A New Computational Method for Free Surface Problems

2005 ◽  
Author(s):  
Jeremy Rice ◽  
Amir Faghri
Keyword(s):  
Free Surface ◽  
Capillary Tube ◽  
Accurate Method ◽  
Computational Method ◽  
Surface Velocity ◽  
Governing Equations ◽  
Two Fluids ◽  
Correction Technique ◽  
Instability Growth ◽  
A New Technique

A new technique, called the surface velocity correction technique (SVC), is developed to track a free surface such as a liquid-vapor interface. SVC is a computationally inexpensive, and accurate method to capture interfacial fluid phenomena. This method uses a finite volume technique to discretize the governing equations, and a semi-Legrangian mesh to locate the interface between two fluids. The effectiveness of this technique is demonstrated through several classical examples and the results are also compared to both analytical and VOF solutions. The examples include: the shape of a meniscus in a capillary tube in mechanical equilibrium, the rise of a meniscus in a capillary tube, and the instability growth of a free flowing cylindrical column of fluid.

scholarly journals A Computational Method for Free Surface Hydrodynamics

1981 ◽  
Vol 103 (2) ◽  
pp. 136-141 ◽  
Author(s):  
C. W. Hirt ◽  
B. D. Nichols
Keyword(s):  
Free Surface ◽  
Computational Method ◽  
Free Fluid ◽  
Immiscible Fluid ◽  
Fluid Interfaces ◽  
Vapor Bubbles ◽  
Piping Systems ◽  
Flow Phenomena ◽  
A New Technique ◽  
Local Average

There are numerous flow phenomena in pressure vessel and piping systems that involve the dynamics of free fluid surfaces. For example, fluid interfaces must be considered during the draining or filling of tanks, in the formation and collapse of vapor bubbles, and in seismically shaken vessels that are partially filled. To aid in the analysis of these types of flow phenomena, a new technique has been developed for the computation of complicated free-surface motions. This technique is based on the concept of a local average volume of fluid (VOF) and is embodied in a computer program for two-dimensional, transient fluid flow called SOLA-VOF. The basic approach used in the VOF technique is briefly described, and compared to other free-surface methods. Specific capabilities of the SOLA-VOF program are illustrated by generic examples of bubble growth and collapse, flows of immiscible fluid mixtures, and the confinement of spilled liquids.

scholarly journals Mathematical modelling of the overflowing cylinder experiment

2003 ◽  
Vol 474 ◽  
pp. 275-298 ◽  
Author(s):  
P. D. HOWELL ◽  
C. J. W. BREWARD
Keyword(s):  
Free Surface ◽  
Surfactant Concentration ◽  
Dynamic Properties ◽  
Vertical Cylinder ◽  
Surfactant Solution ◽  
Surface Concentration ◽  
Experimental Results ◽  
Surface Velocity ◽  
Experimental Apparatus ◽  
Finite Distance

The overflowing cylinder (OFC) is an experimental apparatus designed to generate a controlled straining flow at a free surface, whose dynamic properties may then be investigated. Surfactant solution is pumped up slowly through a vertical cylinder. On reaching the top, the liquid forms a flat free surface which expands radially before over flowing down the side of the cylinder. The velocity, surface tension and surfactant concentration on the expanding free surface are measured using a variety of non-invasive techniques.A mathematical model for the OFC has been previously derived by Breward et al. (2001) and shown to give satisfactory agreement with experimental results. However, a puzzling indeterminacy in the model renders it unable to predict one scalar parameter (e.g. the surfactant concentration at the centre of the cylinder), which must be therefore be taken from the experiments.In this paper we analyse the OFC model asymptotically and numerically. We show that solutions typically develop one of two possible singularities. In the first, the surface concentration of surfactant reaches zero a finite distance from the cylinder axis, while the surface velocity tends to infinity there. In the second, the surfactant concentration is exponentially large and a stagnation point forms just inside the rim of the cylinder. We propose a criterion for selecting the free parameter, based on the elimination of both singularities, and show that it leads to good agreement with experimental results.

Sloshing in Rectangular and Cylindrical Tanks

2002 ◽  
Vol 46 (03) ◽  
pp. 186-200 ◽  
Author(s):  
Pierre C. Sames ◽  
Delphine Marcouly ◽  
Thomas E. Schellin
Keyword(s):  
Free Surface ◽  
Finite Volume ◽  
Temporal Evolution ◽  
Numerical Study ◽  
Computational Method ◽  
Test Cases ◽  
Grid Refinement ◽  
Cylindrical Tank ◽  
Excitation Period ◽  
Cylindrical Tanks

To validate an existing finite volume computational method, featuring a novel scheme to capture the temporal evolution of the free surface, fluid motions in partially filled tanks were simulated. The purpose was to compare computational and experimental results for test cases where measurements were available. Investigations comprised sloshing in a rectangular tank with a baffle at 60% filling level and in a cylindrical tank at 50% filling level. The numerical study started with examining effects of systematic grid refinement and concluded with examining effects of three-dimensionality and effects of variation of excitation period and amplitude. Predicted time traces of pressures and forces compared favorably with measurements.

LOCALIZED RADIAL BASIS FUNCTIONS FOR NO-ARBITRAGE PRICING OF OPTIONS UNDER STOCHASTIC ALPHA–BETA–RHO DYNAMICS

2021 ◽  
Vol 63 (2) ◽  
pp. 203-227
Author(s):  
N. THAKOOR
Keyword(s):  
Radial Basis Functions ◽  
Evaluation Method ◽  
Accurate Method ◽  
Basis Functions ◽  
Computational Method ◽  
Absorbing Boundary ◽  
No Arbitrage ◽  
Radial Basis ◽  
Alpha Beta ◽  
Sabr Model

AbstractClosed-form explicit formulas for implied Black–Scholes volatilities provide a rapid evaluation method for European options under the popular stochastic alpha–beta–rho (SABR) model. However, it is well known that computed prices using the implied volatilities are only accurate for short-term maturities, but, for longer maturities, a more accurate method is required. This work addresses this accuracy problem for long-term maturities by numerically solving the no-arbitrage partial differential equation with an absorbing boundary condition at zero. Localized radial basis functions in a finite-difference mode are employed for the development of a computational method for solving the resulting two-dimensional pricing equation. The proposed method can use either multiquadrics or inverse multiquadrics, which are shown to have comparable performances. Numerical results illustrate the accuracy of the proposed method and, more importantly, that the computed risk-neutral probability densities are nonnegative. These two key properties indicate that the method of solution using localized meshless methods is a viable and efficient means for price computations under SABR dynamics.

scholarly journals Identification of Ellis rheological law from free surface velocity

2019 ◽  
Vol 263 ◽  
pp. 15-23 ◽  
Author(s):  
Abdulrahman Al-Behadili ◽  
Mathieu Sellier ◽  
James N. Hewett ◽  
Roger I. Nokes ◽  
Miguel Moyers-Gonzalez
Keyword(s):  
Free Surface ◽  
Surface Velocity ◽  
Free Surface Velocity

Evaluation of Marangoni convection and free surface velocity of molten tungsten for tungsten divertor

2019 ◽  
Vol 140 ◽  
pp. 117-122 ◽  
Author(s):  
Kohei Hamaguchi ◽  
Eiji Hoashi ◽  
Takafumi Okita ◽  
Kenzo Ibano ◽  
Yoshio Ueda
Keyword(s):  
Free Surface ◽  
Marangoni Convection ◽  
Surface Velocity ◽  
Free Surface Velocity

scholarly journals Discussion on the physical meaning of free surface velocity curve in ductile spallation

2015 ◽  
Vol 64 (3) ◽  
pp. 034601
Author(s):  
Pei Xiao-Yang ◽  
Peng Hui ◽  
He Hong-Liang ◽  
Li Ping
Keyword(s):  
Free Surface ◽  
Physical Meaning ◽  
Velocity Curve ◽  
Surface Velocity ◽  
Free Surface Velocity
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