[mprinkey]

Originally Posted by Simbelmynë

This sounds reasonable. Is this common for FV/FD methods? If so then I guess the test problem is not so useful. Would a backward facing step against experimental data serve as a better test in your oppinion?

This will be true for any numerical scheme that is based on Taylor series interpolation/differencing schemes (FV, FD, or FE)...or any orthogonal polynomial basis (Chebyshev spectral or DG). If, however, your basis functions were Fourier (cosine/sine spectral), this wouldn't be a problem. It comes down to whether or not the continuous solution can be exactly represented by your finite solution basis. You cannot build an exact approximation to x^2 using a finite number of sine and cosine terms, but you can with the first three Chebyshev polynomials: x^2 = 1/2*(T_0(x) + T_2(x))

You will get no where comparing your results to PHYSICAL experimental results to document the order of the method. That is great to establish the physical correctness, but the error bars on even the best fluids experiments are going to be too large to be useful here. Numerical experiments are a different matter.

A common technique is to run a problem with as fine a grid as you can manage to simulate with the highest-order technique you have on hand and use it as the "exact" solution. That is useful and can lead to good error convergence plots for the lower resolution/order simulations. It does not, however, establish that the code is giving the correct answer. You can see this if you accidentally included an extra factor of two in the code. The exact answer may be 1.0, but every version of your results will consistently give 2.0, even the ultra-high resolution, high-order results. So, your answers would be consistent with each other but also completely wrong. If you want to do this, look at the lid driven cavity or backward facing step. There are high-resolution baseline results available, and you can use those to verify your high-order/high-resolution results and then work on the error convergences plots as I outlined above.

You should be able to establish simple flow configuration with closed-form solutions. For incompressible flow, I've used arrays of Taylor vortices...those exact solutions are sine/cosines and will always have H.O.T.s to converge with normal FD/FV/FE schemes. There is also a technique called the Method of Manufactured Solutions that will always give you a way to build whatever solution you like by the construction of source terms. Note that these techniques require a lot of care in setting up the boundary conditions and/or source terms. Remember in particular for the FV scheme, you need to provide the FACE-AVERAGED values of the exact solution for boundary conditions and the CELL-AVERAGED value for source terms.

Good luck.

[FMDenaro]

I suggest using this 3D exact solution

http://www.ann.jussieu.fr/frey/paper...nchmarking.pdf