Optimal Control of Point Sources in Richards-Klute Equation
This article represents an approach to humidity control in porous media, which combines linearization with numerical methods. The main problems and several ideas to solve them are mentioned. The main interest for our research is humidity regulation, described by Richards-Klute equation. The optimization problem is to minimize the difference between a reached state and a desired state.
Modelling moisture transport in porous media requires taking into account the processes of heat transfer, chemical and physical processes, as they have a considerable influence on characteristics of the medium.
First of all, a mathematical model is developed with a number of simplifications: moisture incompressibility, constant external pressure, limitations on transfer or isothermal requirements. Then, it is often preferable to make a transition to linear problem, as this case is explored and it allows us to use more theoretical background for the research. After that, numerical models and time and space discretization are constructed according to the related problem. When the process is represented in a suitable way, control and optimization problems arise and should be solved.
KeywordsControl Optimization Richards-Klute equation
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