# Higher order formulation question

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 July 27, 2012, 09:13 Higher order formulation question #1 New Member   Join Date: Jul 2012 Posts: 2 Rep Power: 0 Hi all This is my first post on here and I'm starting by asking for help 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?

July 27, 2012, 13:47
#2
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Filippo Maria Denaro
Join Date: Jul 2010
Posts: 3,252
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Quote:
 Originally Posted by peterciaran Hi all This is my first post on here and I'm starting by asking for help 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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