On 5/20/21 8:49 AM, 沈键 wrote:
Recently, I am writing codes to solve velocity potential equation which is
laplace equation form to solve the incompressible and inviscid airfoil field.
And after solving the system, I get the potential on each nodes. Then, I use
Datapostprocessor class to calculate solution's derivatives and output to
tecplot format. I find the solution is continous in tecplot, but its
derivative is not. And I have learned that for Q1/Q2,etc element, its
derivative is not continous between adjacent cells in theory, but in
engineering we usually smooth the values between adjacent cells. My question is:
-*Is there any easy way to smooth the values between adjacent cells*？(I
believe dealii has considered this problem, but I just didn't find any
examples from tutorial.)
No "easy" way with DataPostprocessor at least. What DataPostprocessor does is
to faithfully output the gradient, which is indeed a discontinuous function.
The way to do this is to create a (continuous) finite element field onto which
you project the gradient. For example, let's say you define an FE_Q (and
associated DoFHandler) for the x-derivative of your solution. Then you would
want to compute the projection of d/dx u_h into this space via
(phi_i, grad_x) = (phi_i, d/dx u_h)
This requires solving with a mass matrix, but at least the grad_x finite
element function is a continuous function that you can then output.
Best
W.
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Wolfgang Bangerth email: [email protected]
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