Stabilized explicit coupling for fluid–structure interaction using Nitsche's method

Abstract

In this work we propose a stabilized explicit coupling scheme for fluid-structure interaction problems involving a viscous incompressible fluid. The coupled discrete formulation is based on Nitsche's method with a time penalty term giving L 2 -control on the fluid pressure variations at the interface. The scheme is stable, in the energy norm, irrespectively of the fluid-structure density ratio. Numerical experiments, in two and three dimensions, show that optimal time accuracy can be obtained by performing a few defect-correction iterations.Key-words: Fluid-structure interaction, Nitsche's method, fluid incompressibility, time discretization, explicit coupling, loosely coupled schemes, defectcorrection method

Some Numerical Approaches to Solve Fluid Structure Interaction Problems in Blood Flow

“…The explicit coupling scheme without correction had given a stable approximation with poor accuracy. High order accuracy was achieved after a few correction iterations and the results were comparable to that with implicit scheme solution [28].…”

“…Nobile and Vergara [29] proposed Robin interface conditions to be enforced to solve fluid and structure subproblems. Burman and Fernández [28] proposed a stabilized explicit coupling for fluid structure interaction based on Nitsche's scheme. Numerical simulation of fluid structure interaction problems involving a viscous compressible fluid and elastic structure was considered.…”

“…In addition, the implicit partitioned algorithms are also affected by the added mass effect in terms of convergence. Special treatment of the interface conditions needs to be considered [8,16,[28][29][30]. To date, it seems that only the monolithic and implicit schemes are applicable in blood flow simulation involving fluid structure interaction.…”

Partitioned Simulation of Fluid-Structure Interaction

“…For the explicit partitioned solution of fluid-structure interaction problems with incompressible fluids, finite element techniques based on Nitsche's principle have been developed [29,30]. Nitsche's principle weakly enforces a Dirichlet boundary condition, instead of the more traditional strong enforcement of a Dirichlet boundary condition which imposes that the function spaces satisfy this boundary condition.…”

Robin–Robin preconditioned Krylov methods for fluid–structure interaction problems

“…Similar ideas, but on a purely algebraic level, have been investigated in [29,4] where the algebraic Chorin-Temam scheme (see [27]) and the Yosida scheme (see [31,30]), have been extended to the FSI problem. Finally, we mention the work [5] which proposes a global weak formulation relying on the imposition of the kinematic coupling conditions (continuity of the velocity at the interface) by the Nitsche method and a partitioned iterative procedure which, however, leads to non-standard fluid and structure discrete equations.…”