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Source term and property stabilization #28

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merged 6 commits into from
May 28, 2024

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added stabilization to the latent heat source term linearization method and added support for second-order time discretization for the backward (BDF2) scheme. also cleaned up thermophysical properties update to be consistent with Gauss harmonic corrected laplacian scheme.

The near second order converge of the solver using the backward scheme is demonstrated
image

…od and added support for second-order time discretization for the backward (BDF2) scheme. also cleaned up thermophysical properties update to be consistent with Gauss harmonic corrected laplacian scheme
@colemanjs colemanjs requested a review from kincaidkc April 5, 2024 19:38
@colemanjs colemanjs self-assigned this Apr 5, 2024
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The near second order converge of the solver using the backward scheme is demonstrated

When generating these plots are you comparing to an analytical solution or to something generated using the solver at very fine dt? If the latter, I would guess that the deviation from 2nd order accuracy (which appears to be caused by the finest time step value) might be caused at least in part by the error in the reference solution becoming non-negligible compared to the error in the solution at that point

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colemanjs commented Apr 16, 2024

The near second order converge of the solver using the backward scheme is demonstrated

When generating these plots are you comparing to an analytical solution or to something generated using the solver at very fine dt? If the latter, I would guess that the deviation from 2nd order accuracy (which appears to be caused by the finest time step value) might be caused at least in part by the error in the reference solution becoming non-negligible compared to the error in the solution at that point

My reference solution is using BDF2 with a time step of ~1e-8s. This approach is necessary when an analytical solution does not exist. If the solution convergence is monotonic, then I believe that the order of accuracy of the method can be determined from the log(change in error)/log(change in time step) as the time step is halved. Our solutions are not strictly second order, which may be due to setting the source term to the implicit time. We can try averaging this term over time steps, but this may require some special logic when the beam turns on/off.

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colemanjs commented May 28, 2024

The time integration scheme is just one part of achieving second order convergence of the solution. The second part is implementing higher-order integration schemes for the heat source. A future PR will address this, and may be focused on using quadrature methods for the volume integrals of the source term. An example time-step convergence plot is shown with the time-integration for the thermal solve and the quadrature-based heat source integration used together:
image

@colemanjs colemanjs merged commit dc2a693 into ORNL:main May 28, 2024
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