LAUSR

The immediate impulse-response of a confined incompressible fluid is characterized by inertance. For a vessel with one inlet and outlet, this is a single quantity; for multiple ports the generalization is a singular reciprocal inertance matrix which acts on the port-impulses to give the corresponding inflows. The reciprocal inertance coefficients are defined by the boundary fluxes of potential flows. Green's identity converts these coefficients to domain integrals of kinetic energy. For a system discretized with finite elements, a third method is proposed for computing reciprocal inertance coefficients which requires only the stiffness matrix and the solution vectors and no numerical differentiation. References A. Asai. Bubble dynamics in boiling under high heat flux pulse heating. J. Heat Transf., 113(4):973979, 1991. doi:10.1115/1.2911230. A. Asai. Three-dimensional calculation of bubble growth and drop ejection in a bubble jet printer. J. Fluids Eng., 114(4):638641, 1992. doi:10.1115/1.2910079. G. K. Batchelor. An introduction to fluid dynamics. Cambridge University Press, 1967. doi:10.1017/CBO9780511800955. J. D. Beasley. Model for fluid ejection and refill in an impulse drive jet. Soc. Photogr. Sci. Eng., 21(2):7882, 1977. F. Dorfler and F. Bullo. Kron reduction of graphs with applications to electrical networks. IEEE T. Circuits I, 60(1):150163, 2013. doi:10.1109/tcsi.2012.2215780. A. Ern and J.-L. Guermond. Theory and practice of finite elements. Springer, 2004. doi:10.1007/978-1-4757-4355-5. K. Foster and G. A. Parker. Fluidics: Components and circuits. Wiley, 1970. URL https://www.worldcat.org/title/fluidics-components-and-circuits/oclc/138528. C. Geuzaine and J.-F. Remacle. Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities. Int. J. Numer. Meth. Eng., 79(11): 13091331, 2009. doi:10.1002/nme.2579. G. Geymonat and D. Chenais. Introduction, pages xixii. Birkhauser, 1996. doi:10.1007/978-1-4612-2436-5. T. Gustafsson and G. McBain. kinnala/scikit-fem 0.1.17, Nov. 2018. O. Heaviside. Some remarks on the Volta force and seat of electro-motive forces questions, and on impressed force and potential in condenser circuits. J. Soc. Tele.-Eng. Electric., 14(57): 269296, 1885. doi:10.1049/jste-3.1885.0014. H. E. Koenig, Y. Tokad, and H. K. Kesavan. Analysis of discrete physical systems. McGrawHill, 1967. URL https://trove.nla.gov.au/work/21368152?selectedversion=NBD2690879. M. Krizek and P. Neittaanmaki. Superconvergence phenomenon in the finite element method arising from averaging gradients. Numer. Math., 45(1):105116, 1984. doi:10.1007/bf01379664. H. Lamb. Hydrodynamics. Cambridge University Press, 6th edition, 1932. URL https://www.cambridge.org/au/academic/subjects/mathematics/fluid-dynamics-and-solid-mechanics/hydrodynamics-6th-edition. G. D. McBain and S. G. Mallinson. Impulsively generated incompressible two-phase flow and the Asai thermal ink-jet model. In 21st Australasian Fluid Mechanics Conference, 2018. URL https://people.eng.unimelb.edu.au/imarusic/proceedings/21/Contribution_616_final.pdf. K. W. Oh, K. Lee, B. Ahn, and E. P. Furlani. Design of pressure-driven microfluidic networks using electric circuit analogy. Lab Chip, 12(3):515545, 2012. doi:10.1039/c2lc20799k. H. F. Olson. Elements of acoustical engineering. Van Nostrand, 1948. doi:10.1002/sce.3730320378. R. S. Sanford. Physical networks. Prentice-Hall, 1965. URL https://trove.nla.gov.au/work/8815056?q&versionId=10200776. V. L. Streeter. Steady flow in pipes and conduits. In H. Rouse, editor, Engineering Hydraulics: Proceedings of the Fourth Hydraulics Conference, chapter 6, pages 387443. Wiley, 1950. URL https://trove.nla.gov.au/work/17727563.