scholarly journals Erratum: “The angular momentum equation for a finite element of a fluid: A new representation and application to turbulent modeling” [Phys. Fluids 14, 2673 (2002)]

2003 ◽  
Vol 15 (10) ◽  
pp. 3259
Author(s):  
M. Iovieno ◽  
D. Tordella
Keyword(s):  
Finite Element ◽  
Angular Momentum ◽  
Momentum Equation ◽  
Turbulent Modeling

scholarly journals A Tsunami Ball Approach to Storm Surge and Inundation: Application to Hurricane Katrina, 2005

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
Steven N. Ward
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Hurricane Katrina ◽  
Storm Surge ◽  
Volume Density ◽  
Momentum Equation ◽  
Cape Cod ◽  
Laptop Computer ◽  
New Approach ◽  
Advection Term

Most analyses of storm surge and inundation solve equations of continuity and momentum on fixed finite-difference/finite-element meshes. I develop a completely new approach that uses a momentum equation to accelerate bits or balls of water over variable depth topography. The thickness of the water column at any point equals the volume density of balls there. In addition to being more intuitive than traditional methods, the tsunami ball approach has several advantages. (a) By tracking water balls of fixed volume, the continuity equation is satisfied automatically and the advection term in the momentum equation becomes unnecessary. (b) The procedure is meshless in the finite-difference/finite-element sense. (c) Tsunami balls care little if they find themselves in the ocean or inundating land. (d) Tsunami ball calculations of storm surge can be done on a laptop computer. I demonstrate and calibrate the method by simulating storm surge and inundation around New Orleans, Louisiana caused by Hurricane Katrina in 2005 and by comparing model predictions with field observations. To illustrate the flexibility of the tsunami ball technique, I run two “What If” hurricane scenarios—Katrina over Savannah, Georgia and Katrina over Cape Cod, Massachusetts.

Comparison between Analytical and Vectorial Methods of the Synthesis of Equations of Motion

1983 ◽  
Vol 197 (4) ◽  
pp. 265-274
Author(s):  
Z J Goraj
Keyword(s):  
Angular Momentum ◽  
Analytical Method ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Discrete Systems ◽  
Momentum Equation ◽  
Lagrange Equations ◽  
Weak Points ◽  
Complicated Geometry ◽  
Boltzmann Hamel Equations

In this paper the advantages and weak points of the analytical and vectorial methods of the derivation of equations of motion for discrete systems are considered. The analytical method is discussed especially with respect to Boltzmann-Hamel equations, as generalized Lagrange equations. The vectorial method is analysed with respect to the momentum equation and to the generalized angular momentum equation about an arbitrary reference point, moving in an arbitrary manner. It is concluded that, for the systems with complicated geometry of motion and a large number of degrees of freedom, the vectorial method can be more effective than the analytical method. The combination of the analytical and vectorial methods helps to verify the equations of motion and to avoid errors, especially in the case of systems with rather complicated geometry.

The use of a one-dimensional depth-averaged moment of momentum equation for the nonhydrostatic pressure condition

1996 ◽  
Vol 23 (1) ◽  
pp. 150-156 ◽  
Author(s):  
Yee-Chung Jin ◽  
Baozhu Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Channel Flow ◽  
Open Channel ◽  
Open Channel Flow ◽  
Momentum Equation ◽  
Nonuniform Flow ◽  
Pressure Condition ◽  
Nonhydrostatic Pressure ◽  
Averaged Model

A depth-averaged model formulated in the Cartesian coordinate system for curved open-channel flows is extended to solve problems where the effects of nonhydrostatic pressure distribution and nonuniform velocity distribution are significant. The nonhydrostatic pressure condition is added to the z-direction momentum equation assuming that the pressure deviation from the hydrostatic condition at the channel bed decreases linearly to the water surface. The pressure-effect terms are modified in both the moment of momentum and momentum equations. The resulting system of nonlinear equations is solved by a finite-element method. The derived model is then applied to four sophisticated nonuniform flow experiments from the literature. A comparison of the actual experimental results with their numerical prediction results, as calculated with the model, is presented. Generally speaking, a fairly good agreement for the depth-averaged velocities as well as reasonable perturbation profiles were obtained from this comparison. Therefore, it can be said that the depth-averaged model for open-channel flow is reasonably accurate under the given conditions. Key words: open-channel flow, depth-averaged method, finite-element method, nonhydrostatic pressure, nonuniform flow.

scholarly journals Rocking motion of slender elastic body on rigid floor

1986 ◽  
Vol 19 (1) ◽  
pp. 18-27 ◽  
Author(s):  
T. Ichinose
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Angular Momentum ◽  
Elastic Body ◽  
Vibration Mode ◽  
Simple Relationship ◽  
Element Analysis ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Rocking Motion

A single degree of freedom (SDOF) model is presented to describe the rocking behaviour of a slender elastic body on a rigid floor. This model assumes the vibration mode to be a linear combination of flexural and rocking modes. A finite element analysis is also presented, in which following features are observed to support the assumptions of the proposed SDOF model: (1) There exists a simple relationship between the magnitudes of flexural and rocking modes, which relation can be derived from the equilibrium of moment. (2) Angular momentum is conserved at the instances of uplifting and landing.

scholarly journals Transonic accretion and winds around Pseudo-Kerr black holes andcomparison with general relativistic solutions

2022 ◽  
Author(s):  
Abhrajit Bhattacharjee ◽  
Sandip Kumar Chakrabarti ◽  
Dipak Debnath
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Angular Momentum ◽  
Time Scale ◽  
Momentum Equation ◽  
Accretion Flows ◽  
Timing Properties ◽  
Surrounding Space ◽  
General Relativistic ◽  
Corotating Frame

Abstract Spectral and timing properties of accretion flows on a black hole depend on their density and temperature distributions, which, in turn come from the underlying dynamics. Thus, an accurate description of the flow which includes hydrodynamics and radiative transfer is a must to interpret the observational results. In the case of non-rotating black holes, Pseudo- Newtonian description of surrounding space-time enables one to make a significant progress in predicting spectral and timing properties. This formalism is lacking for the spinning black holes. In this paper, we show that there exists an exact form of ‘natural’ potential derivable from the general relativistic (GR) radial momentum equation written in the local corotating frame. Use of this potential in an otherwise Newtonian set of equations, allows us to describe transonic flows very accurately as is evidenced by comparing with solutions obtained from the full GR framework. We study the properties of the sonic points and the centrifugal pressure supported shocks in the parameter space spanned by the specific energy and the angular momentum, and compare with the results of GR hydrodynamics. We show that this potential can safely be used for the entire range of Kerr parameter −1 < a < 1 for modeling of observational results around spinning black holes. We assume the flow to be inviscid. Thus, it is non-dissipative with constant energy and angular momentum. These assumptions are valid very close to the black hole horizon as the infall time scale is much shorter as compared to the viscous time scale.

Simulations of Magnetoviscosity of Dilute Suspensions of Magnetic Ellipsoids

2008 ◽  
Author(s):  
J. H. Sa´nchez ◽  
C. Rinaldi
Keyword(s):  
Brownian Motion ◽  
Angular Momentum ◽  
Momentum Equation ◽  
Orientation Space ◽  
Fluctuation Dissipation ◽  
Ellipsoidal Particles ◽  
Fluctuation Dissipation Theorem ◽  
Dilute Suspensions ◽  
Dilute Suspension ◽  
Rotational Brownian Motion

We studied the rotational Brownian motion of magnetic triaxial ellipsoidal particles (orthotropic particles) suspended in a Newtonian fluid, in the dilute suspension limit, under applied shear and magnetic fields. The algorithm describing the change in the particle magnetization has been derived from the stochastic angular momentum equation using the fluctuation-dissipation theorem and a quaternion formulation of orientation space. Results are presented for the response of dilute suspensions of ellipsoidal particles to constant magnetic and shear flow fields.

A Finite-Element Simulation of Pulsatile Flow in Flexible Obstructed Tubes

1982 ◽  
Vol 104 (2) ◽  
pp. 119-124 ◽  
Author(s):  
E. Rooz ◽  
D. F. Young ◽  
T. R. Rogge
Keyword(s):  
Finite Element ◽  
Pulsatile Flow ◽  
Continuity Equation ◽  
Element Model ◽  
Momentum Equation ◽  
Cross Sectional ◽  
One Dimensional ◽  
Element Simulation ◽  
The One

A finite-element model for pulsatile flow in a straight flexible partially obstructed tube is developed. In the unobstructed sections of the tube the model considers the continuity equation, the one-dimensional momentum equation, and an equation of state relating tube cross-sectional area to pressure. For the obstructed region, a nonlinear relationship between the flow and the pressure drop across the stenosis is considered. The applicability of a model is checked by comparing predicted flow and pressure waveforms with corresponding in-vitro experimental measurements obtained on a mechanical system. These comparisons indicate that the model satisfactorily predicts pressures and flows under variety of frequencies of oscillation and stenosis severities.

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