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How to define fluxes for two dimensional convectiondiffusion equation? 

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September 9, 2015, 11:40 

#21 
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Yes. U and V equals one. I just want to check my local mesh refinement algorithm and want to make sure that it is giving better result than when there is no refinement. Then later on, I would change it to be a dynamic mesh once the procedure turns out to be right.


September 9, 2015, 11:49 

#22  
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Filippo Maria Denaro
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Quote:
local steady refinement can not help improving this kind of solution 

September 9, 2015, 11:55 

#23 
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Why is that so professor? Say, I am validating my results along the centerline where there is a sudden jump of solution from 0 to 1. With local mesh refinement here along the center, should not I be able to manage to get a better solution?


September 9, 2015, 11:58 

#24  
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Filippo Maria Denaro
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this jump will rapidly move far from the refined region 

September 9, 2015, 12:01 

#25 
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In my particular case with the boundary conditions that I am using, this jump remains in steady state. You can imagine a square with top and left sides on 1 and right and bottom sides on 0 initial value. At steady state, the center point of square is where the jump happens. You are right that in transient case, this will keep moving like a wave.


September 9, 2015, 12:08 

#26 
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Filippo Maria Denaro
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your BC.s cannot be prescribed on all the edges of the box but only at left and bottom .....


September 9, 2015, 12:11 

#27 
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Why is that so professor? I remember I have earlier solved 1D inviscid Burgers equation in which I had BC on both of the ends of domain. And how would I deal with the top and right two boundaries if this is the case? Periodic BC?


September 9, 2015, 12:18 

#28 
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Filippo Maria Denaro
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that's wrong, the 1D Burgers equation requires only one BC. to be well posed.


September 9, 2015, 12:21 

#29 
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For that case actually, I had used the initial condition and boundary conditions from the PhD thesis of Marsha Berger(who proposed adaptive mesh refinement for hyperbolic PDE that I want to use). But even with 2 BC, it got solved well.


September 9, 2015, 12:31 

#30  
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Filippo Maria Denaro
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I strongly suggest to better study the character of the equations and the required boundary conditions 

September 9, 2015, 21:19 

#31 
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Thanks professor! So in my two dimensional case, what kind of BC will I need on the other two edges?


September 10, 2015, 03:41 

#32 
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Filippo Maria Denaro
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Tags 
finite difference, finite volume, math, mesh, pde 
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