A 'jump' appears in the temperature when setting non-homogeneous DIRICHLET boundary conditions in adv_diff/ex8

[张超]

Hello, I have recently been learning to use IBAMR. I encountered a problem while trying to modify the adv_diff/ex8 example. I set the temperature boundary condition of the outer circle to be an non-homogeneous DIRICHLET boundary condition. The specific code is:
birkman_adv_diff->registerInhomogeneousBC(
T_var, phi_outer_solid_var, "DIRICHLET", nullptr, nullptr, indicator_function_type, num_of_interface_cells, eta, 50);
I set the temperature to 50. When I gradually output the calculation results, I found that in the outer circle region, the temperature changes with each iteration step. Here are the results of a few steps, and I am not sure if this is normal.

[Ramakrishnan Thirumalaisamy]

Hi,

These examples will show some instability because the terms are discontinuous near the interface. Over time, the instability should subside. If you want you can increase the value of "NUMBER_OF_INTERFACE_CELLS" in input2d file and try. 

If you want to impose inhomogenous Dirichlet boundary condition, you need to use "registerInhomogeneousBC" as shown in line 635 in https://github.com/IBAMR/IBAMR/blob/master/examples/adv_diff/ex8/example.cpp. However, you should pass Dirichlet as the flag and do not need a callback function and pass the Dirichlet value that you want to impose as the function's last argument. See line 265 of https://github.com/IBAMR/IBAMR/blob/master/src/IB/BrinkmanAdvDiffBcHelper.cpp class for more details. 

Also take a look at the README file for this example. The equations are solved in non-dimensional form and imposing \Phi = 50 may cause stability issues. You can try using smaller Dirichlet values at first and then increase them gradually. 

Let me know if you have any questions.

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Best,

Rama