https://eps.mcgill.ca/~mckenzie/reprint/mckenzieetal2006SUTRA-ICE.pdf

Groundwater flow with energy transport and water-ice phase change: Numerical simulations, benchmarks, and application to freezing in peat bogs

Efficient numerical technique for one-dimensional thermal problems with phase change

https://hal.archives-ouvertes.fr/hal-01729631/document

Groundwater flow and heat transport for systems undergoing freeze-thaw : Intercomparison of numerical simulators for 2D test cases

The physics of mathematical frost heave models: A review

Boundary integral equation methods are presented for the solution of some two-dimensional phase change problems. Convection may enter through boundary conditions, but cannot be considered within phase boundaries. A general formulation based on space-time Green's functions is developed using the complete heat equation, followed by a simpler formulation using the Laplace equation. The latter is pursued and applied in detail. An elementary, noniterative system is constructed, featuring linear interpolation over elements on a polygonal boundary. Nodal values of the temperature gradient normal to a phase change boundary are produced directly in the numerical solution. The system performs well against basic analytical solutions, using these values in the interphase jump condition, with the simplest formulation of the surface normal at boundary vertices. Because the discretized surface changes automatically to fit the scale of the problem, the method appears to offer many of the advantages of moving mesh finite element methods. However, it only requires the manipulation of a surface mesh and solution for surface variables. In some applications, coarse meshes and very large time steps may be used, relative to those which would be required by fixed grid domain methods. Computations are also compared to original lab data, describing two-dimensional soil freezing with a time-dependent boundary condition. Agreement between simulated and measured histories is good.

Boundary integral equation solution of moving boundary phase change problems

A REVIEW OF THE COMPLEXITIES IN THE SOLUTION OF THERMAL PROBLEMS ON FREEZING AND THAWING SOILS IS PRESENTED. THE DIFFERENTIAL EQUATIONS GOVERNING THE CONDUCTION OF HEAT, IN WHICH LATENT HEAT IS CONSIDERED AS A HEAT SOURCE, ARE STATED. AN EQUIVALENT CONVOLUTION VARIATIONAL THEOREM IS USED TO CONSTRUCT A TWO-DIMENSIONAL FINITE ELEMENT MODEL WITH LINEAR VARIATION OF TEMPERATURE WITHIN THE ELEMENT. TWO TIME STEP IDEALIZATIONS OF THE EQUATIONS ARE DESCRIBED, AND ALTERNATIVE FORMS OF THE LATENT HEAT MATRIX ARE DERIVED. SOME RESULTS OBTAINED WITH THE SIMPLEST LATENT HEAT MATRIX ARE PRESENTED TO ILLUSTRATE THE VERSATILITY OF THE TECHNIQUE. /RATAOC/

E. W. Brooker

Papers

A thermal analysis for structures on permafrost