On the Characteristic Paths of Unsteady Incompressible Flows with Artificial Compressibility


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Abstract


In this paper the characteristics of unsteady two-dimensional incompressible flows are obtained along with artificial compressibility. At first, the characteristic relations for one-dimensional flow are derived in a routinely manner. Then, they are extended for the two-dimensional case based on a novel approach. Mach cone and conoid passing from a point in an incompressible flow, paths of information propagation and corresponding Riemann variables are extracted using consistency and compatibility relations. It was found that the directions of pseudo acoustic waves within the incompressible flow are functions of artificial compressibility parameter which also shows the subsonic nature of flow. Unlike the compressible flow equations, the cross-section of Mach conoid with x-y plane is an ellipse having major and minor diameters parallel to coordinate axis. The domain of dependence of a point is formed by waves which propagate tangent to the Mach cone. Information propagation directions and velocities are all functions of artificial compressibility parameter.
Finally, this paper leads to following concepts:
a) Physical interpretation of pseudo-wave propagation in two-dimensional unsteady incompressible flow.
b) The influence of artificial compressibility parameter on characteristic paths of incompressible flows equations.
c) Feasibility of numerical flux design based on genuinely two-dimensional characteristics of incompressible flow equations without any simplifying assumption such as using one-dimensional characteristics relations for two-dimensional flows.
Overally, the newly obtained characteristic equations can be used as information propagation patterns for multi-dimensional incompressible flows.
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Keywords


Incompressible Flow; Artificial Compressibility; Two-Dimensional Characteristics; Mach Conoid; Riemann Variables; Wave Angle

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