Introduction of causality in integral methods (Q638711)

Integral equation methods easily fulfill any boundary conditions of direct and inverse problems, for compressible and viscous fluids, but are more rebellious to a proper insertion of causality in the velocity field. On the contrary, finite element methods misfit, in general, non-homogeneous boundary conditions, but easily introduce causality with one-sided derivatives of low-order basis functions, eventually spoiling the inner coherence of the field. In fact, a hyperbolic structure should arise only from causality, and not from the particularities of basis functions or the mesh configurations. In this study, the authors give a way to obtain a right throughflow and source development, ensuring the uniqueness of the solution, and they propose non-isotropic elementary solutions of the Poisson equation, which allow to create the right domains of influence. The possibility to generate the hyperbolic features of supersonic flows with elliptic but non-isotropic elementary solutions is demonstrated, thus allowing to easily improve flow computation programs using elliptic integral equations. The method does not need any linearization and promises to be a good approximation to the non-stationary geometrical acoustics, still needing very few calculation time. Agreement between calculation and experiment is proven, as well for a given throughflow for a prescribed pressure ratio, as for compressors and turbines.