RE: Additional curvilinear terms in the mass and momentum equations  DFlow Flexible Mesh  Delft3D
intro story DFlow FM
DFlow Flexible MeshDFlow Flexible Mesh (DFlow FM) is the new software engine for hydrodynamical simulations on unstructured grids in 1D2D3D. Together with the familiar curvilinear meshes from Delft3D 4, the unstructured grid can consist of triangles, pentagons (etc.) and 1D channel networks, all in one single mesh. It combines proven technology from the hydrodynamic engines of Delft3D 4 and SOBEK 2 and adds flexible administration, resulting in:
An overview of the current developments can be found here. The DFlow FM  team would be delighted if you would participate in discussions on the generation of meshes, the specification of boundary conditions, the running of computations, and all kinds of other relevant topics. Feel free to share your smart questions and/or brilliant solutions!
=======================================================  Sub groups

Message Boards
RE: Additional curvilinear terms in the mass and momentum equations
SS
Steven Sandbach, modified 8 Years ago.
RE: Additional curvilinear terms in the mass and momentum equations
Youngling Posts: 7 Join Date: 3/28/11 Recent Posts 00
Dear Delft3D community,
I am trying to understand the terms used to transform from curvilinear to rectangular coordinates, so that I can compare the momentum conservation equation expressed in curvilinear coordinates (as in the DELFTFLOW manual) with the equivalent equation written for a rectangular grid.
To do this I need to understand the sqrt(G) terms, but these don’t seem to be clearly defined in the manual (they are described simply as ‘coefficents used to transform curvilinear to rectangular coordinates’).
Based on what I have read online and in the manual, it appears to me that sqrt(G_nu_nu) is the grid face length in the nu direction, calculated from sqrt(dx^2+dy^2), where dx and dy are the lengths of the same cell face in x and y directions.
I’m less clear about what is meant by d(nu). I assume nu and xi are the coordinates in computational (M,N) space? And that d(nu)=1 and d(xi)=1? That doesn't seem quite right to me, but it does seem to make sense with what follows.....
If that were the case then for a rectangular grid in which xi corresponds to x and nu to y, the second term in the x momentum equation (9.6 of FLOW manual 3.15.14499) would become U dU/dx. This would also mean that some of the terms disappear – e.g., the 4th term in the momentum equations (9.6 and 9.7 of FLOW manual 3.15.14499) would disappear on a rectangular grid because d (sqrt(G_xi_xi))/ d(nu) would be zero for a rectangular grid with constant dx and dy because sqrt(G_xi_xi) = dx is the same everywhere.
I’d be grateful if anyone familiar with the transformation from curvilinear to cartesian to computational space could clarify this for me!
Thanks in advance.
Regards
Steve
I am trying to understand the terms used to transform from curvilinear to rectangular coordinates, so that I can compare the momentum conservation equation expressed in curvilinear coordinates (as in the DELFTFLOW manual) with the equivalent equation written for a rectangular grid.
To do this I need to understand the sqrt(G) terms, but these don’t seem to be clearly defined in the manual (they are described simply as ‘coefficents used to transform curvilinear to rectangular coordinates’).
Based on what I have read online and in the manual, it appears to me that sqrt(G_nu_nu) is the grid face length in the nu direction, calculated from sqrt(dx^2+dy^2), where dx and dy are the lengths of the same cell face in x and y directions.
I’m less clear about what is meant by d(nu). I assume nu and xi are the coordinates in computational (M,N) space? And that d(nu)=1 and d(xi)=1? That doesn't seem quite right to me, but it does seem to make sense with what follows.....
If that were the case then for a rectangular grid in which xi corresponds to x and nu to y, the second term in the x momentum equation (9.6 of FLOW manual 3.15.14499) would become U dU/dx. This would also mean that some of the terms disappear – e.g., the 4th term in the momentum equations (9.6 and 9.7 of FLOW manual 3.15.14499) would disappear on a rectangular grid because d (sqrt(G_xi_xi))/ d(nu) would be zero for a rectangular grid with constant dx and dy because sqrt(G_xi_xi) = dx is the same everywhere.
I’d be grateful if anyone familiar with the transformation from curvilinear to cartesian to computational space could clarify this for me!
Thanks in advance.
Regards
Steve