems, including CFD, where the governing equations are discretized using the cell-centered finite volume method on unstructured mesh. The flexible infrastructure of the code enables us to implement and test the selected advection schemes very quickly. The test cases include advection of hollow cylinders, Zalesak’s rotating slotted disk, traveling solitary wave, dam breaking problem.

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A Three-Dimensional Version of the Free Surface Capturing Discretization for Staggered Grid Finite Difference Schemes: Implementation into StagYY

10.5194/egusphere-egu21-16228 ◽

2021 ◽

Author(s):

Paul Tackley

Keyword(s):

Free Surface ◽

Finite Difference ◽

Three Dimensional ◽

Small Time ◽

Staggered Grid ◽

Finite Difference Schemes ◽

Finite Volume Scheme ◽

Two Dimensional ◽

Simulation Code ◽

Free Surface Capturing

In order to treat a free surface in models of lithosphere and mantle dynamics that use a fixed Eulerian grid it is typical to use "sticky air", a layer of low-viscosity, low-density material above the solid surface (e.g. Crameri et al., 2012). This can, however, cause numerical problems, including poor solver convergence due to the huge viscosity jump and small time-steps due to high velocities in the air. Additionally, it is not completely realistic because the assumed viscosity of the air layer is typically similar to that of rock in the asthenosphere so the surface is not stress free. &#160;In order to overcome these problems, Duretz et al. (2016) introduced and tested a method for treating the free surface that instead detects and applies special conditions at the free surface. This avoids the huge viscosity jump and having to solve for velocities in the air. They applied it to a two-dimensional staggered grid finite difference / finite volume scheme, a discretization that is in common use for modelling mantle and lithosphere dynamics. Here I document the application of this approach to a three-dimensional spherical staggered grid solver in the mantle simulation code StagYY. Some adjustments had to be made to the two-dimensional scheme documented in Duretz et al. (2016) in order to avoid problems due to undefined velocities for certain boundary topographies. The approach was applied not only to the Stokes solver but also to the temperature solver, including the implementation of a mixed radiative/conductive boundary condition applicable to surface magma oceans/lakes.ReferencesCrameri, F., H. Schmeling, G. J. Golabek, T. Duretz, R. Orendt, S. J. H. Buiter, D. A. May, B. J. P. Kaus, T. V. Gerya, and P. J. Tackley (2012), A comparison of numerical surface topography calculations in geodynamic modelling: an evaluation of the &#8216;sticky air&#8217; method, Geophysical Journal International,189(1), 38-54, doi:10.1111/j.1365-246X.2012.05388.x.Duretz, T., D. A. May, and P. Yamato (2016), A free surface capturing discretization for the staggered grid finite difference scheme, Geophysical Journal International, 204(3), 1518-1530, doi:10.1093/gji/ggv526.

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