# Solve Coupled Equations

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 November 12, 2008, 01:08 Hi I would like to solve c #1 Senior Member   Vishal Nandigana Join Date: Mar 2009 Location: Champaign, Illinois, U.S.A Posts: 208 Rep Power: 11 Sponsored Links Hi I would like to solve coupled equations (using relaxation or Newtons method, but first would like to see for relaxation method). Can you help me which tutorial or solver should i follow in order to solve this problem. Further I have solved a poisson equation adding source terms that are functions of x and y successfully. I had incorporated Dirichlet B.C's for a square 1*1 block (the b.c's are also functions of x and y). May I know how do we incorporate neumann b.cs for the same problem (they are also functions of x and y). Say the four sides are inlet,outlet, upperwall and lowerwall. My B.C's are inlet (AT x =0) - Dirichlet B.C's = (y*(1-y)) (something of this type). Similarly (at y=0) (lowerwall) = -x^3 + sin (x).. Neumann B.C's at x =1 (outlet) = -3-2*sin(x)(some arbitary function) Neumann B.C's at y =1 (upperwall) = 4+sin(y) For the inlet case I have my B.C statements like these... Which works fine.. label inletPatchID = mesh.boundaryMesh().findPatchID("inlet"); fvPatchScalarField& inletT = T.boundaryField()[inletPatchID]; const vectorField& faceCentresInlet = mesh.Cf().boundaryField()[inletPatchID]; forAll(inletT, pointI) { inletT[pointI] = faceCentresInlet[pointI].y()*(1.0 - faceCentresInlet[pointI].y()); } Can anyone let me know how do we incorporate the neumann b.cs for this problem.. Kindly help me out.. Regards Vishal

 November 12, 2008, 23:47 Hi, I need to solve a coupl #2 Senior Member   Vishal Nandigana Join Date: Mar 2009 Location: Champaign, Illinois, U.S.A Posts: 208 Rep Power: 11 Hi, I need to solve a coupled equation which is of the form laplacian(phi) = K * (C1-C2) ( K is some constant) ddt(C1) = laplacian (phi,C1)+ extra terms; ddt(C2) = laplacian(phi,C2)+ extra terms; Could anyone let me know how exactly should i got go about solving this equation. Basically i want to solve a PNP equation, and I don't want it to be solved using relaxation method, I want to solve it using a single matrix (using some newton method or any other iteration techniques). Can anyone throw some light with regard to this, as to what example i have to follow and how I should go about doing this. Kindly help. Thanks Vishal

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