# Convection Term Discretization

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 September 9, 2004, 06:38 Convection Term Discretization #1 Maciej Matyka Guest   Posts: n/a
Hi, I would like to ask about one of my problems which I have doing the new free surface code. I am trying to implement one of high order schemes - VONOS, and found that sometimes people discretize only one part of convection term with higher order schemes, and sometimes they discretize both. I mean i.e. u momentum equation with two part convection term: - d(uu)/dx - d(vu)/dy. In a paper of Sean McKee et. al.: "High-order upwinding and the hydraulic jump", Num. Meth. in Fluids they are discretizing only d(uu)/dx with high order scheme and d(vu)/dy is discretized by centered scheme. On the other side - Griebel et.al. developed NaSt3d code where both parts of the convection term are discretized with high order scheme. Who is doing it good? I should add, that I tested both discretizations, still have problems with my code and need to be sure that that part of the code (core of it) works well to test next parts of it. And last questions - regarding free surface and high order schemes - am I right when apllying the First Order Upwind near the surface or should I derive expressions from other high order schemes to treat convection near free surface?
Thank you, Maciej Matyka http://panoramix.ift.uni.wroc.pl/~maq/eng/

 September 9, 2004, 21:58 Re: Convection Term Discretization #2 Junseok Kim Guest   Posts: n/a In a paper of Sean McKee et. al.: "High-order upwinding and the hydraulic jump", Num. Meth. in Fluids It looks like they use high order discretization, would you be more specific about the pages?

 September 10, 2004, 02:47 Re: Convection Term Discretization #3 Maciej Matyka Guest   Posts: n/a Yes, they do use hogh order approximation and apply it for all terms - I was wrong, now it is clear to me. Sorry. M.

 October 7, 2004, 04:32 discretization of Navier Stokes Eqns #4 Nil Gurbuz Guest   Posts: n/a Hi I am a phd student in math. working on Navier stokes equations I am mainly working on finite difference schemes I wonder whether it is possible to use finite difference discretization with staggered grid but not the control volume method ? I also confuded about how to approximate the fictious points outside the boundary for pressure and V velocities Thanks Nil Gurbuz