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Advection with constant velocity is added to conduction and phase change. Analytical solution from Kuryly et al. 2014 based on a reassessment of solutions by Lunardini.

in 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