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Rayleigh Benard 3D coding with finite differences 

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February 17, 2016, 00:16 
Rayleigh Benard 3D coding with finite differences

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Madhup
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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, 03:18 

#2  
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Filippo Maria Denaro
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please, provide much more details about your code such as formulation, type of discretization, grid arrangement, values of the nondimensional parameters, etc 

February 17, 2016, 05:07 

#3 
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Madhup
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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, 05:11 

#4  
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Filippo Maria Denaro
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if you use a second order discretization and a colocated arrangement, you could have experienced a decouplingmode solution in the pressure equation. Could you post some figures of velocity and pressure fields? 

February 17, 2016, 05:21 

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Madhup
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Here are the figures encl : 

February 17, 2016, 05:42 

#6 
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Filippo Maria Denaro
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it is a decoupling along the gravity axis, you can see the pressure field oscillating ... why don't you try using a staggered grid?


February 17, 2016, 05:52 

#7 
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Madhup
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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, 06:01 

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Filippo Maria Denaro
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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, 06:15 

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Madhup
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February 22, 2016, 00:17 

#10 
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Madhup
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Now i applied staggered grid, please see wvelocity profile , i can see rolls still. Will they apper after long time ?


February 22, 2016, 04:32 

#11 
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Filippo Maria Denaro
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Tags 
finite difference method, fortran code, prandtl number, rayleighbenard 
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