Pressure-based control-volume finite element method for flow at all speeds

We present a collocated pressure-based method for the solution of viscouslinviscid fluid flow problems incorporating compressible and incompressible regimes. The solution domain is discretized using a control-volume-based finite element method. The fully implicit method does not experience any stability difficulties due to compressibility effects at low Mach numbers. The pressure/velocity decoupling problem is fully resolved herein for flow regimes from incompressible through compressible flow. Transonic and supersonic flows are covered by including the pressure/density coupling, which arises in high-speed flows, in the continuity equation. This is done in such a manner that the continuity equation remains a constraint equation for pressure in all flow regimes. Test problems with wide variations in geometry and fluid physics have been successfully solved, demonstrating the generality and computational capability of the method. The scheme is both efficient and robust. The accuracy of the method has been checked by comparing the results with other numerical results available in the literature and with the exact solution.

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