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Stable discretizatin scheme

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Old   July 1, 2013, 21:14
Default Stable discretizatin scheme
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Patricio Javier Valades Pelayo
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Hello, could someone recommend me a discretization scheme (and the place to find it explained) that is stable, for the following:

-Solving a 2D-Unsteady state mass transfer equation on a pipe, using Cylindrical coordinates. Radial and axial spatial coordinates considered & no dependence with respect to tetha (axisymmetrical).

-Assuming the momentum equation yields a fully developed parabolic velocity profile (Laminar flow).

-Considering radial diffusion, axial diffusion and axial convection.

-Outter boundary condition no mass transfer.
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Old   July 7, 2013, 04:52
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Andrey Yakovchuk
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As long as you can model constant density, you need pressure-based segregated solver. Then adjust courant number to achieve stability (no more than 1 for transient flows). Look at www.bakker.org for lectures about solvers and discretisation schemes. Firstly achieve convergense on 1-order upwind then on 2-order upwind scheme for flow (for steady-state), or use 2-order upwind at once for transient problem.

You task is simple, wish you good results
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Old   July 19, 2013, 03:12
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Andrea Aprovitola
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Quote:
Originally Posted by einandr View Post
As long as you can model constant density, you need pressure-based segregated solver. Then adjust courant number to achieve stability (no more than 1 for transient flows). Look at www.bakker.org for lectures about solvers and discretisation schemes. Firstly achieve convergense on 1-order upwind then on 2-order upwind scheme for flow (for steady-state), or use 2-order upwind at once for transient problem.

You task is simple, wish you good results
I agree with the adoption of a segregated solver for this problem. Moreover as you are dealing with mass transfer problem in an incompressibile laminar flow, I would try to adopt finite volume-based discretization schemes using colocated variable ( velocity and pressure defined on centroid of control volume ) rather than finite difference schemes.

You will introduce in your computation an error on the net mass flux over a control volume, at each time step, having the magnitude of the local truncation error on your grid. Hence your stability check will be based on the evaluation of the divergence of the velocity field across the flow domain which has to remain bounded and of the order of LTE. This will give you an info about the global amount of mass transfer due to the numerical procedure.
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