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Convergence problems unsteady conjugate heat flow problem when refining mesh

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Old   December 2, 2020, 04:32
Default Convergence problems unsteady conjugate heat flow problem when refining mesh
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I'am trying to solve an incompressible unsteady conjugate heat flow problem for an uniformly heated cylinder in a laminar flow of water using Comsol. The cylinder is located at the centerline and the inlet boundary is located at 8D and outlet boundary at 25D. The height of the domain is equal to 24D.

All differential equations are dimensionless and are dependent on the Reynolds, Prandtl and Richardson numbers. In this case these numbers are equal to 20, 7 and 1 respectively.
Note that the equations are nondimensionlized by setting \rho and \mu equal to 1 and \frac{1}{Re} respectively for the laminar flow module. Furthermore, bouyancy is added by using the boussinesq approximation and is included in the y term of the volume force as Ri \Theta for which, \Theta = (T - T_0)/(T_w - T_0) is the dimensionless temperature.

For the heat transfer module Cp is set to 1 and k to \frac{1}{Pr Re}

The boundary conditions are:

Uniform inlet velocity of 1
And inflow temperature of T_0 = 0

Upper and lower boundary
Slip boundary conditions and heat conduction normal to the wall set to 0


No slip condition

Temperature of the wall T_w = 1

Outlet conditions

Zero pressure outlet condition

Conduction normal to the wall set to 0


The mesh is mapped with quads elements and are non uniformly distributed. The statistics are shown below:

Number of elements 133200

Minimum skewness 0.4995, average 0.9889

Minimum volume versus circumradius 0.2049, average 0.774

Minimum condition number 0.2692, average 0.7876

Minimum growth rate 0.9628, average 0.9849

Boundary minimum element size 0.0134


I'am using a seggregated solver


Up to around 100000 elements the convergence is good but for finer meshes the error of the segregated solvers shows a fluctuating error after a time of around 40 seconds. The residuals also increase significantly in this period of time. These plots can be found in the attachment. Furthermore, after the error appears ''May have reached a singularity.
Time: 40.593993119146752 s.Last time step is not converged.'' A plot containing undefined values of the variable comp1.T appears and is also included in the attachment. Just before the simulation quits the timestep also decreases significantly. The reciprocal of the time step plot is included in the attachment.

Can anybody help me with this problem. The effort is greatly appreciated.

Best regards,

Sven Beekers
Master student University of Technology Eindhoven


undefined values.png

seggregated solver error.jpg

reciprocal time step.jpg
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convergence, flow, heat, mesh

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