|July 23, 2009, 09:19||
divergence with higher order scheme
Join Date: Jul 2009
Posts: 5Rep Power: 6
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?
|July 23, 2009, 14:53||
Join Date: Mar 2009
Posts: 62Rep Power: 6
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.
|divergence, higher order|
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