An Aid to Learn Computational Fluid Dynamics: Immersed-Boundary-Based Simulation of 2D Flow

Volume 1 ◽  
2004 ◽  
Author(s):  
Sungsu Lee ◽  
Kyung-Soo Yang ◽  
Jong-Yeon Hwang
Keyword(s):  
Complex Geometry ◽  
Mass Conservation ◽  
Computational Method ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Immersed Boundary ◽  
Step Method ◽  
Fractional Step Method ◽  
Navier Stokes Equation ◽  
Finite Volume Approach

Development of geometry-independent computational method and educational codes for simulation of 2D flows around objects of complex geometry is presented. Referred as immersed boundary method, it introduces virtual forcing to governing equations to represent the effect of physical boundaries. The present method is based on a finite-volume approach on a staggered grid with a fractional-step method to solve Navier-Stokes equation and continuity equation. Both momentum and mass forcings are introduced on and inside the object to satisfy no-slip condition and mass conservation. Since Cartesian grid lines in general do not coincide with the immersed boundaries, several interpolation schemes are employed. Several examples are simulated using the method presented in this study and the results agree well with other results. Both user-friendly preprocessor with GUI and FORTRAN-based solver are open to the public for educational purposes.

Ghost Cell Immersed Boundary Method for Simulating Flow over Two Circular Cylinders in Tandem Arrangement

2013 ◽  
Vol 275-277 ◽  
pp. 478-481
Author(s):  
Li Wei Song ◽  
Song Ping Wu
Keyword(s):  
Immersed Boundary Method ◽  
Stokes Equations ◽  
Circular Cylinders ◽  
Navier Stokes ◽  
Immersed Boundary ◽  
Ghost Cell ◽  
Step Method ◽  
Fractional Step Method ◽  
Tandem Arrangement ◽  
Boundary Method

In this work, a ghost cell immersed boundary method is applied to the numerical simulation of a uniform flows over a circular cylinder and two circular cylinders in tandem arrangement. The Navier-Stokes equations are solved using an implicit fractional step method employed on collocated arrangement variables. Immersed boundary method permit the use of structured Cartesian meshes to simulate flows involving complex boundaries. The shedding of vortices and flow interference between two circular cylinders in tandem arrangement are investigated numerically. The calculations are validated against the experimental and numerical results obtained by other researchers to prove the accuracy and effectiveness.

Numerical Simulations of Heat Transfer Problems Using an Immersed Boundary Method on Non-Staggered Grids

2004 ◽  
Author(s):  
J. Rafael Pacheco ◽  
Tamara Rodic ◽  
Arturo Pacheco-Vega ◽  
Robert E. Peck
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Staggered Grid ◽  
Immersed Boundary ◽  
Governing Equations ◽  
Step Method ◽  
Fractional Step Method ◽  
Flow And Heat Transfer ◽  
Grid Technique ◽  
Transfer Problems

This paper describes the use of the immersed boundary technique for simulating fluid flow and heat transfer problems over or inside complex geometries. The methodology is based on a fractional step method to integrate in time. The governing equations are discretized and solved on a regular mesh with a finite volume non-staggered grid technique. Several phenomenologically different fluid flow and heat transfer problems are simulated using the technique proposed in this study. The accuracy of the method is second-order, and the efficiency is verified by favorable comparison with previous numerical and experimental results.

Numerical Study of The Interference Effects in Small Vertical Axis Wind Turbines

2005 ◽  
Author(s):  
Yuko Sato ◽  
Tetuya Kawamura
Keyword(s):  
Coordinate System ◽  
Wind Turbines ◽  
Numerical Study ◽  
Cross Flow ◽  
Vertical Axis ◽  
Navier Stokes ◽  
Step Method ◽  
Fractional Step Method ◽  
Navier Stokes Equation ◽  
Stationary Coordinate System

Two dimensional flows around multiple small wind turbines installed in a line are investigated by numerical simulation. The turbines which studied in this research are cross-flow type with vertical axis. Incompressible Navier-Stokes equation is solved by the finite difference method based on the Fractional Step method. Overset grid system is employed in this simulation. A rotating coordinate system, which rotates at the same speed of the turbines, is used for a vicinity of the rotor and a stationary coordinate system is used for the other area. The interference among lined cross-flow wind turbines is investigated for their urban area use.

Numerical Analysis of Electroosmosis in a Micro-Cavity

2008 ◽  
Author(s):  
Dolfred V. Fernandes ◽  
Sangmo Kang ◽  
Yong K. Suh
Keyword(s):  
Electric Fields ◽  
Stokes Equations ◽  
Ionic Species ◽  
Navier Stokes ◽  
Immersed Boundary ◽  
Bench Mark ◽  
Step Method ◽  
Fractional Step Method ◽  
Navier Stokes Equations ◽  
Micro Cavity

The bulk motion of an aqueous solution induced by the application of DC and AC electric fields is studied numerically. The physical model consists of a rectangular micro-cavity filled with dilute, symmetric, binary electrolyte and two completely polarizable cylindrical electrodes. The electric double layer (EDL) model coupled with Navier-Stokes equations governing the electroosmotic flow has been described. The ion-transport in the domain is obtained by solving Poisson-Nernst-Plank equations. We employed IB (immersed boundary) technique for the implementation of boundary conditions and semi-implicit fractional-step method for solving the momentum equations. The Poisson equation for potential distribution is coupled with Nernst-Plank equations for ionic species distribution and solved using CGSTAB iteration solver. Numerical codes are validated using bench-mark problems; driven-cavity-flow and flow over a cylinder. The electric field is almost completely balanced by the accumulation of the counter-ions at the electrodes, at steady state the potential in the most part of domain is zero. The flow field is found predominant in the region near the electrodes.

scholarly journals Development of a Parallel 3D Navier–Stokes Solver for Sediment Transport Calculations in Channels

Computation ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 84
Author(s):  
Gokhan Kirkil
Keyword(s):  
Sediment Transport ◽  
Message Passing ◽  
Message Passing Interface ◽  
Curvilinear Coordinates ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Step Method ◽  
Fractional Step Method ◽  
Fully Implicit ◽  
Parallel Version

We propose a method to parallelize a 3D incompressible Navier–Stokes solver that uses a fully implicit fractional-step method to simulate sediment transport in prismatic channels. The governing equations are transformed into generalized curvilinear coordinates on a non-staggered grid. To develop a parallel version of the code that can run on various platforms, in particular on PC clusters, it was decided to parallelize the code using Message Passing Interface (MPI) which is one of the most flexible parallel programming libraries. Code parallelization is accomplished by “message passing” whereby the computer explicitly uses library calls to accomplish communication between the individual processors of the machine (e.g., PC cluster). As a part of the parallelization effort, besides the Navier–Stokes solver, the deformable bed module used in simulations with loose beds are also parallelized. The flow, sediment transport, and bathymetry at equilibrium conditions were computed with the parallel and serial versions of the code for the case of a 140-degree curved channel bend of rectangular section. The parallel simulation conducted on eight processors gives exactly the same results as the serial solver. The parallel version of the solver showed good scalability.

Large Eddy Simulations of a Hydrocyclone

2002 ◽  
Author(s):  
Francisco Jose´ de Souza ◽  
Aristeu Silveira Neto
Keyword(s):  
Turbulence Models ◽  
Fluid Flows ◽  
Scale Model ◽  
Staggered Grid ◽  
Subgrid Scale ◽  
Step Method ◽  
Fractional Step Method ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Subgrid Scale Modeling

Subgrid-scale modeling, which characterizes Large Eddy Simulation (LES), has been used to predict the behavior of a water-fed hydrocyclone operating without an air core. The governing equations were solved by a fractional step method on a staggered grid. The Smagorinsky subgrid-scale model was employed to account for turbulent effects. Numerical results actually capture the main features of the flow pattern and agree reasonably well with experiments, suggesting that LES represents an interesting alternative to classical turbulence models when applied to the numerical solution of fluid flows within hydrocyclones.

scholarly journals Conjugate Solutions of Navier-Stokes Equation with Deformed Pore Structure

2014 ◽  
Vol 8 ◽  
pp. 30-48
Author(s):  
V.I. Popkov ◽  
V.I. Astafiev ◽  
V.P. Shakshin ◽  
S.V. Zatsepina
Keyword(s):  
Stokes Equation ◽  
Deformation Theory ◽  
Cluster Structure ◽  
Mass Conservation ◽  
Navier Stokes ◽  
Porous Space ◽  
Navier Stokes Equation ◽  
Linear Solution ◽  
Regional Problems ◽  
Final Speed

Within the framework of block self-organizing of geological bodies with use of deformation theory the mathematical solution of a problem for effective final speed is proposed. The analytical and numerical integrated solutions of Navier-Stokes equation for deformable porous space were obtained. The decisions of multi-scaled regional problems «on a flow basis» were also presented: from lithology of rock space - to a well and from a well - to petro-physics. The evolutionary transformation of the linear solution of the equation on mass conservation up to the energetically stable non-linear solution of the equation on preserving the number of movements is also offered. Basing upon the analytical solution of Navier-Stokes equation and model of A.N. Kolmogorov we have obtained the energy model of turbulence pulsing controlled chaos, conjugated with risk stability of average well inflow and cluster structure of Earth defluidization.

Numerical Study of Density-Currents Using the Non-Staggered Grid Fractional-Step-Method

2000 ◽  
Author(s):  
J. Rafael Pacheco ◽  
Arturo Pacheco-Vega ◽  
Sigfrido Pacheco-Vega
Keyword(s):  
Numerical Study ◽  
Density Variation ◽  
Staggered Grid ◽  
Mapping Technique ◽  
Fractional Step ◽  
Density Currents ◽  
Step Method ◽  
Fractional Step Method ◽  
New Approach ◽  
Flow Equations

Abstract A new approach for the solution of time-dependent calculations of buoyancy driven currents is presented. This method employs the idea that density variation can be pursued by using markers distributed in the flow field. The analysis based on the finite difference technique with the non-staggered grid fractional step method is used to solve the flow equations written in terms of primitive variables. The physical domain is transformed to a rectangle by means of a numerical mapping technique. The problems analyzed include two-fluid flow in a tank with sloping bottom and colliding density currents. The numerical experiments performed show that this approach is efficient and robust.

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