Abstract:
A new approach to the simulation of slow slightly-compressible gas flows based on the system of equations distinct from the Navier–Stokes equations is under consideration. A peculiarity of substantially subsonic gas flows consists in the fact that on the one hand they are similar to liquid flows as the speed of small perturbations propagation is much higher than the gas velocity, but on the other hand, they show the property of medium compressibility. While Mach number tends to zero pressure-density coupling is violated. In the considered problems, gas is slightly-compressible, i. e. strong density drops are not observed even in the case, when the medium compressibility can not be neglected. At the same time, the pressure changes more perceptibly. Unlike the traditional approach to computation of gasdynamic flows in such cases, the pressure instead of the density should be considered as the primary dependent variable. In the paper, the procedure of pressure decomposition into two components — a volume-averaged part and a dynamic part — is proposed. To derive the dimensionless form of the equations, different reference values for these components are used that allows eliminating singularities at Mach number tending to zero. The notions of increments of volume-average and dynamic pressure parts as the difference between the current value of the corresponding component and its value on the previous time level are introduced. A special computational algorithm including the solution of elliptic equation for the increment of the dynamic component is developed. The test predictions indicate high accuracy and robustness of the proposed methods.
Keywords:slightly-compressible gas flows, low Mach number, quasigasdynamic system of equations, decomposed pressure, pressure increments.
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