# Definition of Residuals in pressure-based and density-based solvers

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 April 20, 2010, 10:15 Definition of Residuals in pressure-based and density-based solvers #1 Member   Rain Join Date: Apr 2009 Posts: 40 Rep Power: 8 Dear all, I have a question regarding the definition of residuals in the different solvers in Fluent 12.0. For the pressure-based solver, I understand that the residual is defined as the imbalance of the linear discretized equations. I recognise this definition from CFX, for which the expression is similar. In the documentation, it is written that the residual for the density-based solver is defined as the "time rate of change of the conserved variable" (Section 26.13.1). I am unsure about the meaning of "time rate" in this context, assuming it is a steady state solution. I hope that someone can clear this out. I guess that the calculated magnitude of the residuals are generally of the same order for pressure-based and density-based solvers, since the recommended values given in the documentation for judging convergence do not seem to differ between the two. Still, it would be interesting for me to understand in detail how the residuals are calculated. Best Regards, Reine

 April 20, 2010, 14:36 #2 Senior Member   Chris Join Date: Jul 2009 Location: Ohio, USA Posts: 169 Rep Power: 8 The solution may be steady, but it's solved by marching in time from an initial condition. Think of it like solving dU/dt = -dE/dx - dF/dy - dG/dz + S, where U is the vector of conserved variables, E, F, and G are the fluxes, and S is a source term. (The Euler and NS equations can be case in this form. See, for example, Anderson's CFD book.) You can solve the equation by time marching, either implicitly or explicitly, from an initial condition until dU/dt = 0. This is where the "time rate of change of the conserved variable" comes from.

 April 21, 2010, 04:08 Got it #3 Member   Rain Join Date: Apr 2009 Posts: 40 Rep Power: 8 Chris, thank you for your reply. I had not read up on the time marching procedure in Fluent so I did not really understand the time discretization in steady state. In CFX, there is more direct control of the steady state time step than in Fluent. Now I can see the similarity between the codes.

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