A numerical algorithm on boundary conditions for directly solving vorticity transport equations

2000 ◽  
Author(s):  
Zhiyun Lu
Keyword(s):  
Boundary Conditions ◽  
Numerical Algorithm ◽  
Transport Equations ◽  
Vorticity Transport

Model of vortex flow of charge in a vessel with turbine impeller

1987 ◽  
Vol 52 (8) ◽  
pp. 1888-1904
Author(s):  
Miloslav Hošťálek ◽  
Ivan Fořt
Keyword(s):  
Boundary Conditions ◽  
Equations Of Motion ◽  
Theoretical Data ◽  
Eddy Diffusion ◽  
Quantitative Agreement ◽  
Creeping Flow ◽  
Model Parameters ◽  
Mean Flow ◽  
Two Dimensional Flow ◽  
Vorticity Transport

A theoretical model is described of the mean two-dimensional flow of homogeneous charge in a flat-bottomed cylindrical tank with radial baffles and six-blade turbine disc impeller. The model starts from the concept of vorticity transport in the bulk of vortex liquid flow through the mechanism of eddy diffusion characterized by a constant value of turbulent (eddy) viscosity. The result of solution of the equation which is analogous to the Stokes simplification of equations of motion for creeping flow is the description of field of the stream function and of the axial and radial velocity components of mean flow in the whole charge. The results of modelling are compared with the experimental and theoretical data published by different authors, a good qualitative and quantitative agreement being stated. Advantage of the model proposed is a very simple schematization of the system volume necessary to introduce the boundary conditions (only the parts above the impeller plane of symmetry and below it are distinguished), the explicit character of the model with respect to the model parameters (model lucidity, low demands on the capacity of computer), and, in the end, the possibility to modify the given model by changing boundary conditions even for another agitating set-up with radially-axial character of flow.

Thermal Transport Equations and Boundary Conditions at the Nanoscale

2019 ◽  
pp. 37-44
Author(s):  
Marc Calvo-Schwarzwälder ◽  
Matthew G. Hennessy ◽  
Pol Torres ◽  
Timothy G. Myers ◽  
F. Xavier Alvarez
Keyword(s):  
Boundary Conditions ◽  
Thermal Transport ◽  
Transport Equations

Static Deflection and Free Vibration of Nonprismatic Beam Structures Solved by DQEM Using EDQ

2000 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Numerical Algorithm ◽  
Equilibrium Equation ◽  
Static Deflection ◽  
Beam Structures ◽  
Prismatic Beam ◽  
Vibration Problems ◽  
Analysis Models ◽  
Element Boundary

Abstract The development of (DQEM) analysis models of static deformation and free vibration problems of generic non-prismatic beam structures was carried out. The DQEM uses the extended differential quadrature (EDQ) to discretize the buckling equilibrium equation defined on each element, the transition conditions defined on the inter-element boundary of two adjacent elements and the boundary conditions of the beam. Numerical results solved by the developed numerical algorithm are presented. They prove that the DQEM efficient.

Influence of Axially Distributed Force on the Vibration of Euler-Bernoulli Beam Structures Solved by DQEM Using EDQ

2007 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Boundary Conditions ◽  
Numerical Algorithm ◽  
Differential Quadrature ◽  
Analysis Model ◽  
Bernoulli Beam ◽  
Beam Structures ◽  
Differential Quadrature Element Method ◽  
Quadrature Element Method ◽  
Euler Bernoulli Beam ◽  
Element Boundary

The influence of axially distributed force on the vibration of Euler-Bernoulli beam structures is analyzed by differential quadrature element method (DQEM) using extended differential quadrature (EDQ). The DQEM uses the differential quadrature to discretize the governing differential eigenvalue equation defined on each element, the transition conditions defined on the inter-element boundary of two adjacent elements and the boundary conditions of the beam. Numerical results solved by the developed numerical algorithm are presented. The convergence of the developed DQEM analysis model is efficient.

A Conservative Formulation and a Numerical Algorithm for the Double-Gyre Nonlinear Shallow-Water Model

2015 ◽  
Vol 8 (4) ◽  
pp. 634-650 ◽  
Author(s):  
Dongyang Kuang ◽  
Long Lee
Keyword(s):  
Boundary Conditions ◽  
Shallow Water ◽  
Numerical Algorithm ◽  
Shallow Water Equations ◽  
Ocean Basin ◽  
Height Anomaly ◽  
Fractional Step ◽  
Step Algorithm ◽  
Gyre Circulation ◽  
Double Gyre

AbstractWe present a conservative formulation and a numerical algorithm for the reduced-gravity shallow-water equations on a beta plane, subjected to a constant wind forcing that leads to the formation of double-gyre circulation in a closed ocean basin. The novelty of the paper is that we reformulate the governing equations into a nonlinear hyperbolic conservation law plus source terms. A second-order fractional-step algorithm is used to solve the reformulated equations. In the first step of the fractional-step algorithm, we solve the homogeneous hyperbolic shallow-water equations by the wave-propagation finite volume method. The resulting intermediate solution is then used as the initial condition for the initial-boundary value problem in the second step. As a result, the proposed method is not sensitive to the choice of viscosity and gives high-resolution results for coarse grids, as long as the Rossby deformation radius is resolved. We discuss the boundary conditions in each step, when no-slip boundary conditions are imposed to the problem. We validate the algorithm by a periodic flow on an f-plane with exact solutions. The order-of-accuracy for the proposed algorithm is tested numerically. We illustrate a quasi-steady-state solution of the double-gyre model via the height anomaly and the contour of stream function for the formation of double-gyre circulation in a closed basin. Our calculations are highly consistent with the results reported in the literature. Finally, we present an application, in which the double-gyre model is coupled with the advection equation for modeling transport of a pollutant in a closed ocean basin.

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