RE: Additional curvilinear terms in the mass and momentum equationsRE: Additional curvilinear terms in the mass and momentum equationshttps://oss.deltares.nl/c/message_boards/find_thread?p_l_id=1806765&threadId=2162922021-02-27T19:57:12Z2021-02-27T19:57:12ZRE: Additional curvilinear terms in the mass and momentum equationsSteven Sandbachhttps://oss.deltares.nl/c/message_boards/find_message?p_l_id=1806765&messageId=2162912012-11-29T12:31:08Z2012-11-29T12:30:57ZDear Delft3D community,<br /><br />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 DELFT-FLOW manual) with the equivalent equation written for a rectangular grid.<br />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’).<br /><br />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.<br /><br />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.....<br /><br />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. <br /><br />I’d be grateful if anyone familiar with the transformation from curvilinear to cartesian to computational space could clarify this for me! <br /><br />Thanks in advance.<br /><br />Regards<br /><br />SteveSteven Sandbach2012-11-29T12:30:57Z