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peterciaran July 27, 2012 09:13

Higher order formulation question
 
Hi all

This is my first post on here and I'm starting by asking for help :confused:

I'm trying to build a simple code that will solve the advection equation. Starting from a simple upwind scheme then to a central differencing scheme then on to a third order scheme.

The first two schemes as you'd expect worked easily however once I've tried to move to third order I cant get any results.

so by using a finite volume formulation and polynomial fitting I get a formulation ranging from node E to W-3.

So my 1D formulation becomes;

AE(phi,i+1)+(1-AP)(Phi,i)-AW(phi,i-1)-AW1(phi,i-2)-AW2(phi,i-2)-AW3(phi,i-3)=D

So when i solve this in matrix form the result does not travel in the x direction at all but instead just reduces the values more and more.

an anyone help me?

FMDenaro July 27, 2012 13:47

Quote:

Originally Posted by peterciaran (Post 373931)
Hi all

This is my first post on here and I'm starting by asking for help :confused:

I'm trying to build a simple code that will solve the advection equation. Starting from a simple upwind scheme then to a central differencing scheme then on to a third order scheme.

The first two schemes as you'd expect worked easily however once I've tried to move to third order I cant get any results.

so by using a finite volume formulation and polynomial fitting I get a formulation ranging from node E to W-3.

So my 1D formulation becomes;

AE(phi,i+1)+(1-AP)(Phi,i)-AW(phi,i-1)-AW1(phi,i-2)-AW2(phi,i-2)-AW3(phi,i-3)=D

So when i solve this in matrix form the result does not travel in the x direction at all but instead just reduces the values more and more.

an anyone help me?

You should address more issue about your scheme...as I assume you are working on the equation d/dt phi + u d/dx phi = 0 (u = constant) please use notation "i" for the space-location and "n" for time-location


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