A brief introduction to fluidstructure. O. Souček
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1 A brief introduction to fluidstructure interactions O. Souček
2 Fluid-structure interactions Important class computational models Civil engineering Biomechanics Industry Geophysics From From M. Madlik
3 Fluid-structure interactions Main technical computational difficulties: Typically problems with changing domain Interaction forces exerted by the fluid deform the structure, affecting the motion of the fluid Conflict of descriptions fluid Eulerian vs. structure (solid) Lagrangian Two basic computational approaches Interaction approach Fluid and solid parts are solved for iteratively, one by one Main advantage allows the use of traditional solvers for the standard fluid and elasticity problems, the only difficulty is implementation of interaction (convergence)
4 Fluid-structure interactions Two basic computational approaches Interaction approach Fluid and solid parts are solved for iteratively, one by one Weak coupling (fluid and solid at a time) vs. strong coupling (sub timelevel interactions) Main advantage allows the use of traditional solvers for the standard fluid and elasticity problems, the only difficulty is implementation of interaction (convergence) Disadvantage slow, harder to parallelize (sequentional comuptation), convergence issues Monolithic approach Both fluid and solid equations are formulated and solved for together Advantage unified approach, parallelizable, allows also for unified space-time discretization Disadvantage typically very large both linear and non-linear problems, hard to treat numerically
5 Continuum mechanics in moving domains Continuum Mechanics on Arbitrary Moving Domains Eulerian (present) configuration Langangian configuration Referential configuration arbitrarily moving v.r.t. E. and L. conf.
6 Continuum mechanics in moving domains - KINEMATICS Lagrangian-to-Eulerian map displacement velocity Deformation gradient, jacobian
7 Continuum mechanics in moving domains - KINEMATICS Lagrangian-to-Eulerian map a generalized space-time perspective Space-time deformational gradient
8 Continuum mechanics in moving domains - KINEMATICS Referential-to-Eulerian map Mesh displacement Mesh velocity Mesh deformation gradient, Jacobian
9 Continuum mechanics in moving domains - KINEMATICS Referential-to-Eulerian map a generalized space-time perspective Space-time deformational gradient
10 Continuum mechanics in moving domains - KINEMATICS Lagrangian-to-referential map displacement velocity Deformation gradient, jacobian
11 Continuum mechanics in moving domains - KINEMATICS Lagrangian-to-referential map
12 Continuum mechanics in moving domains - KINEMATICS Lagrangian-to-Referential map a generalized space-time perspective Space-time deformational gradient
13 Continuum mechanics in moving domains - KINEMATICS
14 Continuum mechanics in moving domains - KINEMATICS Fundamental kinematic relationships
15 Continuum mechanics in moving domains - KINEMATICS Transport theorems
16 Continuum mechanics in moving domains - KINEMATICS Transport theorems
17 Continuum mechanics in moving domains - KINEMATICS Transport theorems for surface integrals Transport theorems for line integrals
18 MASTER BALANCE EQUATIONS Using Reynold s t.t.:
19 MASTER BALANCE EQUATIONS Rankine-Hugoniot conditions
20 MASTER BALANCE EQUATIONS
21 MASTER BALANCE EQUATIONS may be written as with
22 MASTER BALANCE EQUATIONS may be written as with
23 MASTER BALANCE EQUATIONS
24 MASTER BALANCE EQUATIONS
25 CONSERVATION LAWS
26 CONSERVATION LAWS
27 CONSERVATION LAWS
28 CONSERVATION LAWS
29 CONSERVATION LAWS
30 CONSERVATION LAWS
31 CONSERVATION LAWS
32 CONSERVATION LAWS
33 CONSERVATION LAWS From: M. Mádlik 2010, Interaction of a Fluid Flow with an Elastic Body, Ph.D. Thesis
34 CONSERVATION LAWS From: M. Mádlik 2010, Interaction of a Fluid Flow with an Elastic Body, Ph.D. Thesis
35 Single continuum model From: M. Mádlik 2010, Interaction of a Fluid Flow with an Elastic Body, Ph.D. Thesis
36 Single continuum model From: M. Mádlik 2010, Interaction of a Fluid Flow with an Elastic Body, Ph.D. Thesis
37 Single continuum model From: M. Mádlik 2010, Interaction of a Fluid Flow with an Elastic Body, Ph.D. Thesis
38 Single continuum model From: M. Mádlik 2010, Interaction of a Fluid Flow with an Elastic Body, Ph.D. Thesis Lagrangian descr. In the solid part ALE in the fluid part
39 Single continuum model From: M. Mádlik 2010, Interaction of a Fluid Flow with an Elastic Body, Ph.D. Thesis Lagrangian descr. In the solid part ALE in the fluid part
40 Single continuum model From: M. Mádlik 2010, Interaction of a Fluid Flow with an Elastic Body, Ph.D. Thesis
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