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A 3D common-refinement method for non-matching meshes in partitioned variational fluid-structure analysis. (English) Zbl 1416.74089
Summary: We present a three-dimensional (3D) common-refinement method for non-matching unstructured meshes between non-overlapping subdomains of incompressible turbulent fluid flow and nonlinear hyperelastic structure. The fluid flow is discretized using a stabilized Petrov-Galerkin method, and the large deformation structural formulation relies on a continuous Galerkin finite element method. An arbitrary Lagrangian-Eulerian formulation with a nonlinear iterative force correction (NIFC) coupling is achieved in a staggered partitioned manner by means of fully decoupled implicit procedures for the fluid and solid discretizations. To begin, we first investigate the accuracy of common-refinement method (CRM) to satisfy the traction equilibrium condition along the fluid-elastic interface with non-matching meshes. We systematically assess the accuracy of CRM against the matching grid solution by varying grid mismatch between the fluid and solid meshes over a tubular elastic body. We demonstrate the second-order accuracy of CRM through uniform refinements of fluid and solid meshes along the interface. We then extend the error analysis to transient data transfer across non-matching meshes between the fluid and solid solvers. We show that the common-refinement discretization across non-matching fluid-structure grids yields accurate transfer of the physical quantities across the fluid-solid interface. We next solve a 3D fluid-structure interaction (FSI) problem of a cantilevered hyperelastic plate behind a circular bluff body and verify the accuracy of coupled solutions with respect to the available solution in the literature. By varying the solid interface resolution, we generate various non-matching grid ratios and quantify the accuracy of CRM for the nonlinear structure interacting with a laminar flow. We illustrate that the CRM with the partitioned NIFC treatment is stable for low solid-to-fluid density ratio and non-matching meshes for the 3D FSI problem. Finally, we demonstrate the 3D parallel implementation of the common-refinement with the NIFC method for a realistic engineering problem of drilling riser undergoing complex vortex-induced vibration with strong added mass effects and turbulent wake flow.

74S05 Finite element methods applied to problems in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76D05 Navier-Stokes equations for incompressible viscous fluids
74B20 Nonlinear elasticity
Full Text: DOI
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