Level set function–based immersed interface method and benchmark solutions for fluid flexible‐structure interaction

Summary Using a hybrid Lagrangian‐Eulerian approach, a level set function–based immersed interface method (LS‐IIM) is proposed for the interaction of a flexible body immersed in a fluid flow. The LS‐IIM involves finite volume method for the fluid solver, Galerkin finite element method for the struct...

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Veröffentlicht in:International journal for numerical methods in fluids Jg. 91; H. 3; S. 134 - 157
Hauptverfasser: Thekkethil, Namshad, Sharma, Atul
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Bognor Regis Wiley Subscription Services, Inc 30.09.2019
Schlagworte:
benchmark
Benchmarks
Boundary conditions
Channel flow
Complexity
Computation
Computational fluid dynamics
Differential equations
Differential geometry
Eulerian‐Lagrangian
finite element
Finite element method
finite volume
Finite volume method
Flexible bodies
Flexible structures
Fluid flow
fluid‐structure interaction
Galerkin method
Iterative methods
level set
Solvers
Stream discharge
Stream flow
ISSN:0271-2091, 1097-0363
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Zusammenfassung:Summary Using a hybrid Lagrangian‐Eulerian approach, a level set function–based immersed interface method (LS‐IIM) is proposed for the interaction of a flexible body immersed in a fluid flow. The LS‐IIM involves finite volume method for the fluid solver, Galerkin finite element method for the structural solver, and a block‐iterative partitioned method–based fully implicit coupling between the two solvers. The novelty of the proposed method is a level set function–based direct implementation of fluid‐solid interface boundary conditions in both the solvers. Another novelty is the computation of the level set function from a geometric method instead of differential equations commonly used in level set methods—the novel geometric as compared to the traditional method is found to be more accurate and less time‐consuming. The LS‐IIM is demonstrated as second‐order accurate. Verification study is presented first separately for both the solvers and then together for four fluid‐structure interaction (FSI) problems, with different levels of complexity including lid‐driven flow, channel flow, and free‐stream flow. Benchmark solutions are presented for two class of FSI problems: first, easy to set up and less time‐consuming and, second, a reasonably challenging and complex FSI problem involving sharp edges and forced‐motion of the flexible structure. The benchmark solutions are proposed at steady state for the first problem, after a verification study with two open‐source solvers and, at periodic state, after a validation with published experimental results for the second problem. Our benchmark solutions may be useful for verification study in future. A geometric method–based computation of level set function and its usage for accurate implementation of fluid‐solid interface boundary conditions (BCs) in both the fluid and structural solvers are the novel feature of the proposed method for computational fluid‐structure interaction (CFSI). A simple and another complex FSI benchmark problems are proposed, and the steady and periodic solutions for the respective problems are presented for verification study in future.
Bibliographie:ObjectType-Article-1
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ISSN:0271-2091
1097-0363
DOI:10.1002/fld.4746