[overture] Re: differentiation on the grid boundary
- From: Bill Henshaw <henshaw@xxxxxxxx>
- To: overture@xxxxxxxxxxxxx
- Date: Mon, 21 May 2012 07:22:16 -0700
Hi Mostafa,
Normally if I knew the analytic solution I would just differentiate
it analytically. However, if you want to estimate the derivatives of
the analytic solution then you can fill in a grid function, including
the ghost points, with the analytic solution and then call the
Overture derivative routines. The derivative routines will
use the values on the ghost points.
I hope that answers your question.
...Bill
On 05/20/2012 01:52 PM, mostafa amini afshar wrote:
Dear Bill
I would like to ask for your kind help regarding the differentiation of mapped
grid functions.
I am interested to calculate the first and second derivatives of a grid function to forth order of accuracy. Actually I have two distinct grid functions: one is the numerical solution (calculated to
4th order) and the other is just the analytical solution for the same problem. There are two lines of the ghost points. The objective is to calculate a specific relationship containing the
derivatives of the solutions and then comparing them in Overture.
The derivatives of the computational solution uses the values on two ghost layers that have been assigned by the solver. Now if i want to calculate the derivative of the analytical solution on the
same boundary, the derivative uses the values on the ghost layers that are specified by myself and are the analytical solution on the ghost points. These are totally different than those specified
by the solver in the case of computational solution.
Of course this way of treating the ghost points, gives two sets of different results for the derivatives on the boundary. This would also influence the derivatives of analytical solution of the
points in the first layer in to the grid as they still use the values of ghost points that are assigned by myself.
I would highly appreciate it if could kindly please tell me the way i can
surmount this problem while calculating the derivatives of the analytical
solution on the boundary points.
Best regards
Mostafa
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