The Hierarchy of Fluid Dynamic Equations: Foundations of the Second Mathematization Wave of Fluid Dynamics

This book is devoted to the most general governing equations of the fluid  mechanics, namely the Navier-Stokes equations and their derivatives. These equations are presented in various manners: for several coordinate systems, for laminar and turbulent flows, for different thermodynamic states of gases, in dimensional and non-dimensional forms, and in an incompressible situation. All that is valid also for the different versions of the Navier-Stokes equations, where appropriate. The only way to solve the fluid dynamic equations for complex three-dimensional problems consists in the use of numerical integration methods. To deal with this request it is very helpful to formulate the complete set of governing equations in vector or vector-matrix form. This is true also for two equations turbulence models as well as for the description of non-equilibrium effects of thermodynamics. These requirements are fully addressed in this book. Graduate and doctoral students, who are concerned with the numerical solutions of the fluid dynamic equations for specific problems, may find in this book the suggestions regarding the degree of approximation which could be adequate for the task they consider. Further, persons who are interested in the evolution of the mathematical description of fluid dynamic issues, both from the scientific and also the historical side, may discover suggestions, advices and motivations in this book.