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cfd-lab:~/en/tools/sor-relaxation-planneronline
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SOR Relaxation Planner

Plot omega choice, approximate optimum, convergence factor, and iteration estimate for Poisson/SOR iterations.

visual calculatorNumerics & Stability

Read the flow shape before trusting the number.

This page turns a CFD setup into regime, scale, and dominant-effect cues. Adjust the calculator below and compare the moving graphic with the computed result.

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input scale
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model
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check
SORPoisson solverrelaxationlinear solver
formula
KaTeX rendered
omega_opt ˜= 2/[1 + sqrt(1 - rho_Jˆ2)]rho_J ˜= cos(pi/N)\begin{aligned}\text{omega\_opt \~{}= 2/[1 + sqrt(1 - rho\_J\^{}2)]}\\[0.35em]\text{rho\_J \~{}= cos(pi/N)}\end{aligned}
ASCII sourceomega_opt ~= 2/[1 + sqrt(1 - rho_J^2)], rho_J ~= cos(pi/N)
estimated SOR convergence factoromegarho
rounded N
64
omega optimum approx
1.9065
spectral radius
1.00000
iterations estimate
1.382e+7

Use as an intuition tool for elliptic pressure/Poisson smoothers. Multigrid changes the effective spectrum.