Variational methods as the most effective mechanism for modeling physical interrelated fields in continuous medium. I. Overview of the theory

In order to solve the problem of choosing the most effective mechanism for mathematical modeling of Interrelated physical fields in continuous media are considered using the variational approach. It summarizes the current theory on the subject, based on the use of variational principles, or variational equations. Specifies the criteria for their selection, discusses the features of this method. Is provided specific example. In the second part of the work will be done the analysis of the cases, when the variational approach is only possible to produce mathematical models of multiphysical phenomena. The appendix describes the dissipative function (dissipative potential) in the case of a homogeneous viscous heat-conducting fluid, which plays an important role in the modeling of irreversible processes.