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March 14, 2018, 05:54 |
How to compute residuals in SIMPLE alghoritm
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#1 |
Senior Member
Join Date: Dec 2017
Posts: 153
Rep Power: 8 |
Dear All,
I am implementing the SIMPLE alghoritm and I have a couple of questions about the calculation of residuals: 1) The residual is usually computed as the L-2 norm of the vector (Ax-b), where A is the momentum matrix for the ith velocity component, b is the rhs and x is the ith component of velocity vector computed at the previous iteration. A and b are the updated matrix and rhs at the current iteration. Is that right? 2) How do you scale the residuals? Thank you for the help, AliE |
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March 14, 2018, 06:30 |
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#2 | |
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,773
Rep Power: 71 |
Quote:
To define exactly the residual you should consider all components at that same iteration r_k =(A.x)_k - b_k Scaling is general done using the residual at the guess iteration k=0 |
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March 14, 2018, 06:42 |
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#3 | |
Senior Member
Join Date: Dec 2017
Posts: 153
Rep Power: 8 |
Quote:
Yes, I have just realized that we are talking about the same thing. So the first point is ok. Using the first value of the residual as reference is good, but I have seen around that people uses also aC*vel, where the aC is the diagonal coef. related to the ith equation and vel the corresponding velocity component... So which one select? |
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March 14, 2018, 06:49 |
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#4 |
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,773
Rep Power: 71 |
From a theoretical point of view, I prefer to scale the residual using a homogeneous quantity, that is the residual at the zero-th iteration...
However, if the original problem is correctly scaled by a proper non-dimensionalization, I think that there is no need to scale the residual. I mean that the norm of the residual (that we can practically compute) is comparable to the norm of the error (that we cannot compute) if the matrix is well-conditionated, that is a spectral norm ||A||=O(1). |
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