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How to define fluxes for two dimensional convection-diffusion equation? |
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September 9, 2015, 12:40 |
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#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.
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September 9, 2015, 12:49 |
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#22 | |
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Filippo Maria Denaro
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Quote:
local steady refinement can not help improving this kind of solution |
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September 9, 2015, 12:55 |
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#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?
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September 9, 2015, 12:58 |
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#24 | |
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Filippo Maria Denaro
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Quote:
this jump will rapidly move far from the refined region |
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September 9, 2015, 13:01 |
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#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.
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September 9, 2015, 13:08 |
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#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 .....
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September 9, 2015, 13:11 |
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#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?
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September 9, 2015, 13:18 |
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#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.
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September 9, 2015, 13:21 |
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#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.
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September 9, 2015, 13:31 |
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#30 | |
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Filippo Maria Denaro
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Posts: 6,892
Rep Power: 73 |
Quote:
I strongly suggest to better study the character of the equations and the required boundary conditions |
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September 9, 2015, 22:19 |
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#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?
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September 10, 2015, 04:41 |
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#32 |
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Filippo Maria Denaro
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Rep Power: 73 |
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Tags |
finite difference, finite volume, math, mesh, pde |
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