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Younglin's CFD Blog
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Under-Relaxation Planner

Visualize how relaxation factor changes correction size, damping speed, and overshoot risk in SIMPLE-like 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
under-relaxationSIMPLEsolver stabilityresidual
formula
KaTeX rendered
phi_new = phi_old + alpha Delta phiresidual_N ˜= residual_0 (1-alpha)ˆN\begin{aligned}\text{phi\_new = phi\_old + alpha Delta phi}\\[0.35em]\text{residual\_N \~{}= residual\_0 (1-alpha)\^{}N}\end{aligned}
ASCII sourcephi_new = phi_old + alpha Delta phi, residual_N ~= residual_0 (1-alpha)^N
Under-relaxation responseapplied correctionalpha damps each nonlinear correction before update0% risk1e+01e-21e-41e-6idealized residual damping per nonlinear iteration
applied correction
0.5000
withheld correction
0.5000
residual after N
0.0002
iterations to 95% damping
4.3219
overshoot risk
0.0%
setting
balanced
alpha
0.5000
raw correction
1.0000

This is an intuition tool for nonlinear fixed-point damping. Real stability also depends on mesh quality, discretization, boundary conditions, and coupling strategy.

under-relaxationSIMPLEsolver stabilityresidual