MATHEMATICAL METHOD OF COMPUTATIONAL FLUID DYNAMICS PROBLEMS SOLVING - Глазок, О. М. (Science-based technologies, 2014)
A mathematical method of solving of systems of nonlinear equations, produced by the numeral model of hydrodynamic problem, is offered. Application of the method is illustrated on the example of two-dimensionsl hydrodynamic problem, described by the Navier-Stokes equations. For the difference scheme on a rectangular calculation mesh it is suggested to utilize the iteration-based method of solving, based on the construction of auxiliary target function, the value of which characterizes the norm of discrepancy of the system. Auxiliary differential equation which sets a condition on speed of convergence of iteration process is introduced. This equation contains the parameter of quality of dynamic process of search of solution, that allows to controll the speed of convergence. An approach which allows to achieve diminishing of dimension of search space due to the use of expressions of some of unknown values through the others ones is offered. An approach to organization of sectional solution of computing task on the multiprocessor or distributed computer system is offered.