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Velocity Potential (velocity + potential)
Selected AbstractsTreatment of Neumann boundaries in the complex variable boundary element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 2 2004Kozo Sato Abstract For potential flow, the complex variable boundary element method (CVBEM) is formulated in terms of the velocity potential , and the stream function ,. In actual flow problems, , and ,,/,n are given along Dirichlet and Neumann boundaries, respectively. In the CVBEM, the Neumann-type condition ,,/,n is not directly handled, and, instead, , is used to define Neumann boundaries. Owing to this discrepancy, numerical difficulties are raised along Neumann boundaries. The current study addresses two such difficulties: (1) multiple Neumann boundaries and (2) branch cuts across Neumann boundaries. The first problem is due to the fact that , along multiple boundaries cannot be specified a priori, and the second problem is due to the discontinuous jump inherent in , for sink/source singularities. To overcome these difficulties, a new formulation of the CVBEM to solve for the unknown , values and a proper way of branch-cut placement are proposed, and these techniques are verified against example problems. Copyright © 2004 John Wiley & Sons, Ltd. [source] Hydroelastic vibrations of flexible rectangular tanks partially filled with liquidINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2007Ding Zhou Abstract In this paper, the three-dimensional vibratory characteristics of flexible rectangular tanks partially filled with liquid are studied. The surface waves of the liquid are taken into account in the analysis. Both the bulging modes of the tank-wall vibration and the sloshing modes of the liquid oscillation are investigated. The vibrating modes of the liquid,tank system are divided into four distinct categories: double symmetric modes (SS); antisymmetric,symmetric modes (AS); symmetric,antisymmetric modes (SA) and double antisymmetric modes (AA). Each of these categories is separately investigated. The velocity potential of the liquid is analytically deduced by using a combination of the superposition method and the method of separation of variables. According to the liquid,tank interface conditions and the orthogonality of trigonometric functions, the coefficients in the solution of liquid velocity potential are expressed in the integral forms including the tank,wall dynamic deflection. A set of reasonable static beam functions is constructed as the admissible functions of the tank-wall vibration. The eigenfrequency equation of the liquid,tank system is derived by using a combination of the Rayleigh,Ritz method and the Galerkin method. Convergence study demonstrates the high accuracy and small computational cost of the proposed approach. Finally, some numerical results are presented for the first time. Copyright © 2006 John Wiley & Sons, Ltd. [source] Non-linear finite element analysis of large amplitude sloshing flow in two-dimensional tankINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2004J. R. Cho Abstract This paper is concerned with the accurate and stable finite element analysis of large amplitude liquid sloshing in two-dimensional tank under the forced excitation. The sloshing flow is formulated as an initial-boundary-value problem based upon the fully non-linear potential flow theory. The flow velocity field is interpolated from the velocity potential with second-order elements according to least square method, and the free surface conditions are tracked by making use of the direct time differentiation and the predictor,corrector method. Meanwhile, the liquid mesh is adapted such that the incompressibility condition is strictly satisfied. The accuracy and stability of the numerical method introduced are verified from the comparison with the existing reference solutions. As well, the numerical results are compared with those obtained by the linear theory with respect to the liquid fill height and the excitation amplitude. Copyright © 2004 John Wiley & Sons, Ltd. [source] An explicit formulation for the evolution of nonlinear surface waves interacting with a submerged bodyINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2007Christopher P. Kent Abstract An explicit formulation to study nonlinear waves interacting with a submerged body in an ideal fluid of infinite depth is presented. The formulation allows one to decompose the nonlinear wave,body interaction problem into body and free-surface problems. After the decomposition, the body problem satisfies a modified body boundary condition in an unbounded fluid domain, while the free-surface problem satisfies modified nonlinear free-surface boundary conditions. It is then shown that the nonlinear free-surface problem can be further reduced to a closed system of two nonlinear evolution equations expanded in infinite series for the free-surface elevation and the velocity potential at the free surface. For numerical experiments, the body problem is solved using a distribution of singularities along the body surface and the system of evolution equations, truncated at third order in wave steepness, is then solved using a pseudo-spectral method based on the fast Fourier transform. A circular cylinder translating steadily near the free surface is considered and it is found that our numerical solutions show excellent agreement with the fully nonlinear solution using a boundary integral method. We further validate our solutions for a submerged circular cylinder oscillating vertically or fixed under incoming nonlinear waves with other analytical and numerical results. Copyright © 2007 John Wiley & Sons, Ltd. [source] Generation of Arbitrary Lagrangian,Eulerian (ALE) velocities, based on monitor functions, for the solution of compressible fluid equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10-11 2005B. V. Wells Abstract A moving mesh method is outlined based on the use of monitor functions. The method is developed from a weak conservation principle. From this principle a conservation law for the mesh position is derived. Using the Helmholtz decomposition theorem, this conservation law can be converted into an elliptic equation for a mesh velocity potential. The moving mesh method is discretized using standard finite elements. Once the mesh velocities are obtained an arbitrary Lagrangian,Eulerian (ALE) (Journal of Computational Physics 1974; 14:227) fluid solver is used to update the solution on the adaptive mesh. Results are shown for the compressible Euler equations of gas dynamics in one and two spatial dimensions. Two monitor functions are used, the fluid density (which corresponds to a Lagrangian description), and a function which includes the density gradient. A variety of test problems are considered. Copyright © 2005 John Wiley & Sons, Ltd. [source] A numerical method to solve the m -terms of a submerged body with forward speedINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2002W.-Y. Duan Abstract To model mathematically the problem of a rigid body moving below the free surface, a control surface surrounding the body is introduced. The linear free surface condition of the steady waves created by the moving body is satisfied. To describe the fluid flow outside this surface a potential integral equation is constructed using the Kelvin wave Green function whereas inside the surface, a source integral equation is developed adopting a simple Green function. Source strengths are determined by matching the two integral equations through continuity conditions applied to velocity potential and its normal derivatives along the control surface. After solving for the induced fluid velocity on the body surface and the control surface, an integral equation is derived involving a mixed distribution of sources and dipoles using a simple Green function and one component of the fluid velocity. The normal derivatives of the fluid velocity on the body surface, namely the m -terms, are then solved by this matching integral equation method (MIEM). Numerical results are presented for two elliptical sections moving at a prescribed Froude number and submerged depth and a sensitivity analysis undertaken to assess the influence of these parameters. Furthermore, comparisons are performed to analyse the impact of different assumptions adopted in the derivation of the m -terms. It is found that the present method is easy to use in a panel method with satisfactory numerical precision. Copyright © 2002 John Wiley & Sons, Ltd. [source] Effect of late 1970's climate shift on tropospheric biennial oscillation,role of local Indian Ocean processes on Asian summer monsoonINTERNATIONAL JOURNAL OF CLIMATOLOGY, Issue 4 2010Prasanth A Pillai Abstract The tropical climate has undergone noticeable changes on interdecadal time scales. The climate shift that occurred in the late 1970s attained enormous attention owing to its global-scale variations in ocean temperature, heat content and El Nino Southern Oscillation (ENSO) properties. Earlier studies presented the effect of this shift on ENSO and the Asian summer monsoon,ENSO relationship. The present study is an attempt to investigate the effect of late 1970's climate shift on tropospheric biennial oscillation (TBO), which is an important tropical phenomenon that includes both air,sea processes in the tropical Indian and Pacific Ocean regions. TBO is the tendency for the Asian,Australian monsoon system to alternate between relatively strong and weak years. The study comprises a detailed analysis of the TBO cycle in the time periods before (1951,1975) and after (1978,2002) the climate shift in 1976 with the help of National Centers for Environmental Prediction (NCEP)/National Center for Atmospheric Research (NCAR) data sets of 200-hPa velocity potential; the Indian Ocean sea surface temperature (SST) and circulation are more obvious after the shift, although they were significant in the Pacific Ocean before 1976. The effect of ENSO in the biennial cycle is reduced with climate shift. The persistence of Asian-to-Australian summer monsoon has weakened in recent decades, as it is controlled by ENSO. Local oceanic processes in the Indian Ocean and local monsoon Hadley circulation have an increased role in the biennial oscillation of the Asian summer monsoon after 1976. Copyright © 2009 Royal Meteorological Society [source] Simulation of Indian summer monsoon: sensitivity to cumulus parameterization in a GCMINTERNATIONAL JOURNAL OF CLIMATOLOGY, Issue 8 2007S. K. Deb Abstract Hindcasts for the Indian summer monsoons (ISMs) of 2002 and 2003 have been produced from a series of numerical simulations performed with a general circulation model using different cumulus parameterization schemes. Ten sets of ensemble simulations have been produced without using any vegetation scheme but by prescribing the monthly observed SST from the ECMWF (European Centre for Medium Range Weather Forecasts) analyses. For each ensemble, ten simulations have been realised with different initial conditions that are also prepared from the ECMWF data: five each from the April and May analyses of both the years. Stream function, velocity potential with divergent winds at 200 hPa, winds at 850 hPa and rainfall patterns with their anomalies have been analysed and interpreted. The large-scale upper and lower level circulation features are simulated satisfactorily. The spatial structure of predicted July monsoon rainfall over India shows a fair agreement with the GPCP (observed) pentad rainfall distribution. The variability associated with all-India June,July simulated rainfall time series matches reasonably well with the observations in 2003, but the model fails to simulate the observed variability in July 2002. Further evaluation of the model-produced precipitation in seasonal simulations is done with the help of empirical orthogonal functions (EOFs) of the GPCP rainfall over India. Since the first four EOFs explain a significant part of the total variance of the observed rainfall, the simulated precipitation is projected on to these modes. Thus, the differences in simulated and observed rainfall fields manifest in the time series of their expansion coefficients, which are utilised for inter-comparison/evaluation of model simulations. Copyright © 2006 Royal Meteorological Society [source] Remote weather associated with South Pacific subtropical sea-level high propertiesINTERNATIONAL JOURNAL OF CLIMATOLOGY, Issue 7 2004Richard Grotjahn Abstract The subtropical highs in sea-level pressure (SLP) are little studied and incompletely understood. In recent years, three groups of theories, i.e. tropical divergent circulations, subtropical Rossby wavetrains, and midlatitude frontal cyclone interactions, have been proposed for remote maintenance of these highs. The latter is presented here as a remote forcing of these highs for the first time in the reviewed literature. The focus of the study is upon illuminating associations between these mechanisms and the South Pacific subtropical high in SLP (SP high). Precipitation, outgoing longwave radiation, velocity potential, and divergent winds are used as proxy markers for the remote forcing mechanisms. The tools used include composites, one-point correlations, autocorrelations, cross-correlations, and cross-spectra. Observational evidence, in monthly and daily data, is examined that appears to support each mechanism. Associations seen in monthly data are better understood in daily data at various lags. Convection over Amazonia, coordinated with suppressed convection in the western tropical Pacific, leads to enhanced SLP on the tropical side of the high. Midlatitude weather systems are the strongest influence upon the maximum SLP and the SLP on the higher latitude side of the high. The western side is associated with both middle-and lower-latitude phenomena, such as the South Pacific convergence zone. Various properties of the high have a strong period around 45 days. Associations to the Madden,Julian oscillation and El Niño,southern oscillation are explored and are strong only for the tropical side of the SP high. Copyright © 2004 Royal Meteorological Society [source] Numerical simulation of non-viscous liquid pinch off using a coupled level set boundary integral methodPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2007Maria Garzon The pinch off of an inviscid fluid column is described using a potential flow model with capillary forces. The interface velocity is obtained via a Galerkin boundary integral method for the 3D axisymmetric Laplace equation, whereas the interface location and the velocity potential on the free boundary are both approximated using level set techniques on a fixed domain. The algorithm is validated computing the Raleigh-Taylor instability for liquid columns which provides an analytical solution for short times. The simulations show the time evolution of the fluid tube and the algorithm is capable of handling pinch-off and after pinch-off events. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Individual and combined influence of El Niño,Southern Oscillation and Indian Ocean Dipole on the Tropospheric Biennial OscillationTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 647 2010Prasanth A. Pillai Abstract Tropospheric biennial oscillation (TBO) is the tendency of a strong monsoon to be followed by a weaker one and vice versa. It involves both oceanic and atmospheric processes in the tropical Indian and Pacific Ocean regions. The present study analyses the effect of dynamical processes of the Indian and Pacific Oceans like the Indian Ocean Dipole (IOD) and El Niño,Southern Oscillation (ENSO) on the TBO. The 200 hPa velocity potential, 850 hPa zonal wind and sea-surface temperature datasets obtained from NCEP/NCAR reanalysis for the period 1950,2006 are used for the study of the TBO. The IOD and TBO have both in-phase (positive/negative IOD with positive/negative TBO) and out-of-phase (positive/negative IOD with negative/positive TBO) relationships. On the other hand, La Niña is associated with the positive phase of TBO and El Niño with the negative phase. In the presence of El Niño (La Niña), positive (negative) IOD is associated with negative (positive) TBO and in the absence of ENSO, positive (negative) IOD is associated with positive (negative) phase of TBO. When ENSO is associated with TBO, it tends to dominate the biennial transition irrespective of IOD. In-phase Indian to Australian monsoon transition of TBO is controlled by ENSO. IOD,TBO association is strong and significant in the absence of ENSO only. The biennial reversal is confined to the Indian Ocean in the TBO cycle associated with IOD only. Thus IOD can be considered as the local forcing for the biennial monsoon cycle, and ENSO the remote effect. Copyright © 2010 Royal Meteorological Society [source] Instabilities of Boussinesq models in non-uniform depthINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2009F. Løvholt Abstract The von Neumann method for stability analysis of linear waves in a uniform medium is a widely applied procedure. However, the method does not apply to stability of linear waves in a variable medium. Herein we describe instabilities due to variable depth for different Boussinesq equations, including the standard model by Peregrine and the popular generalization by Nwogu. Eigenmodes are first found for bathymetric features on the grid scale. For certain combinations of Boussinesq formulations and bottom profiles stability limits are found in closed form, otherwise numerical techniques are used for the eigenvalue problems. Naturally, the unstable modes in such settings must be considered to be as much a result of the difference method as of the underlying differential (Boussinesq) equations. Hence, modes are also computed for smooth depth profiles that are well resolved. Generally, the instabilities do not vanish with refined resolution. In some cases convergence is observed and we thus have indications of unstable solutions of the differential equations themselves. The stability properties differ strongly. While the standard Boussinesq equations seem perfectly stable, all the other formulations do display unstable modes. In most cases the instabilities are linked to steep bottom gradients and small grid increments. However, while a certain formulation, based on velocity potentials, is very prone to instability, the Boussinesq equations of Nwogu become unstable only under quite demanding conditions. Still, for the formulation of Nwogu, instabilities are probably inherent in the differential equations and are not a result of the numerical model. Copyright © 2008 John Wiley & Sons, Ltd. [source] | |||||||||||||