Prof. Kenji
Kajiwara (Institute of Mathematics for Industry, Kyushu University, Japan)
Title: Construction and simulation of discrete integrable model for soil water
infiltration problem
Abstract: In this talk, we propose an integrable
model and its discretization describing one-dimensional soil water infiltration
problem. The model is formulated as the nonlinear boundary value problem for a
nonlinear diffusion-convection equation, which is transformed to the Burgers equation by
a certain independent variable transformation incorporating the dependent variable,
called the hodograph transformation or the reciprocal transformation. We construct the
discrete model preserving the underlying integrability nature and formulate it as the
self-adaptive moving mesh scheme. If we require the numerical stability and
high-precision coincidence with the special case where the exact solution is obtained,
we need some investigation and modification of the discrete model from the point of view
different from integrability. We discuss this point and show some numerical
results.
This talk is based on the paper arXiv:1705.03129 by D. Triadis (Kyushu/La Trobe) , P.
Broadbridge (La Trobe), K. Maruno (Waseda) and myself.
Seminars are held at 2:00 pm on Wednesdays in the Access Grid Room ( Carslaw Building, 8th floor, room 829), unless otherwise noted.
Applied Maths Seminar webpage