SUMMARYA novel parallel monolithic algorithm has been developed for the numerical simulation of large-scale fluid structure interaction problems. The governing incompressible Navier-Stokes equations for the fluid domain are discretized using the arbitrary Lagrangian-Eulerian formulation-based side-centered unstructured finite volume method. The deformation of the solid domain is governed by the constitutive laws for the nonlinear Saint Venant-Kirchhoff material, and the classical Galerkin finite element method is used to discretize the governing equations in a Lagrangian frame. A special attention is given to construct an algorithm with exact total fluid volume conservation while obeying both the global and the local discrete geometric conservation law. The resulting large-scale algebraic nonlinear equations are multiplied with an upper triangular right preconditioner that results in a scaled discrete Laplacian instead of a zero block in the original system. Then, a one-level restricted additive Schwarz preconditioner with a block-incomplete factorization within each partitioned sub-domains is utilized for the modified system. The accuracy and performance of the proposed algorithm are verified for the several benchmark problems including a pressure pulse in a flexible circular tube, a flag interacting with an incompressible viscous flow, and so on.
Abstract. A fully coupled numerical algorithm has been developed for the numerical simulation of large-scale fluid structure interaction problems. The incompressible
ical Galerkin finite element is used to discretize the governing equations in a Lagrangian frame. The time integration method for the structure domain is based on the Newmark type generalized−α method while the first-order backward difference is used in the fluid domain. The implementation of the preconditioned coupled iterative solvers is based on the PETSc library for improving the efficiency of the parallel code. The present numerical algorithm is validated for a steady and unsteady Newtonian fluid interacting with an elastic rectangular bar behind a circular cylinder and a three-dimensional elastic solid confined in a rectangular channel.
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