Analytical solutions of integrable nonlinear diffusion equations for modelling groundwater infiltration and metal solidification

Dimetre Triadis (La Trobe University, Australia)

Thursday 26th September, 2019 14:00-15:00 Maths 311B


The current most general integrable model for unsaturated one-dimensional groundwater infiltration governed by the Richards equation has been known since the 1980s. However, exact solutions for many simple, physically relevant boundary conditions have yet to be derived. We derive exact series solutions for conditions of surface saturation. Here the use of efficient, iterative, symbolic-computation algorithms removes restrictions on the number of terms that can be obtained in the final infiltration series. 

The above integrable solutions of Richards’ equation are intimately related to classes of Stefan boundary value problems. We utilise compatible theoretical advances to generalise the class of boundary fluxes that can be treated analytically for Stefan solidification problems with nonlinear heat conduction.

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