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July 23, 2009, 09:19 |
divergence with higher order scheme
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#1 |
New Member
Chandra
Join Date: Jul 2009
Posts: 5
Rep Power: 17 |
Hi,
I am doing DNS and am in process of implementing higher order schemes. I am done with implementing it in momentum equation etc. However, when it comes to calculate divergence in a cell, i.e. Div = du/dx+dv/dy+dw/dz, I am getting a bit confused whether I should implement higher order scheme here as well or I should keep it just second order accurate. I am asking it because if 2nd order accurate, du/dx = (u[i+1]-u[i])/(x[i+1]-x[i]) etc. on staggered grids. It gives a feeling of the rate of mass accumulation in the cell, a physically meaningful quantity. However, if we change this to 4th order discretization, du/dx = f(u[i+2], u[i+1], u[i], u[i-1]) etc. which doesn't look like giving mass accumulation in the cell in discrete manner. Could anyone please point out which one should be preferred? Thanks! |
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July 23, 2009, 14:53 |
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#2 |
Member
Join Date: Mar 2009
Posts: 62
Rep Power: 17 |
Usually you should keep the same order of discretization on all spatial derivatives if you want to have a pure 4 order scheme let's say. Otherwise your DNS will be only 2nd order.
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divergence, higher order |
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