⚙ Von Neumann Stability Analysis
ThermoFluidCalc — Section 4 : CFD Numerical Tools — Calculator #19
Reference : Gupta, §2.8
🔨 Input Parameters
Finite-Difference Scheme
FTCS Advection — G = 1 − iσ sin(θ)
FTCS Diffusion — G = 1 − 4r sin²(θ/2)
Upwind 1st Order — G = 1 − σ(1−cosθ) − iσ sinθ
Lax-Friedrichs — G = cosθ − iσ sinθ
Lax-Wendroff — G = 1 − σ²(1−cosθ) − iσ sinθ
Crank-Nicolson Diffusion — G = [1 − r(1−cosθ)] / [1 + r(1−cosθ)]
Implicit Euler Diffusion — G = 1 / [1 + 2r(1−cosθ)]
Leapfrog Advection — G = −iσ sinθ ± √(1 − σ² sin²θ)
σ (Courant number = uΔt/Δx)
r (diffusion number = αΔt/Δx²)
Number of θ points
▶ Analyse Stability