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Riemann Wave-Speed Estimator

Compute HLLE/Rusanov wave-speed envelope and explicit dt limit from left/right Euler states with a wave-fan sketch.

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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Riemann solverHLLECFLcompressible numerics
formula
KaTeX rendered
S_L = min(u_L-a_Lu_R-a_R)S_R = max(u_L+a_Lu_R+a_R)dt = CFL dx / max(|S|)\begin{aligned}\text{S\_L = min(u\_L-a\_L}\\[0.35em]\text{u\_R-a\_R)}\\[0.35em]\text{S\_R = max(u\_L+a\_L}\\[0.35em]\text{u\_R+a\_R)}\\[0.35em]\text{dt = CFL dx / max(|S|)}\end{aligned}
ASCII sourceS_L = min(u_L-a_L, u_R-a_R), S_R = max(u_L+a_L, u_R+a_R), dt = CFL dx / max(|S|)
HLLE/Rusanov wave-speed envelopeS_Lcontact approxS_R
a_L / a_R
374.17 / 334.66
S_L (m/s)
-374.166
S_R (m/s)
374.166
spectral radius
374.166
dt max (s)
1.336e-5

These bounds are useful for first-pass explicit time-step limits and Rusanov/HLLE flux dissipation estimates.

Riemann solverHLLECFLcompressible numerics