Mathematical models and methods for numerical problems with discontinuous solutions. (Q2785559)

In the monograph the authors discuss a unique technique for the mathematical modeling of nonstationary processes in media containing thin inclusions. It is assumed that the inclusion characteristics differ essentially from those of the main medium. NEWLINENEWLINENEWLINEThe monograph consists of 11 chapters. In the first three chapters the models of some nonstationary processes are proposed. These models are described by the equations of nonstationary diffusion, convection diffusion transfer and other equations of parabolic type. The classical and generalized statements of the problems are formulated. The corresponding Cauchy problems are solved according to the Crank-Nicholson scheme. Chapter~4 presents the modeling of axisymmetric heat transfer in revolution bodies in the presence of thin weakly heat permeable inclusion. In Chapters~5 and 6 the filtration flows in the bottom of the arch dam are modeled. Chapter~7 discusses the correctness of solutions to one- and two-dimensional nonlinear equations of parabolic type with discontinuous solutions. In Chapters~8 and 9 the method of finite elements is substantiated for the calculation of initial boundary value problems for hyperbolic type equations admitting solution discontinuities in spatial variables. Chapters~10 and 11 deal with the description of systems of automatic calculation of physical and mechanical fields and the solution of concrete practical problems of hydraulic and power engineering. NEWLINENEWLINENEWLINEThe book can be useful for many experts in calculus and engineers in the corresponding areas of modeling of fields of various nature.