
Re: I need to know exactly how Flow Simulation solves the NavierStokes equations.
Bill McEachern Oct 15, 2009 9:22 AM (in response to 1KZQAJL)Have you looked in the Technical reference document: It is typically located here: C:\Program Files\SolidWorks Corp\SolidWorks Flow Simulation\lang\english\Docs on the insstalled computer.
Maybe this sectionis of interest (obviously it didn't paste well but it should be enough to se if thsi is what you want):
Form of the Numerical Algorithm
Let index 'n' denotes the timelevel, and '*' denotes intermediate values of the flow
parameters. The following numerical algorithm is employed to calculate flow parameters
on timelevel (n+1) using known values on timelevel (n):
ρ
* = ρ(pn+δp,T*,y*),
Here
U = (ρu, ρT, ρκ, ρε, ρy)Tis the full set of basic variables excluding pressure p,
u
δp = pn+1  pn is an auxiliary variable that is called
a pressure correction. These parameters are discrete functions stored at cell centers. They
are to be calculated using the discrete equations (1.35)(1.40) that approximate the
governing differential equations. In equations (1.35)(1.40)
Ah, divh, gradh and Lh =
div
δp. This
equation is defined in such a way that the final momentum field
ρun+1 calculated from
(1.35) satisfies the discrete fully implicit continuity equation. Final values of the flow
parameters are defined by equations (1.37)(1.40).
(
n ) n
+ =
Δ
*
*
U U
U  U
n
,
n
, (1.35)
( )
,
t t t
L p
Δ−Δ
+
Δ
n
h
h
δ
= ρ ρ ρ
div u
(1.37)
ρ
un+ = ρu* −Δ ⋅grad δ
p
nn
+1 = pn +δp , (1.38)ρ
Tn+1 = ρT* ,ρκ n+1 = ρκ *,ρε n+1 = ρε * ,ρyn+1 = ρy* , (1.39)
ρ
n+1 = ρ (pn+1,T n+1,y n+1 ). (1.40)
To solve the asymmetric systems of linear equations that arise from approximations of
momentum, temperature and species equations (1.35), a preconditioned generalized
conjugate gradient method (Ref. 9) is used. Incomplete LU factorization is used for
preconditioning.
Iterative Methods for Symmetric Problems
To solve symmetric algebraic problem for pressurecorrection (1.36), an original
doublepreconditioned iterative procedure is used. It is based on a specially developed
multigrid method (Ref. 10).
Chapter Numerical Solution Technique
136
Methods to Resolve Linear Algebraic Systems
Iterative Methods for Nonsymmetrical Problems
A
h p S
t
hgradh are discrete operators that approximate the corresponding differential operatorswith second order accuracy.
Equation (1.35) corresponds to the first step of the algorithm when fully implicit discrete
convection/diffusion equations are solved to obtain the intermediate values of momentum
and the final values of turbulent parameters, temperature, and species concentrations.
The elliptic type equation (1.36) is used to calculate the pressure correction
concentrations in fluid mixtures, and

Re: I need to know exactly how Flow Simulation solves the NavierStokes equations.
1KZQAJL Oct 15, 2009 5:53 PM (in response to Bill McEachern)Thank you, Bill.
I was able to find the Technical Reference document in our computers at school using the path you suggested.
Ray Adamic
