💨
Advection–Diffusion Explorer
u
t
+ c·u
x
= ν·u
xx
📖 Help / Theory
PDE Parameters
c (advection speed)
1.00
ν (diffusivity)
0.005
Péclet Pe = c·L/ν
—
Initial Condition
Shape
Gaussian
Square Pulse
Sine Mode
Double Gaussian
Triangle
Amplitude A
1.0
Width σ
0.08
Numerical Setup
Grid N
300
CFL ν_adv
0.80
Scheme
Upwind + FTCS
Lax-Wendroff + CN
Central + CN
Display
Exact solution
Numerical
Pure diffusion only
Pure advection only
Initial profile
Fill under curve
Animation
Speed
0.1
×
Loop at T
5.0
Live Stats
Péclet Pe:
—
L² error:
—
σ(t) spread:
—
peak center x:
—
∫u dx (mass):
—
💨 Evolution
🔀 Decomposition
📊 Péclet Regimes
📐 x–t Diagram
▶ Play
⏭ Step
↺ Reset
t = 0.000
CFL 0.80
Pe —
u(x,t) — Translation + Spreading
|u_exact − u_numerical|
Advection only vs Diffusion only vs Full Adv-Diff
Low Pe — Diffusion-dominated
Medium Pe — Balanced
High Pe — Advection-dominated
x–t Heatmap + Advection Characteristics
t = 0.000
Pe = —
CFL = —
L² = —
mass = —
Upwind+FTCS
📖 Advection–Diffusion — Theory & Resources
×