МОДЕЛЬ ТЕЧЕНИЯ НЕСЖИМАЕМОЙ И СЖИМАЕМОЙ ЖИДКОСТИ

Abstract

Most mathematical models of complex systems are solved by numerical methods, which, though producing an approximate solution , but due to the lack of alternative approaches are the only ones. The vast majority of numerical methods for solving systems of nonlinear equations reduced to the organization of so-called iterative process: the process of successive approximations to the root system. To find the next approximation one way or another sought an increment that is added to or subtracted from the previous approximation of unknowns. Depending on how you define the data increments numerical methods differ in speed and stability of convergence to the desired root. The end of the iterative process is considered to meet the requirements that describe the desired achievement of a solution. A wide range of abstract methods of numerical solution of systems of nonlinear algebraic equations (SNAE) boils down to two main groups : I - methods based on linearization of the functions in the system ( for example, simple iteration, chords and Newton); II - methods based for logical operations with many elements of the system (method bisection of the interval). Most effective in terms of speed and stability of convergence are methods of the first group. However, their use often requires adaptation to a particular type of SNAE. So to solve the problem of flux, depending on the system of equations requires a serious revision of methods of numerical solution. Because SNAE describing arbitrary flow distribution in hydraulic systems saturated trailing relationship arbitrary type, which can also vary depending on the values of the unknowns directly in an iterative process, using a general purpose numerical methods is impossible. Also unacceptable approximation no relations typical functions such as f ( q )= r×q 2, as was done in the prior models. In the most rigid in terms of including the mass factors integrated load flow formulation of the problem must be assumed that the method of numerical solution of the hydraulic systems (HS) model should be universal so that the speed of convergence and reliability combined with the applicability for all variety of structures and properties of the elements of arbitrary hydraulic systems.