# Rayleigh Benard 3D coding with finite differences

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 February 17, 2016, 01:16 Rayleigh Benard 3D coding with finite differences #1 New Member   Madhup Join Date: Feb 2016 Posts: 6 Rep Power: 9 I am developing a simple fortran solver in finite difference. My domain is 2pi*2pi*1 as taken by S. Chandrasekhar. My equations are having non dimensional parameters as Reynolds Number, Rayleigh Number and Prandtl No. The code is running well but w- velocity contours(heating at bottom and cold at top) are coming only positive and negative alternatively and i am not getting rolls as expected. Can someone explain it.? Thanks in advance

February 17, 2016, 04:18
#2
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Filippo Maria Denaro
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Quote:
 Originally Posted by cfdprojects I am developing a simple fortran solver in finite difference. My domain is 2pi*2pi*1 as taken by S. Chandrasekhar. My equations are having non dimensional parameters as Reynolds Number, Rayleigh Number and Prandtl No. The code is running well but w- velocity contours(heating at bottom and cold at top) are coming only positive and negative alternatively and i am not getting rolls as expected. Can someone explain it.? Thanks in advance

please, provide much more details about your code such as formulation, type of discretization, grid arrangement, values of the non-dimensional parameters, etc

 February 17, 2016, 06:07 #3 New Member   Madhup Join Date: Feb 2016 Posts: 6 Rep Power: 9 I am implementing Pressure- velocity method, and using pressure poisson equation for divergence free flow. Ra=1800, Re=1.0, Pr=1. Grid is uniform in x and y while clustered with cos function in z direction(gravity). discreatisation is done utilizing fourth order Central differencing for diffusion terms, while third order Kawamura and K. Kuwahara upwinding for convective terms. thanks for reply.

February 17, 2016, 06:11
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Filippo Maria Denaro
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Quote:
 Originally Posted by cfdprojects I am implementing Pressure- velocity method, and using pressure poisson equation for divergence free flow. Ra=1800, Re=1.0, Pr=1. Grid is uniform in x and y while clustered with cos function in z direction(gravity). thanks for reply.

if you use a second order discretization and a colocated arrangement, you could have experienced a decoupling-mode solution in the pressure equation.
Could you post some figures of velocity and pressure fields?

February 17, 2016, 06:21
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Quote:
 Originally Posted by FMDenaro if you use a second order discretization and a colocated arrangement, you could have experienced a decoupling-mode solution in the pressure equation. Could you post some figures of velocity and pressure fields?

Here are the figures encl :
Attached Images
 Temp.jpg (31.3 KB, 18 views) W-velocity.jpg (35.6 KB, 17 views) w-velocity in z-direction.jpg (46.1 KB, 8 views)

 February 17, 2016, 06:42 #6 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,676 Rep Power: 71 it is a decoupling along the gravity axis, you can see the pressure field oscillating ... why don't you try using a staggered grid? cfdprojects likes this.

February 17, 2016, 06:52
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 Originally Posted by FMDenaro it is a decoupling along the gravity axis, you can see the pressure field oscillating ... why don't you try using a staggered grid?
Yes i am using collocated grid till now. Would you please suggest me some writeup on staggered grid implementation in view of this problem.

February 17, 2016, 07:01
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Filippo Maria Denaro
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 Originally Posted by cfdprojects Yes i am using collocated grid till now. Would you please suggest me some writeup on staggered grid implementation in view of this problem.

a second order discretization on staggered grid is a very old and well suited formulation, you can find that in any CFD textbook. For example, see the book of Peric & Ferziger

February 17, 2016, 07:15
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 Originally Posted by FMDenaro a second order discretization on staggered grid is a very old and well suited formulation, you can find that in any CFD textbook. For example, see the book of Peric & Ferziger

Thankyou. I will apply it and come back.

February 22, 2016, 01:17
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Now i applied staggered grid, please see w-velocity profile , i can see rolls still. Will they apper after long time ?
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 W-velocity.jpg (52.3 KB, 16 views)

February 22, 2016, 05:32
#11
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Filippo Maria Denaro
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Quote:
 Originally Posted by cfdprojects Now i applied staggered grid, please see w-velocity profile , i can see rolls still. Will they apper after long time ?

from this plot I see still oscillations

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