A NURBS-BASED FINITE ELEMENT FORMULATION FOR INCOMPRESSIBLE FLUID DYNAMICS AND FLUID-STRUCTURE INTERACTION WITH RIGID BODIES

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PATRÍCIA TONON
MATEUS GUIMARÃES TONIN
LUIS FELIPE ESPATH
ALEXANDRE LUIS BRAUN

Abstract

IN THE PRESENT WORK, A NUMERICAL INVESTIGATION IS PERFORMED USING A NURBS-BASED FINITE ELEMENT FORMULATION APPLIED TO CLASSICAL PROBLEMS OF INCOMPRESSIBLE FLUID DYNAMICS AND FLUID-STRUCTURE INTERACTION. MODEL CAPABILITIES RELATED TO REFINEMENT TECHNIQUES ARE ANALYZED USING A FINITE ELEMENT FORMULATION WITH NURBS (NON UNIFORM RATIONAL B-SPLINES) BASIS FUNCTIONS, WHERE B-SPLINES AND LOW-ORDER LAGRANGIAN C0 ELEMENTS CAN BE CONSIDERED AS PARTICULAR CASES. AN EXPLICIT TWO-STEP TAYLOR-GALERKIN MODEL IS UTILIZED FOR TIME AND SPACE DISCRETIZATION OF THE FUNDAMENTAL FLOW EQUATIONS AND TURBULENCE IS TAKEN INTO ACCOUNT BY USING LARGE EDDY SIMULATION (LES) AND THE SMAGORINSKY’S SUB-GRID SCALE MODEL. THE INCOMPRESSIBILITY CONSTRAINT IS CIRCUMVENTED BY APPLYING THE PSEUDO-COMPRESSIBILITY HYPOTHESIS. FLUID-STRUCTURE INTERACTION (FSI) IS CONSIDERED USING AN ALE KINEMATIC FORMULATION AND A CONSERVATIVE PARTITIONED COUPLING SCHEME, WHERE THE RIGID BODY APPROACH FOR LARGE ROTATIONS IS ADOPTED. COMPUTATIONAL FLUID DYNAMICS (CFD) AND FSI APPLICATIONS ARE ANALYZED IN ORDER TO EVALUATE ACCURACY ASSOCIATED WITH THE DIFFERENT REFINEMENT PROCEDURES UTILIZED. RESULTS OBTAINED HERE SHOW THAT HIGH ORDER BASIS FUNCTIONS WITH APPROPRIATE REFINEMENT AND NON-UNIFORM PARAMETERIZATION LEAD TO BETTER RESULTS WHEN COMPARED WITH LOW-ORDER LAGRANGIAN MODELS.

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