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Computational Fluid Dynamics: Dissipation Function Density Based Solver

  1. Feb 14, 2018 at 5:51 AM #1

    ((((As a correction dissipation function in picture should have square of divergence of U))))

    Hi, first of all I am aware that we have to discretize the non linear navier stokes equations to reach the almost exact solution, and pressure based or density based algorithms are deployed for that reason. But for the energy equation of navier stokes, dissipation function as in picture/attachment takes place and even if we apply finite difference or discretize the velocities we obtain square of those velocities and there is still a non linearity. But I know that pressure based or density based solvers should have linear algebraic matrix equations ( for instance pressure based algorithm uses segregated solution method which cares the linear algebraic system). MY QUESTİON is: How is the dissipation function treated especially for density based solver which include compressible flow ?? Dissipation function has non-linearity even if finite difference/discretization is applied so how do we handle this situation??
    Last edited: Feb 14, 2018 at 8:39 AM
  2. jcsd
  3. Feb 14, 2018 at 9:39 AM #2
    I don't think density based solvers are used to solve the Navier-Stokes equation because of the non-linearitites as you pointed out. For compressible flow, a common explicit method used is the MacCormack method and a common implicit method is the Beam-Warming scheme.
  4. Feb 15, 2018 at 8:18 AM #3
    thanks for return, but if we have steady state compressible viscous flow what kind of method is required? By the way, MacCormack or Beam Warming depends on time we can not use them I think
  5. Feb 15, 2018 at 12:47 PM #4
    Those methods will still work, they will produce a solution which eventually converges to the steady state value. If the problem is at steady state then that must mean that you expect a laminar flow. What is the Reynolds number for the system? Can you give more details on the problem you are attempting to solve? There may be simplifications to the governing equation depending on the parameters of the system.
  6. Feb 15, 2018 at 12:50 PM #5
    but as far as I see MacCormack and Beam Warming has time steps or try to find solution time by time which mean unsteady state situation, How those still work (without asymptotic time limit because of computational expense)??
    (By the way I know that for LOW mach number compressible flow may be considered as incompressible flow and SIMPLE SIMPLER PISO SIMPLEC algorithm may be used for steady state compressible(just for low mach number) but what method is used for STEADY STATE HIGH mach number compressible flow FOR HIGH AND LOW REYNOLD NUMBER??)

    Also as far as I have searched in this link page 25 https://brage.bibsys.no/xmlui/bitstream/handle/11250/234395/441754_FULLTEXT01.pdf?sequence=1 there is compressible simple method which has segregated iteration but still some non linearities exist for instance non linear terms originated from dissipation function in equation 13's source term must be exist in page 19 . How do we explain this situation?
    Last edited: Feb 15, 2018 at 3:07 PM
  7. Feb 16, 2018 at 3:36 PM #6
    Pardon, I would like to ask why I can not receive enough responses to my question. I consider there are many qualitative brains in this forum, why don't you help me about my question??? Am I not explicit enough?? Thanks to only NFuller, I got some kind of clue.

    By the way, If there is someone who cares my question he/she can deeply look at my post 5 and 1, thus I believe I am going to be understood well...
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