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The accepted answer above is very misleading and @nat-chouf has it correct. In the spirit of the original question, running a pseudo-spectral mode of isotropic turbulence, then zero-ing out $k>\frac{2}{3}k_\textrm{max}$ at each time-step will absolutely remove energy from the model, assuming that energy is moved to these higher wavenumbers.


Let's stick with the case of either piecewise constants or (bi-/tri-)linear functions onto which to project first, and I'm going to talk about "linear" in the following even though on quadrilateral/hexahedral meshes, that's not quite correct. In any case, you are trying to solve the following problem if you have no constraints on the values of your ...

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