scholarly journals Implicit Euler-Lagrange difference scheme for three-dimensional gasdynamics calculations using concerted approximations to mass and momentum balance equations

2016 ◽  
pp. 1-24 ◽  
Author(s):  
Vladimir Anontol’evich Gasilov ◽  
Alexander Yur’evich Krukovskiy ◽  
Yuri Andreevich Poveschenko ◽  
Ilia Pavlovich Tsygvintsev
Keyword(s):  
Difference Scheme ◽  
Three Dimensional ◽  
Momentum Balance ◽  
Balance Equations

Method of Virtual Power Applied to Cosserat Surfaces With Deformable Directors

1993 ◽  
Vol 46 (11S) ◽  
pp. S266-S278
Author(s):  
Boris Krajnc Alves ◽  
Jacob Lubliner
Keyword(s):  
Direct Method ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Momentum Balance ◽  
Power Method ◽  
Virtual Power ◽  
Balance Equations ◽  
Dimensional Theory ◽  
Momentum Balance Equation ◽  
Cosserat Surface

Following a brief outline of the method of virtual power, the local equations of motion for a Cosserat surface with inextensible directors are derived by means of this method. The model obtained coincides with the results derived from three-dimensional theory by Simo and Fox. Subsequently the model is extended so as to account for deformable directors. Besides the linear-momentum and moment-of-momentum balance equations, one additional scalar equation is derived. This equation replaces the director-momentum balance equation of Naghdi and therefore eliminates the necessity of introducing constitutive restrictions. The equivalence between the model derived by the virtual-power method and the results from the direct method of Naghdi are finally noted.

The Efficiency of Tidal Fences: A Brief Review and Further Discussion on the Effect of Wake Mixing

2013 ◽  
Author(s):  
Takafumi Nishino ◽  
Richard H. J. Willden
Keyword(s):  
Energy Balance ◽  
Theoretical Investigation ◽  
Three Dimensional ◽  
Physical Factors ◽  
Balance Equations ◽  
Order Model ◽  
Near Wake ◽  
New Model ◽  
Actuator Disk ◽  
Limiting Efficiency

Recent discoveries on the limiting efficiency of tidal fences are reviewed, followed by a new theoretical investigation into the effect of wake mixing on the efficiency of ‘full’ tidal fences (i.e. turbines arrayed regularly across an entire channel span). The new model is based on the momentum and energy balance equations but includes several unclosed terms, which depend on the actual (three-dimensional) characteristics of turbine near-wake mixing and therefore need to be modelled empirically. The new model agrees well with three-dimensional actuator disk simulations when those unclosed terms are assessed based on the simulations themselves, suggesting that this low-order model could serve as a basis to analyse how various physical factors (such as the design of turbines) affect the limiting efficiency of tidal fences via changes in those terms describing the characteristics of turbine near-wake mixing. Also discussed is the effect of wake mixing on the efficiency of ‘partial’ tidal fences.

scholarly journals A Finite-Volume Solution with a Bidirectional Upwind Difference Scheme for the Three-Dimensional Radiative Transfer Equation

2007 ◽  
Vol 64 (11) ◽  
pp. 4098-4112 ◽  
Author(s):  
Haruma Ishida ◽  
Shoji Asano
Keyword(s):  
Radiative Transfer ◽  
Difference Scheme ◽  
Finite Volume ◽  
Spherical Harmonic ◽  
Transfer Equation ◽  
Three Dimensional ◽  
Harmonic Series ◽  
Simultaneous Linear Equation ◽  
Upwind Difference Scheme ◽  
Cloud Models

Abstract A new calculation scheme is proposed for the explicitly discretized solution of the three-dimensional (3D) radiation transfer equation (RTE) for inhomogeneous atmospheres. To separate the independent variables involved in the 3D RTE approach, the spherical harmonic series expansion was used to discretize the terms, depending on the direction of the radiance, and the finite-volume method was applied to discretize the terms, depending on the spatial coordinates. A bidirectional upwind difference scheme, which is a specialized scheme for the discretization of the partial differential terms in the spherical harmonic-transformed RTE, was developed to make the equation determinate. The 3D RTE can be formulated as a simultaneous linear equation, which is expressed in the form of a vector–matrix equation with a sparse matrix. The successive overrelaxation method was applied to solve this equation. Radiative transfer calculations of the solar radiation in two-dimensional cloud models have shown that this method can properly simulate the radiation field in inhomogeneous clouds. A comparison of the results obtained using this method with those using the Monte Carlo method shows reasonable agreement for the upward flux, the total downward flux, and the intensities of radiance.

A Calculation Scheme for Three-Dimensional Viscous Incompressible Flows

1987 ◽  
Vol 109 (4) ◽  
pp. 345-352 ◽  
Author(s):  
M. Reggio ◽  
R. Camarero
Keyword(s):  
Incompressible Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Numerical Data ◽  
Momentum Balance ◽  
Navier Stokes ◽  
Test Cases ◽  
Pressure Gradients ◽  
Navier Stokes Equations

A numerical procedure to solve three-dimensional incompressible flows in arbitrary shapes is presented. The conservative form of the primitive-variable formulation of the time-dependent Navier-Stokes equations written for a general curvilinear coordiante system is adopted. The numerical scheme is based on an overlapping grid combined with opposed differencing for mass and pressure gradients. The pressure and the velocity components are stored at the same location: the center of the computational cell which is used for both mass and the momentum balance. The resulting scheme is stable and no oscillations in the velocity or pressure fields are detected. The method is applied to test cases of ducting and the results are compared with experimental and numerical data.

scholarly journals The Evolution and Arrest of a Turbulent Stratified Oceanic Bottom Boundary Layer over a Slope: Downslope Regime

2019 ◽  
Vol 49 (2) ◽  
pp. 469-487 ◽  
Author(s):  
Xiaozhou Ruan ◽  
Andrew F. Thompson ◽  
John R. Taylor
Keyword(s):  
Boundary Layer ◽  
Mixed Layer ◽  
Three Dimensional ◽  
Wall Stress ◽  
Bottom Boundary Layer ◽  
Ekman Transport ◽  
Momentum Balance ◽  
Bottom Boundary ◽  
Obukhov Length ◽  
Turbulent Characteristics

AbstractThe dynamics of a stratified oceanic bottom boundary layer (BBL) over an insulating, sloping surface depend critically on the intersection of density surfaces with the bottom. For an imposed along-slope flow, the cross-slope Ekman transport advects density surfaces and generates a near-bottom geostrophic thermal wind shear that opposes the background flow. A limiting case occurs when a momentum balance is achieved between the Coriolis force and a restoring buoyancy force in response to the displacement of stratified fluid over the slope: this is known as Ekman arrest. However, the turbulent characteristics that accompany this adjustment have received less attention. We present two estimates to characterize the state of the BBL based on the mixed layer thickness: Ha and HL. The former characterizes the steady Ekman arrested state, and the latter characterizes a relaminarized state. The derivation of HL makes use of a newly defined slope Obukhov length Ls that characterizes the relative importance of shear production and cross-slope buoyancy advection. The value of Ha can be combined with the temporally evolving depth of the mixed layer H to form a nondimensional variable H/Ha that provides a similarity prediction of the BBL evolution across different turbulent regimes. The length scale Ls can also be used to obtain an expression for the wall stress when the BBL relaminarizes. We validate these relationships using output from a suite of three-dimensional large-eddy simulations. We conclude that the BBL reaches the relaminarized state before the steady Ekman arrested state. Calculating H/Ha and H/HL from measurements will provide information on the stage of oceanic BBL development being observed. These diagnostics may also help to improve numerical parameterizations of stratified BBL dynamics over sloping topography.

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