A 3D common-refinement method for non-matching meshes in partitioned variational fluid–structure analysis

Abstract

We present a three-dimensional (3D) common-refinement method for non-matching meshes between discrete non-overlapping subdomains of incompressible fluid 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 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 cylindrical tubular elastic body. We demonstrate 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 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 benchmark 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. Finally, we demonstrate the 3D parallel implementation of common-refinement with NIFC scheme for a realistic engineering problem of drilling riser undergoing complex vortex-induced vibration with strong added mass effects.

A variational flexible multibody formulation for partitioned fluid-structure interaction: Application to bat-inspired drones and unmanned air-vehicles

“…Based on the type of constraint and the variations in Eqs. (30) and (31) and δC AB = Bδq, one can write the constraint forces as F AB = λB T . The matrix B T is the Jacobian of the constraint denoted by c (η s h ) T in Eq.…”

“…It is essential that the fluid tractions and structural displacements are transferred across the fluid-structure interface in a locally accurate and conservative manner. For generic non-matching meshes in the structural and fluid domains at the interface, local and global conservative methods such as quadrature projection [30] and common-refinement technique [29,31] as well as globally conservative methods such as radial basis function mapping [32,33] can be utilized. However, for the flexible multibody system considered in the present study, the local conservative methods of projection and common-refinement can become somewhat complicated to implement considering multiple structural components along with the joints and connections in between them.…”

Effects of Geometric Porosity in the Trailing Edge of a Flexible Pitching Plate

“…The two solvers interface at the boundary between the structural and fluid bodies with a radial basis function applied to the surface of the plate. Further details of the numerical methods utilised can be found in [3,4].…”

A novel 3D variational aeroelastic framework for flexible multibody dynamics: Application to bat-like flapping dynamics

“…In a typical partitioned-based aeroelastic scheme, the surface boundary data must be transferred along the interface between the fluid and structural domains to satisfy a Dirichlet-type interface conditon (displacements or velocity) and a Neumann-type (fluid momentum flux or traction) interface condition. A proper care during interpolation and projection process is required to transfer the physical data accurately across non-matching meshes between the partitioned fluid and structural domains [26,30,31]. Global and local energy conservation should be satisfied during the aeroelastic coupling while maintaining the accuracy of data transfer along the interface via Dirichlet-Neumann coupling.…”