A staggered-grid finite volume method for the vorticity-velocity equations

The basic goal of this study is to present a numerical simulation model for turbulent water flow issued on frozen scoured beds. The model uses a finite volume method to solve the equations of motion and transport equations for two dimensions on a transformed rectangular domain using boundary-fitted coordinates. The internal characteristics of the mean flow of submerged horizontal jets including surface profiles on frozen scoured beds are computed by a two-dimensional k–ε turbulence model. Computations are carried out at different frozen-scoured bed profiles. A staggered grid system is adapted for variable arrangements to avoid the well-known checkerboard oscillations in pressure and velocity. The SIMPLE algorithm is adapted for the computation. No experimental studies were performed during this investigation. The diffusion characteristics of the submerged jet, growth of boundary layer thickness, velocity distribution within the boundary layer, and shear stress at the scour are investigated and compared with the results of others. Key words: boundary-fitted coordinates, local scour, k–ε model, finite volume method, horizontal jets, submerged jets.

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The Sweep Efficiency of Viscoelastic Polymer Solution

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.316-317.975 ◽

2013 ◽

Vol 316-317 ◽

pp. 975-978

Author(s):

Hai Mei Jiang ◽

Jin Qing Zhang ◽

Shu Xu Zhang ◽

Xiao Kang Sun

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Weissenberg Number ◽

Staggered Grid ◽

Viscoelastic Flows ◽

Sweep Efficiency ◽

Model Fluid ◽

Stable Solutions ◽

Volume Method ◽

Main Factor

A finite volume method for the numerical solution of viscoelastic flows is presented in this paper. The flow of a differential upper-convected Maxwell (UCM) model fluid through an abrupt expansion has been chosen as a prototype example. The equations are solved using the finite volume method (FVM) in a staggered grid. Stable solutions are found for high Weissenberg number (We), further extending the range of simulations with the FVM. Numerical results show the viscoelasticity of polymer solutions is the main factor influencing sweep efficiency.

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A Three-Dimensional, Immersed Boundary, Finite Volume Method for the Simulation of Incompressible Heat Transfer Flows around Complex Geometries

International Journal of Chemical Engineering ◽

10.1155/2017/1726519 ◽

2017 ◽

Vol 2017 ◽

pp. 1-14 ◽

Cited By ~ 1

Author(s):

Hassan Badreddine ◽

Yohei Sato ◽

Matthias Berger ◽

Bojan Ničeno

Keyword(s):

Heat Transfer ◽

Finite Volume Method ◽

Finite Volume ◽

Three Dimensional ◽

Staggered Grid ◽

Immersed Boundary ◽

Convection Flow ◽

Complex Geometries ◽

Volume Method ◽

Benchmark Solutions

The current work focuses on the development and application of a new finite volume immersed boundary method (IBM) to simulate three-dimensional fluid flows and heat transfer around complex geometries. First, the discretization of the governing equations based on the second-order finite volume method on Cartesian, structured, staggered grid is outlined, followed by the description of modifications which have to be applied to the discretized system once a body is immersed into the grid. To validate the new approach, the heat conduction equation with a source term is solved inside a cavity with an immersed body. The approach is then tested for a natural convection flow in a square cavity with and without circular cylinder for different Rayleigh numbers. The results computed with the present approach compare very well with the benchmark solutions. As a next step in the validation procedure, the method is tested for Direct Numerical Simulation (DNS) of a turbulent flow around a surface-mounted matrix of cubes. The results computed with the present method compare very well with Laser Doppler Anemometry (LDA) measurements of the same case, showing that the method can be used for scale-resolving simulations of turbulence as well.

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Three-dimensional numerical simulation of viscoelastic flow through an abrupt contraction geometry

e-Polymers ◽

10.1515/epoly.2005.5.1.546 ◽

2005 ◽

Vol 5 (1) ◽

Author(s):

Young Il Kwon ◽

Dongjin Seo ◽

Jae Ryoun Youn

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Interpolation Method ◽

Three Dimensional ◽

Grid Method ◽

Viscoelastic Flow ◽

Staggered Grid ◽

Algebraic Equations ◽

Accelerate Convergence ◽

Volume Method

AbstractA numerical scheme for simulating three-dimensional viscoelastic flow was developed. The three-dimensional finite volume method (FVM) based on a non-staggered grid and the semi-implicit method for pressure-linked equations (SIMPLE) were adopted to solve the continuity and momentum equations. As we used a non-staggered grid, the momentum interpolation method (MIM) was employed to avoid checkerboard type pressure fields. Viscoelastic properties of the fluid were described by the Phan-Thien and Tanner (PTT) model, which was treated by the compressive interface capturing scheme for arbitrary meshes (CICSAM). The elastic viscous split stress scheme (EVSS) was used to decouple the velocity and the stress fields. Algebraic equations obtained by the above schemes were handled by an iterative solver and a multi-grid method was applied to accelerate convergence. In order to verify the scheme developed in this study, Newtonian flow in a rectangular duct was studied and the resulting velocity fields were compared with the analytical flow fields. Then viscoelastic flow in 4:1 contraction geometry, one of the most frequently used benchmarking problems, was predicted by applying the fully three-dimensional finite volume method.

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