Knowledge card
Finite-domain Truncation
Mathematical Modelling — Fluid Dynamics & Heat TransferNumerical analysis; boundary-layer similarity theory
Symbol
The far field η → ∞ replaced by a finite η_max: chosen large enough that the profiles arrive FLAT (f′, θ and their slopes below tolerance), and verified by doubling — if results shift when η_max doubles, it was too small.
Dimension I
Definition
What it is — and what it is not
- What it is
- S1A finite computational far field: the conditions at η → ∞ are imposed at η_max instead.
Dimension II
In practice
How to deal with it
- How to deal with it
- S2Choose η_max so the profiles arrive flat (|f′|, |θ|, |f″|, |θ′| all below tolerance at η_max), then DOUBLE it and confirm f″(0) and θ′(0) do not move at the reported precision.
- Warnings
- S3Too small an η_max silently biases the wall values — the far-field decay gets clipped and the residual equations force artificial curvature near the boundary.
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