A new VOF-based numerical scheme for the simulation of fluid flow with free surface. Part II: application to the cavity filling and sloshing problems

2003 ◽  
Vol 42 (7) ◽  
pp. 791-812 ◽  
Author(s):  
Min Soo Kim ◽  
Jong Sun Park ◽  
Woo Il Lee
Keyword(s):  
Fluid Flow ◽  
Free Surface ◽  
Numerical Scheme ◽  
Surface Part ◽  
Cavity Filling

The Introduction of Micro Cells to Treat Pressure in Free Surface Fluid Flow Problems

1995 ◽  
Vol 117 (4) ◽  
pp. 683-690 ◽  
Author(s):  
Peter E. Raad ◽  
Shea Chen ◽  
David B. Johnson
Keyword(s):  
Fluid Flow ◽  
Free Surface ◽  
Pressure Field ◽  
Flow Simulation ◽  
New Method ◽  
Computational Domain ◽  
Critical Feature ◽  
Flow Problems ◽  
Macro Cell ◽  
Marker And Cell Method

A new method of calculating the pressure field in the simulation of two-dimensional, unsteady, incompressible, free surface fluid flow by use of a marker and cell method is presented. A critical feature of the new method is the introduction of a finer mesh of cells in addition to the regular mesh of finite volume cells. The smaller (micro) cells are used only near the free surface, while the regular (macro) cells are used throughout the computational domain. The movement of the free surface is accomplished by the use of massless surface markers, while the discrete representation of the free surface for the purpose of the application of pressure boundary conditions is accomplished by the use of micro cells. In order to exploit the advantages offered by micro cells, a new general equation governing the pressure field is derived. Micro cells also enable the identification and treatment of multiple points on the free surface in a single surface macro cell as well as of points on the free surface that are located in a macro cell that has no empty neighbors. Both of these situations are likely to occur repeatedly in a free surface fluid flow simulation, but neither situation has been explicitly taken into account in previous marker and cell methods. Numerical simulation results obtained both with and without the use of micro cells are compared with each other and with theoretical solutions to demonstrate the capabilities and validity of the new method.

scholarly journals Modeling Free Surface Flows Using Stabilized Finite Element Method

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Deepak Garg ◽  
Antonella Longo ◽  
Paolo Papale
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Surface ◽  
Numerical Scheme ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Computer Code ◽  
Free Surface Flows ◽  
Surface Flows ◽  
Element Method

This work aims to develop a numerical wave tank for viscous and inviscid flows. The Navier-Stokes equations are solved by time-discontinuous stabilized space-time finite element method. The numerical scheme tracks the free surface location using fluid velocity. A segregated algorithm is proposed to iteratively couple the fluid flow and mesh deformation problems. The numerical scheme and the developed computer code are validated over three free surface problems: solitary wave propagation, the collision between two counter moving waves, and wave damping in a viscous fluid. The benchmark tests demonstrate that the numerical approach is effective and an attractive tool for simulating viscous and inviscid free surface flows.

Numerical Solution of Thermal and Fluid Flow With Phase Change by VOF Method

2000 ◽  
Author(s):  
Hidemi Shirakawa ◽  
Yasuyuki Takata ◽  
Takehiro Ito ◽  
Shinobu Satonaka
Keyword(s):  
Fluid Flow ◽  
Free Surface ◽  
Phase Change ◽  
Calculation Result ◽  
Bubble Growth ◽  
Present Method ◽  
Spherical Shape ◽  
Superheated Liquid ◽  
One Dimensional ◽  
Solidification Problem

Abstract Numerical method for thermal and fluid flow with free surface and phase change has been developed. The calculation result of one-dimensional solidification problem agrees with Neumann’s theoretical value. We applied it to a bubble growth in superheated liquid and obtained the result that a bubble grows with spherical shape. The present method can be applicable to various phase change problems.

Ideal planar fluid flow over a submerged obstacle: Review and extension

2021 ◽  
Vol 63 ◽  
pp. 377-419
Author(s):  
Larry K. Forbes ◽  
Stephen J. Walters ◽  
Graeme C. Hocking
Keyword(s):  
Fluid Flow ◽  
Free Surface ◽  
Steady State ◽  
Gravity Waves ◽  
Classical Problem ◽  
Time Dependent ◽  
Time Dependent Behaviour ◽  
Critical Overview ◽  
Dependent Behaviour ◽  
Obstacle Height

A classical problem in free-surface hydrodynamics concerns flow in a channel, when an obstacle is placed on the bottom. Steady-state flows exist and may adopt one of three possible configurations, depending on the fluid speed and the obstacle height; perhaps the best known has an apparently uniform flow upstream of the obstacle, followed by a semiinfinite train of downstream gravity waves. When time-dependent behaviour is taken into account, it is found that conditions upstream of the obstacle are more complicated, however, and can include a train of upstream-advancing solitons. This paper gives a critical overview of these concepts, and also presents a new semianalytical spectral method for the numerical description of unsteady behaviour. doi:10.1017/S1446181121000341

scholarly journals Unsplit complex frequency-shifted PML implementation using auxiliary differential equations for seismic wave modeling

Geophysics ◽  
2010 ◽  
Vol 75 (4) ◽  
pp. T141-T154 ◽  
Author(s):  
Wei Zhang ◽  
Yang Shen
Keyword(s):  
Free Surface ◽  
Finite Difference ◽  
Differential Equations ◽  
Seismic Wave ◽  
Numerical Scheme ◽  
Complex Frequency ◽  
Order Accuracy ◽  
First Order ◽  
Time Marching ◽  
Interior Domain

The complex-frequency-shifted perfectly matched layer (CFS-PML) technique can efficiently absorb near-grazing incident waves. In seismic wave modeling, CFS-PML has been implemented by the first-order-accuracy convolutional PML technique or second-order-accuracy recursive convolution PML technique. Both use different algorithms than the numerical scheme for the interior domain to update auxiliary memory variables in the PML and thus cannot be used directly with higher-order time-marching schemes. We work with an unsplit-field CFS-PML implementation using auxiliary differential equations (ADEs) to update the auxiliary memory variables. This ADE CFS-PML results in complete first-order differential equations. Thus, the numerical scheme for the interior domain can be used to solve ADE CFS-PML equations. We have implemented ADE CFS-PML in the finite-difference time-domain method and in anonstaggered-grid finite-difference method with the fourth-order Runge-Kutta scheme, demonstrating its straightforward implementation in different numerical time-marching schemes. We have also theoretically analyzed the role of the scalingfactor of CFS-PML; it transforms the PML to a transversely isotropic material, reducing the effective wave speed normal to the PML layer and bending the wavefront toward the normal direction of the PML layer. Our numerical tests indicate that the optimal value reduces the points per dominant wavelength at the outermost boundary to three, about half the value required by the numerical scheme. We also have found that the PML equations should be derived taking the free-surface boundary condition into account in finite-difference methods. Otherwise, the free surface in the PML layer causes instability or ineffective absorption of surface waves. Tests show that we can use a narrow-slice mesh with ADE CFS-PML to simulate full wave propagation efficiently in models with complex structure.

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