# modify fvMatrix / coupled equations / higher order diffusion

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 May 7, 2011, 06:20 modify fvMatrix / coupled equations / higher order diffusion #1 New Member   Jinming Lu Join Date: May 2011 Posts: 2 Rep Power: 0 Dear OpenFOAM community, I've just started using OpenFOAM, trying to solve an equation of the type df/dt = laplacian(laplacian(f)) for higher order diffusion To my limited knowledge (please correct if I am wrong), simple diffusion df/dt = laplacian(f) is already implemented and Code: ```fvScalarMatrix fEqn ( fvm::ddt(f) - fvm::laplacian(f) );``` creates an equation of the type (for the implicit case) (F - F0)*V/deltaT - A*F where F is a vector/list containing the cell values of f to be calculated, F0 those of the previous time step, V is the volume, deltaT is the time step, and A denotes the "discretized laplacian" (coefficient matrix). A naive solution of df/dt = laplacian(laplacian(f)) would be creating an equation of the type (F - F0)*V/deltaT - A*A*F, i.e. multiplying the fvMatrix A obtained from fvm::laplacian(f) by itself. I would be grateful if someone could give me a hint on the implementation or how to solve the coupled problem df/dt == laplacian(g) laplacian(f) == g Thanks in advance. Best regards, Jinming