Stable discretizatin scheme
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.
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:)
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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