Computation of Gas Flows at Low Mach Number (I<0.01)

A review of problems and numerical methods for solving the Navier-Stokes equations for compressible fluid at low Mach number (M< 0.01) is given. Turbo machinery cooling, flows in gas epitaxial reactors in semiconductor processing, fire research, flows in the combustion chamber of a reciprocating engine and other combustion chambers etc. are some examples of such flows. There are considered the reasons why efficiency decreasing may occur in numerical predicting some flows. It is shown that at the present time the difficulties of predicting low-Mach-number flows are overcome using the Low-Mach-number equations. The Low-Mach-number equations are the reduced Navier-Stokes equations under the condition that the Mach number is sufficiently low. We give a form of the full Navier-Stokes equations (without any reduction) which provide efficient numerical predicting flows at all speeds including low-Mach-number flows. A new implicit finite difference method for solving the full Navier-Stokes equations is presented. The second part of the work is devoted to discussion of numerical results.