2 Replies Latest reply on Oct 15, 2009 5:53 PM by 1-KZQAJL

    I need to know exactly how Flow Simulation solves the Navier-Stokes equations.

      I am working on my doctor of mechanical engineering at Cleveland State University in Ohio.

       

      I am doing a simulation of food being baked in different types of ovens.

       

      I need to know how Flow Simulation solves the Navier-Stokes equations. I have already seen the tutorials and online help system, and neither describes in full detail how Flow Simuation solves those equations.

       

      Does Flow Simulation use the SIMPLE (Semi-implicit pressure linked equations) method for example?

       

      And how does Flow Simulation use radiative surfaces, and moving surfaces to solve for the variables in the Navier-Stokes equations?

       

      Please attach a file if most efficient.

        • Re: I need to know exactly how Flow Simulation solves the Navier-Stokes equations.
          Bill McEachern

          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 time-level, and '*' denotes intermediate values of the flow

          parameters. The following numerical algorithm is employed to calculate flow parameters

          on time-level (n+1) using known values on time-level (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 * (1.36)

          (1.37)

           

          1 t p , h

          ρ

           

          un+ = ρu* −Δ ⋅grad δ

          p

          n

          n

          +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 pressure-correction (1.36), an original

          double-preconditioned iterative procedure is used. It is based on a specially developed

          multigrid method (Ref. 10).

          Chapter Numerical Solution Technique

          1-36

          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 operators

          with 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

           

          =(u1,u2,u3)T is the velocity vector, y = (y1, y2, ..., yM)T is the vector of component

          concentrations in fluid mixtures, and