initial residual and final residual
Hi FOAMERs,
what is the definition of the initial residual and final residual, which can be used to decide convergence ? 
The initial residual is evaluated based on the current values of the field before solving an equation for a particular field . The final residual is evaluated after the solution of the equation is performed.
The intial residual is more important to decide whether a computation converges, or not. 
Hi Anne,
can you give some rule of thumbs for values, which should be achieved for the initial/final residual and how many iterations should be used for pEqn per cycle e.g. for a transient simulation with a standard PCG solver. Best Timo 
Initial residual: e^4 or e^5 is a good result. Final residual has to be smaller (e^8).
I cannot answer your 2nd question. 
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Hi, based on this definition, I was curious as to why the final residual in one time step NOT equal to initial residual in NEXT time step? 
Assuming you are solving in steady state, it is because the equations are nonlinear.
If you solve the momentum equation for U, at the next iteration, P and phi will have been changed. Therefore, the initial residual will be different from the final residual of the last iteration. If you were to solve a linear equation, noncoupled with any other variables, in steadystate, then you would solve it in a single iteration... and therefore your "next initial" residual would be your last final one... Quote:

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If I understand it right, Say : U =f(p,phi,t) where f is a complex function If t0 =0: During 1 st iteration, we start with a p0, phi0 and dt time step and get U1 =f(p0, phi0,dt) as well as p1, phi1 values. The corresponding final error/ residual is calculated from U1 and true U expected. Before 2nd iteration starts, a (say) U12 is calculated based on new available values: U12 =f(p1,phi1,dt) and this is used to calculate the initial error/ residual before the 2nd time step starts. and then we go on to calculate U2 =f(p1, phi1, dt+dt) and corresponding p2, phi2 and final error/ residual at the end of 2nd time step and so on.... 
Yup, That is exactly so.
OpenFOAM is a segregated solver, that is U, V, W, phi and P are solved segregated. This is why such a thing happen. There are block coupled solvers in foamextend, but those are still linear solver and don't implement a nonlinear newton method or something like that. Quote:

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