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Advection with constant velocity is here added to conduction and phase change. Analytical solution are proposed from Kurylyk et al. 2014 paper based on a reassessment of solutions by Lunardini. Although not physically realistic (constant velocity) these solutions can be used for benchmarking purposes: “Lack of fidelity to physical processes does not limit ability to serve as benchmark”.

The paper Kurylyk et al. 2014 describes at depth the analytical solutions available, the suggested benchmark cases and SUTRA code runs to compare with these solutions. The recommanded benchmark 2 and 3 are included in the InterFrost project as TH1 cases (differing by flow velocities). The recommanded benchmark 1 (Neuman case) is an option to complement the Lunardini case provided as T1.

One may refer to “Analytical solutions for benchmarking cold regions subsurface water flow and energy transport models: One-dimensional soil thaw with conduction and advection” by B. Kurylyk, J. McKenzie, K. MacQuarrie, C. Voss in Advances in Water Resources 70 (2014) 172–184

Another source is the presentation by Barret Kurylyk of these items for the kick off meeting (Kurylyk).

Initial and boundary conditions:

Parameter set:

Analytical solutions contained in file.

The approach used for SUTRA code is summed up in two figures providing the domain simulated and the approach for freezing curve function to approximate the step function with a linear curve: