# Solution Convergence

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 May 13, 2007, 20:48 Solution Convergence #1 Ken Adams Guest   Posts: n/a Hi all, I'm solving a pure heat conduction problem. The residual and surface integral of the total wall heat flux are monitored during calculations. The plots show that surface integral of the total wall heat flux reaches steady state after about 50 iterations, however the residual falls off and then rises in the first 100 iterations but ripples in the following 400 iterations. I'm wondering if there is any explanation to those behaviors. Thank you. Ken

 May 14, 2007, 00:56 Re: Solution Convergence #2 gopal Guest   Posts: n/a hi! you havent mentioned whether it s a time dependent analysis, however fluent runs the pseudo time steps till the steady state is reached.the residual map rippled coz every iteration is initialized by the new updated values,which tend to converge.

 May 14, 2007, 14:00 Re: solver #3 ravi Guest   Posts: n/a i have already in a tutorial that segregated solver is pressure based solver and coupled solver is density based solver, can u explain it clearly what it actually means it will be very helpful to me bye

 May 14, 2007, 14:00 Re: solver #4 ravi Guest   Posts: n/a i have read in a tutorial that segregated solver is pressure based solver and coupled solver is density based solver, can u explain it clearly what it actually means it will be very helpful to me bye

 May 15, 2007, 03:09 Re: solver #5 gopal Guest   Posts: n/a pressure based formulation is for incompressible flows,where we dont have any discontinuities in the flow such as shocks and boundry layer serparation,primitive variables, p, v , t are used in this formulation. density based formalation, we take density as a variable in contrast to the first type. here flux of flow variables are considered for fomulation such as rho*v,rho*E etc. u cn c the book computational fluid dynamics by t.j.chung, 2nd chapter for clarity.

 May 15, 2007, 03:43 Re: solver #6 ritmat Guest   Posts: n/a the history of fluent said that pressure based formulation was for imcompressible and density based for compressible, but they have now improved their equations and you can use both of them for your problem.

 May 15, 2007, 12:17 Re: solver #7 ravi Guest   Posts: n/a hi gopal what is the significance of the courant number in solving steady navier stokes equations using coupled implicit solver for compressible fluid flows.

 May 16, 2007, 00:56 Re: solver #8 gopal Guest   Posts: n/a higher the courant number, faster the convergence, but it depends upon the problem too, some problems needs very less around 0.5 to 1, and some problems, u can go to 100 even.it is preferred to initialize the solution with low courant no. and increase it ass the iteration no goes up. courant no is the stability criterion for the solution u can find the CFL number(another name) in CFD literature. though u start the problem as steady state, fluent will run the pseudo time steps, once the steady state is reached the transient term will disappear. theres no thing called steady flow. hope ur doubt is cleared now!

 May 16, 2007, 14:13 Re: solver #9 ravi Guest   Posts: n/a hi gopal thanks for reply what do u actually mean by psuedo time steps? while solving turbulence problems, suppose we select K-e solver, the model is based on reynolds averaged navier stokes equations, so time averaging is done to eliminate the fluctuating components in flow, so on that basis only the pseudo time steps will come? or do u mean any other? waiting for reply

 May 17, 2007, 01:00 Re: solver #10 gopal Guest   Posts: n/a suppose u have a nozzle proble(C-D), physically if you give a pressure diff.of 3 atm, flow starts immediately but only stabilises after 2 or 3 secs. it wont take its final form immediately, numerically too this time lag must be given,and fluent cosiders the dou rho/dou t term even though you didnt difine the problem as unsteady.this is applicable for the turbulence equation also. the time defining transient term dou rho/dou t, is a must in the unsteady flow,and is not a must in the steady flow, this assuption is good for physical understanding only. vat do u mean by a steady flow, all of a sudden u wont get the steady flow.inertiaal effects create the lag for the flow to reach steady flow.

 May 17, 2007, 05:48 Re: solver #11 ravi Guest   Posts: n/a hi gopal thanks for reply. i will cme back to u soon

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