A high-resolution pressure-based algorithm for fluid flow at all speeds.

*(English)*Zbl 0991.76047Summary: We present a new collocated finite-volume-based solution procedure for predicting viscous compressible and incompressible flows. The technique is equally applicable in the subsonic, transonic, and supersonic regimes. Pressure is selected as a dependent variable in preference to density because changes in pressure are significant at all speeds as opposed to variations in density, which become very small at low Mach numbers. The newly developed algorithm has two new features: (i) the use of the normalized variable and space formulation methodology to bound the convective fluxes, and (ii) the use of a high-resolution scheme in calculating interface density values to enhance the shock-capturing property of the algorithm. The virtues of the developed method are demonstrated by solving a wide range of flows spanning the subsonic, transonic, and supersonic spectrum. Results obtained indicate higher accuracy when calculating interface density values using a high-resolution scheme.

##### MSC:

76M12 | Finite volume methods applied to problems in fluid mechanics |

76N15 | Gas dynamics, general |

76D05 | Navier-Stokes equations for incompressible viscous fluids |

##### Keywords:

all speed flows; pressure-based algorithm; collocated finite-volume-based procedure; normalized variable; space formulation; high-resolution scheme; shock-capturing property
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\textit{F. Moukalled} and \textit{M. Darwish}, J. Comput. Phys. 168, No. 1, 101--130 (2001; Zbl 0991.76047)

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