A Monolithic Fem Solver for an Ale Formulation of Fluid-Structure Interaction with Configuration for Numerical Benchmarking (original) (raw)
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A fully-coupled partitioned finite volume–finite volume and hybrid finite volume–finite element fluid–structure interaction scheme is presented. The fluid domain is modelled as a viscous incompressible isothermal region governed by the Navier–Stokes equations and discretised using an edge-based hybrid-unstructured vertex-centred finite volume methodology. The structure, consisting of a homogeneous isotropic elastic solid undergoing large, non-linear deformations, is discretised using either an elemental/nodal-strain finite volume approach or isoparametric Q8 finite elements and is solved using a matrix-free dual-timestepping approach. Coupling is on the solver sub-iteration level leading to a tighter coupling than if the subdomains are converged separately. The solver is parallelised for distributed-memory systems using METIS for domain-decomposition and MPI for inter-domain communication. The developed technology is evaluated by application to benchmark problems for strongly-coupled fluid–structure interaction systems. It is demonstrated that the scheme results in full coupling between the fluid and solid domains, whilst furnishing accurate solutions.
ArXiv, 2021
We analyse three time integration schemes for unfitted methods in fluid structure interaction. In Alghorithm 1 we propose a fully discrete monolithic algorithm with P1 P1 stabilized finite elements for the fluid problem; for this alghorithm we prove well-posedness, unconditional stability and convergence in the case of linearized problem (see Propositions 2.4.2, 2.4.3 and Theorem 3.3.7, respectively). The analysis optimal convergence rates as expected from the Euler scheme, and the supposed regularity of the solution to the continuous problem. Moreover we introduce two algorithms that allow for a partitioning of the coupled problem by exploiting an explicit-implicit treatment of the transmission conditions. Algorithm 2 represents, essentially, a simplification of Algorithm 1 since it simply treat the solid elastic forces in explicit form using the displacement and velocities of the structure evaluated in the previous time steps. Instead, Algorithm 3, is really a splitting algorithm ...
A Monolithic Approach to Fluid-structure Interaction
2020
This paper compares partitioned and monolithic solution procedures for the numerical simulation of fluid-structure interactions. Their different stability properties are illustrated and the role of structural prediction for a partitioned method is discussed. A grid refinement study has been carried out to assess the temporal accuracy of these methods. Moreover, their computational cost as well as their computational efficiency is compared. Numerical experiments are presented for a one-dimensional model problem of a piston interacting with a fluid.