Fully finite volume method on a curvilinear grid-based arbitrary Lagrangian Eulerian approach for computational fluid flexible-structure interaction

Abstract

For Computational Fluid flexible-Structure Interaction (CFfSI), this paper in on proposition of a unified fluid-dynamic and elastic stresses-based fully Finite Volume Method (FVM)—for both fluid and structural dynamics—on a curvilinear grid for both fluid and structure subdomains. Further, a hybrid method is proposed for the dynamic curvilinear-grid generation in the fluid subdomain. Arbitrary Lagrangian Eulerian (ALE) framework-based governing equations are presented for fluid-flow while those for the structural deformations are presented in the Lagrangian framework; along with the fluid-solid interfacial conditions. Solution methodology is presented, for the ALE method on the curvilinear grid, using a fully implicit pressure projection method for the flow solver and a pseudo-transient time stepping method for the structural solver; along with a fully implicit coupling between the two solvers. For the ALE method-based in-house CFfSI solver, an excellent agreement with the published numerical results is demonstrated (for steady and periodic flow-profiles/structural-deformations) on four different CFfSI problems. Further, a II-order accuracy in space as well as time is demonstrated for the present ALE method. After the validation and order of accuracy studies, a performance study is presented for our CFfSI solver on a dynamic-grid—generated by the proposed hybrid method as compared to a traditional method. The hybrid method resulted in up to 30% reduction in computational time for the four CFfSI problems; used in the validation study. An ALE method, based on a novel fully-FVM and hybrid method for dynamic curvilinear-grid generation, is presented here—for an easy-to-implement, stable, and computationally-efficient CFfSI development.