Regensburg 2022 – wissenschaftliches Programm
BP 18.7: Vortrag
Mittwoch, 7. September 2022, 17:00–17:15, H15
Turning the Corner on the Image Method in Linear Elasticity and Low-Reynolds-Number Hydrodynamics — •Tyler Lutz, Lukas Fischer, Sonja Richter, and Andreas Menzel — Institut für Physik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106 Magdeburg
In both linear elasticity and low-Reynolds-number hydrodynamics, extensions of the image method---familiar from elementary electrostatics---have been developed to deduce the displacement (resp. velocity) fields arising from point forces applied in the vicinity of a single, flat, infinitely extended boundary. In this work, we assess the applicability of these methods to domains described by multiple, mutually orthogonal boundaries in 2 and 3 dimensions. Already in the case of a single flat boundary, the necessary image forces depend on the specific boundary conditions considered; the images become progressively more complex as one goes from free-slip to no-slip and stress-free surfaces. By iterating the image method for forces near corners or edges, we explicitly show that this method fails to generate a self-consistent image if any more than one boundary is anything other than a free-slip surface. For the situations in which the image method may be successfully applied, we explicitly construct and survey the qualitative features of the point-force Green's function near corners.