An iterative-marching method for solving problems of fluid and gas mechanics problems

A possibility is studied of applying the idea of global iterations with aspect to the pressure for the complete Navie–Stokes equations for a fluid as well as for a gas, for stationary and unstationary problems, for two and three dimensional problems. We give a generalization for the results published earlier and present new results concerning stability and convergence of the iterative-marching method, and its testing on the problems of motion of a fluid (twist fluid flows with bubbles; internal and surface waves generation by an eddy pair) and gas motions (flows in a nozzle with a bubble; shock wave formation resulting from viscous effects).
The main conclusion is as follows. The proposed method allows us to develop numerical algorithms for various problems of fluid and gas mechanics based on a common principle. These algorithms are simple because their basic element is a marching procedure. The above implies the possibility of developing rather universal programs.