Lid driven cavity problem

thegodfather · December 2, 2012, 00:59

I'm trying to develop a finite volume stream function vorticity based solver for a lid driven cavity problem.. I want to use first order upwind scheme for discretization of the advection term... But to use it, the direction of velocities at all cell faces are to be known before hand... How do I incorporate this in my code? Plus, how do I determine the values of velocities at cell faces from cell centre velocities? Is it ok to do linear interpolation for that?

FMDenaro · December 2, 2012, 05:37

you can use linear interpolation, for example for a generic transport equation, the flux component along x writes

u_face_west = 0.5*(u(i-1,j)+u(i,j))
u_plus = 0.5*(u_face+|u_face|)
u_minus = 0.5*(u_face-|u_face|)
flux_west = u_plus*Phi(i-1,j) + u_minus*Phi(i,j)

December 2, 2012, 00:59	Lid driven cavity problem	#1
thegodfather New Member Aniket Sachdeva Join Date: Mar 2012 Posts: 22 Rep Power: 14	I'm trying to develop a finite volume stream function vorticity based solver for a lid driven cavity problem.. I want to use first order upwind scheme for discretization of the advection term... But to use it, the direction of velocities at all cell faces are to be known before hand... How do I incorporate this in my code? Plus, how do I determine the values of velocities at cell faces from cell centre velocities? Is it ok to do linear interpolation for that?

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December 2, 2012, 05:37		#2
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,882 Rep Power: 73	you can use linear interpolation, for example for a generic transport equation, the flux component along x writes u_face_west = 0.5(u(i-1,j)+u(i,j)) u_plus = 0.5(u_face+\|u_face\|) u_minus = 0.5(u_face-\|u_face\|) flux_west = u_plusPhi(i-1,j) + u_minus*Phi(i,j)