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Home Forums CFD foundation course: Forum Lesson 7 – Doubt in General form of Governing Equations Reply To: Lesson 7 – Doubt in General form of Governing Equations

  • Rahul

    Member
    February 1, 2023 at 4:47 pm

    Out of the terms marked in the equation, S represents the source term. This can be different terms depending on if the equation is for energy, momentum etc. For example, in case of energy equation this can be used to represent the internal heat generation, if required. In case of momentum equations, this can be used to model the pressure gradient,gravitational force,viscous force etc.

    The other term (gamma),  represents the diffusion coefficient used for the corresponding equation, and varies accordingly. In the energy equation, the thermal conductivity,k is the diffusion coefficient. For the momentum equations, this takes the value of the coefficient of viscosity.

    To obtain the other governing equations from the given general equation, it is not sufficient to replace only the values of phi with 1,v, and u for the continuity and momentum equations. To obtain the continuity equation, substitute phi with 1, gamma with zero and S with zero. For the u and v momentum equations, along with substituting for phi, gamma should be substituted with the dynamic viscosity and S with the corresponding source term which includes the pressure gradient, gravitational force, viscous force etc. Similarly for the energy and species transport equations.

    You could try substituting these and comparing with the equations from standard CFD text books like the book by Versteeg and Malalasekera

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