Dear PyFR developers I have a question regarding regarding the precision of the interpolation and gradient operators of the FR/SD methods in *hexahedral *meshes.
Let's say that I initialize a variable in the solution points using a general polynomial expression $f$: $f(x, y, z) = (x + y + z)^p$ Where $p$ is the order of the polynomial and $x, y, z$ is the position in the physical space of a given solution point. Then, I use the interpolation operators (Legendre/Lagrange interpolation basis based on the elements' solution points) to compute the numerical interpolated values of $f$ in the flux/Gauss points $f_g$. I have observed that, if the flux reconstruction scheme is of order $m$ then the interpolation operators will interpolate exactly a function $f$ of order $p = m - 1$ in any type of *hexahedral *mesh, am I right? Moreover, regarding the approximation of the gradients $\nabla f$ at the flux/gauss points $\nabla f_g$ I have observed that this extrapolated gradient will be numerically exact for $p = m - 1$ in *cartesian hexahedral* meshes. However, for *non-cartesian hexahedral* meshes I observed that I can only compute numerically exact the gradient of a function $f$ of order $p = m - 2$. This implies 0th truncation errors of the gradient computation for the FR2/SD2 method in general non-cartesian hexahedral meshes... Do you know of any references which discuss about the topics that I have described beforehand? Thank you very much for your help and insight, Gonzalo -- You received this message because you are subscribed to the Google Groups "PyFR Mailing List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web, visit https://groups.google.com/d/msgid/pyfrmailinglist/04f1671f-a2ae-4cee-aa3a-86b7193340af%40googlegroups.com.
