V&V Procedures for CFD Labs
58:160 Intermediate Mechanics of Fluids (2013)
By: Maysam Mousaviraad, Timur Dogan
The purpose of this document is to summarize and demonstrate V& V procedures to be used in CFDLab reports.
Nomenclature:
Sg1: solution from fine grid Sg2: solution from medium grid Sg3: solution from coarse grid Rg: grid convergence ratio rg: grid refinement ratio Pg: order of accuracy for grid
Pgest: theoretical order of accuracy, 2 for 2nd order and 1 for 1st order schemes P: ratio of accuracy of grid and theoretical accuracy
δ*REg1: grid error from Richardson Extrapolation based on fine mesh solution Ug: grid uncertainty based on FS method
1
Formulae:
εg21= Sg2- Sg1
εg32= Sg3- Sg2
Rg=
32 21 g g
ε ε
If monotonically converged (0<Rg<1), then:
( )
g g gg r
P ln ln
21 32
= ε
ε
gest g
P P= P
δ*REg1=
) 1 (
21
−
Pg
g g
r ε
( )
( )
>
−
≤
<
−
=
1 P if 8
. 14 4 . 16
1 P 0 if 85
. 0 45 . 2
1
* 1
*
REg REg
g
P P U
δ δ
2
Following examples demonstrate grid studies for friction factor of laminar pipe flows.
Example:
003415424 .
0
* ) 8 . 14 4 . 16 ( 1
0006 . 0 ) 1 (
249535 .
2 1 49907 . 2
49907 . ) 2 ln(
) ln(
0157815 .
0
0027916 .
0 2
1
* 21
1
*
21 32
2 3 32
1 2 21
=
−
=
>
−
− =
=
=
=
=
=
=
−
=
−
=
−
=
−
=
=
g REg
P g
g REg
gest g
g g g
g
g g g
g g g g
P U
P
r P P P P r
S S
S S r
g
δ δ ε
ε ε ε
ε
3
