Re: [firedrake] Cell center on extruded mesh
For the distances between cell centres, yes. It feels like you're performing some operations that aren't particularly finite element-y? Would you be using the approximate gradient in a variational form immediately, or are there further calculations you want to carry out? In the former case, I think there's a nice FE way to get what you want. In the latter case, we can probably hack something up if we're smart enough... On 22 September 2015 at 18:42, Buesing, Henrik < HBuesing@eonerc.rwth-aachen.de> wrote:
------------------------------ *Von:* firedrake-bounces@imperial.ac.uk [firedrake-bounces@imperial.ac.uk]" im Auftrag von "Andrew McRae [A.T.T.McRae@bath.ac.uk] *Gesendet:* Dienstag, 22. September 2015 18:59 *An:* firedrake@imperial.ac.uk *Betreff:* Re: [firedrake] Cell center on extruded mesh
Can you say a bit more about how you plan to use this? I wonder to what end you would like these values? I would like to approximate \grad(pw) on a DG0 Function space by (p('+') - p('-'))/|x('+')-x('-')|, where x are the cell centers. On a hexahedral mesh this should just give \Delta x, \Delta y, \Delta z, right?
Henrik
On 22 September 2015 at 17:52, Buesing, Henrik < HBuesing@eonerc.rwth-aachen.de> wrote:
Dear Firedrakers,
on an extruded mesh:
*meshbase = RectangleMesh(Nx, Ny, Lx, Ly, quadrilateral=True) mesh = ExtrudedMesh(meshbase, Nz, Delta_z) horiz_elt = FiniteElement("DG", quadrilateral, 0) vert_elt = FiniteElement("DG", interval, 0) elt = OuterProductElement(horiz_elt, vert_elt) *How can I access the element center and the center of the element faces? Thank you!
Henrik
-- Dipl.-Math. Henrik Büsing Applied Geophysics and Geothermal Energy E.ON Energy Research Center RWTH Aachen University ----------------------------------------------- Mathieustr. 10 | Tel +49 (0)241 80 49907 52074 Aachen, Germany | Fax +49 (0)241 80 49889 ----------------------------------------------- http://www.eonerc.rwth-aachen.de/GGE hbuesing@eonerc.rwth-aachen.de -----------------------------------------------
________________________________ Von: firedrake-bounces@imperial.ac.uk [firedrake-bounces@imperial.ac.uk]" im Auftrag von "Andrew McRae [A.T.T.McRae@bath.ac.uk] Gesendet: Dienstag, 22. September 2015 20:42 An: firedrake@imperial.ac.uk Betreff: Re: [firedrake] Cell center on extruded mesh
For the distances between cell centres, yes.
It feels like you're performing some operations that aren't particularly finite element-y? True. I try to mimic a finite volume (two-point flux approximation) scheme here. Would you be using the approximate gradient in a variational form immediately, or are there further >calculations you want to carry out? I would want to use it directly.
In the former case, I think there's a nice FE way to get what you want. I'm not bound to the FV way here. I just want to solve the attached PDE system. Doing it the FE way would have the additional benefit of having a lot more freedom discretisation-wise. Doing it the FV way, I just happen to know what kind of approximation works (upwinding of the relative permeabilities kr\alpha(Sw), fluxes across element faces)
In the latter case, we can probably hack something up if we're smart enough... On 22 September 2015 at 18:42, Buesing, Henrik <HBuesing@eonerc.rwth-aachen.de<mailto:HBuesing@eonerc.rwth-aachen.de>> wrote: ________________________________ Von: firedrake-bounces@imperial.ac.uk<mailto:firedrake-bounces@imperial.ac.uk> [firedrake-bounces@imperial.ac.uk<mailto:firedrake-bounces@imperial.ac.uk>]" im Auftrag von "Andrew McRae [A.T.T.McRae@bath.ac.uk<mailto:A.T.T.McRae@bath.ac.uk>] Gesendet: Dienstag, 22. September 2015 18:59 An: firedrake@imperial.ac.uk<mailto:firedrake@imperial.ac.uk> Betreff: Re: [firedrake] Cell center on extruded mesh
Can you say a bit more about how you plan to use this? I wonder to what end you would like these values? I would like to approximate \grad(pw) on a DG0 Function space by (p('+') - p('-'))/|x('+')-x('-')|, where x are the cell centers. On a hexahedral mesh this should just give \Delta x, \Delta y, \Delta z, right?
Henrik On 22 September 2015 at 17:52, Buesing, Henrik <HBuesing@eonerc.rwth-aachen.de<mailto:HBuesing@eonerc.rwth-aachen.de>> wrote: Dear Firedrakers, on an extruded mesh: meshbase = RectangleMesh(Nx, Ny, Lx, Ly, quadrilateral=True) mesh = ExtrudedMesh(meshbase, Nz, Delta_z) horiz_elt = FiniteElement("DG", quadrilateral, 0) vert_elt = FiniteElement("DG", interval, 0) elt = OuterProductElement(horiz_elt, vert_elt) How can I access the element center and the center of the element faces? Thank you! Henrik -- Dipl.-Math. Henrik Büsing Applied Geophysics and Geothermal Energy E.ON Energy Research Center RWTH Aachen University ----------------------------------------------- Mathieustr. 10 | Tel +49 (0)241 80 49907<tel:%2B49%20%280%29241%2080%2049907> 52074 Aachen, Germany | Fax +49 (0)241 80 49889<tel:%2B49%20%280%29241%2080%2049889> ----------------------------------------------- http://www.eonerc.rwth-aachen.de/GGE hbuesing@eonerc.rwth-aachen.de<mailto:hbuesing@eonerc.rwth-aachen.de> -----------------------------------------------
-- Dipl.-Math. Henrik Büsing Institute for Applied Geophysics and Geothermal Energy E.ON Energy Research Center RWTH Aachen University ------------------------------------------------------ Mathieustr. 10 | Tel +49 (0)241 80 49907 52074 Aachen, Germany | Fax +49 (0)241 80 49889 ------------------------------------------------------ http://www.eonerc.rwth-aachen.de/GGE hbuesing@eonerc.rwth-aachen.de ------------------------------------------------------ Von: firedrake-bounces@imperial.ac.uk [mailto:firedrake-bounces@imperial.ac.uk] Im Auftrag von Andrew McRae Gesendet: 22 September 2015 20:42 An: firedrake@imperial.ac.uk Betreff: Re: [firedrake] Cell center on extruded mesh For the distances between cell centres, yes. It feels like you're performing some operations that aren't particularly finite element-y? Would you be using the approximate gradient in a variational form immediately, or are there further calculations you want to carry out? In the former case, I think there's a nice FE way to get what you want. [Buesing, Henrik] @Andrew: So, what would be the FE way of doing this? Henrik In the latter case, we can probably hack something up if we're smart enough... On 22 September 2015 at 18:42, Buesing, Henrik <HBuesing@eonerc.rwth-aachen.de<mailto:HBuesing@eonerc.rwth-aachen.de>> wrote: ________________________________ Von: firedrake-bounces@imperial.ac.uk<mailto:firedrake-bounces@imperial.ac.uk> [firedrake-bounces@imperial.ac.uk<mailto:firedrake-bounces@imperial.ac.uk>]" im Auftrag von "Andrew McRae [A.T.T.McRae@bath.ac.uk<mailto:A.T.T.McRae@bath.ac.uk>] Gesendet: Dienstag, 22. September 2015 18:59 An: firedrake@imperial.ac.uk<mailto:firedrake@imperial.ac.uk> Betreff: Re: [firedrake] Cell center on extruded mesh
Can you say a bit more about how you plan to use this? I wonder to what end you would like these values? I would like to approximate \grad(pw) on a DG0 Function space by (p('+') - p('-'))/|x('+')-x('-')|, where x are the cell centers. On a hexahedral mesh this should just give \Delta x, \Delta y, \Delta z, right?
Henrik On 22 September 2015 at 17:52, Buesing, Henrik <HBuesing@eonerc.rwth-aachen.de<mailto:HBuesing@eonerc.rwth-aachen.de>> wrote: Dear Firedrakers, on an extruded mesh: meshbase = RectangleMesh(Nx, Ny, Lx, Ly, quadrilateral=True) mesh = ExtrudedMesh(meshbase, Nz, Delta_z) horiz_elt = FiniteElement("DG", quadrilateral, 0) vert_elt = FiniteElement("DG", interval, 0) elt = OuterProductElement(horiz_elt, vert_elt) How can I access the element center and the center of the element faces? Thank you! Henrik -- Dipl.-Math. Henrik Büsing Applied Geophysics and Geothermal Energy E.ON Energy Research Center RWTH Aachen University ----------------------------------------------- Mathieustr. 10 | Tel +49 (0)241 80 49907<tel:%2B49%20%280%29241%2080%2049907> 52074 Aachen, Germany | Fax +49 (0)241 80 49889<tel:%2B49%20%280%29241%2080%2049889> ----------------------------------------------- http://www.eonerc.rwth-aachen.de/GGE hbuesing@eonerc.rwth-aachen.de<mailto:hbuesing@eonerc.rwth-aachen.de> -----------------------------------------------
participants (2)
-
Andrew McRae
-
Buesing, Henrik