Using of Hamilton mechanics methods for modeling dynamic processes on the Earth surface

Abstract

This paper presents the methods of mathematical modeling and managing on some dangerous dynamic processes on the Earth surface such as floods, wildfires, desertification, oil spills on the water surface and others. We call these processes by a common name - distribution processes. The Hamilton mechanics methods permit to describe uniformly wide class of dynamic processes - both the processes of control determined with the ordinary differential equations and the processes in the continuous beds. The basic model of the distributed processes was presented in form of Hamilton – Jacoby equation. The concept of the normal speed of the process front movement suggested. The indicatrix and figurotrise of spread, which determine the configuration of the distribution process, are introduced. A model of processes with dissipation is proposed. Classification of processes according to the degree of their mobility is given. Using the figurotrises a new approach to numerical modeling of the processes front propagation based on Godunov’s method of the movable grids proposed. Its essence is that the calculated grid is not given a priory, but it is determined by current solution of the problem. It moves and develops with the solution. The movable grid method can serve as a basis for creating agent models of propagation processes. A separate section of the paper is devoted to describing a method for managing the processes. In particular, the fundamentals of the so-called localization control, which consists in building an obstacle insurmountable for the process, are outlined. The proposed methods and algorithms are illustrated by numerical examples. The models presented in this paper was a theoretical basis for designing and developing some management systems of the distribution processes control.