THE SHIFTED BOUNDARY METHOD: FROM DARCY FLOW TO SOLID MECHANICS
The Shifted Boundary method: From Darcy Flow to Solid Mechanics
Nabil Atallah (Duke University)
26 Giugno 2019 ore 10:00
Aula Buzano - Dipartimento di Scienze Matematiche - Politecnico di Torino
Abstract:
Embedded methods obviate the need to mesh the geometry by immersing it in a preexisting grid. However, the ease in mesh generation comes at the expense of boundary condition enforcement at the mathematical and data structure levels. Unfortunately, standard embedded boundary methods suffer from the small-cut grid cells, which have adverse effects on the algebraic solve and are difficult to implement due to the need to perform complex cell cutting operations at boundaries.
In this seminar, dr Atallah presents a new, stable, and simple embedded boundary method, called “Shifted Boundary” method (or, in short, SB method), that eliminates the long-standing numerical issues mentioned above by defining a surrogate domain consisting of all un-cut elements of the mesh that lie inside the computational domain. To correct for the discrepancy between the true and surrogate boundaries, while avoiding a reduction in convergence rates and maintaining consistency with the original problem-definition, a Taylor extrapolation at the surrogate boundary was enforced through Nitsche's method. He will demonstrate and perform a numerical analysis of the SB method for the Darcy flow and solid mechanics equations.
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