This benchmark is testing the extended version of a classical heat conduction equation termed ‘heat conduction equation with phase change’ (with a slight abuse of notations, we also call it simply ‘T+freezing’ equation). The initialboundary value problem (IBVP) for this equation models such processes as ice formation and ice melting in watersaturated porous medium. Since the equation is strongly nonlinear in the temperature variable $T$ to be solved for and contains multiple parameters which may affect accuracy of finite element discretization, a carefully designed model and code verification must be performed.
In this note, we consider the socalled twophase Stefan problem which describes melting of a semiinfinite solid slab (in our case, an ice slab), and for which the closedfrom analytical solution in $x\in(0,\infty)$ is available. We apply the IBVP for our T+freezing equation – with the porosity $\phi$ being set to 1 – to model such melting process and solve the problem in OpenGeoSys (OGS6). This is done in a relatively large but finite spatial interval by extracting the initial condition, as well as the Dirichlet boundary conditions from the reference analytical data. The results obtained in this interval at various timesteps for the two modeling approaches are compared.
The detailed Stefan problem description, geometric setup, material and model parameters used in the related OGS implementation can be found in this document this PDF. The figures below are taken from this documentation and serve for illustrative purposes to give a hint about the modeled process and simulations outcome.
In the corresponding OGS project file Twophase_Stefan_problem.prj
the time discretization is different for the “real case study” whose results are presented in the documentation and for the ctest
case, and must be altered manually.
This article was written by Tymofiy Gerasimov. If you are missing something or you find an error please let us know.
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Last revision: April 3, 2024
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