A stabilised immersed framework on hierarchical b-spline grids for fluid-flexible structure interaction with solid–solid contact

Kadapa, Chennakesava; Dettmer, Wulf G.; Perić, D.

doi:10.1016/j.cma.2018.02.021

Cited by 54 publications

(83 citation statements)

References 39 publications

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“…However, the application of Dirichlet boundary conditions seems to require special consideration since all the quadratic Bernstein polynomials are not interpolatory. While the popular Nitsche method, which has been adopted extensively for problems in solid and fluid mechanics, can be used for imposing the Dirichlet boundary conditions in the present work, we show that the Dirichlet boundary conditions can be applied using the standard elimination approach by extending the mapping technique for the mesh generation proposed in Section 2.3. This mapping technique not only ensures strong imposition of Dirichlet boundary conditions but also eases the task of implementation of the proposed scheme into the existing finite element codes.…”

Section: Element Design Mesh Generation and Application Of Dirichlementioning

confidence: 87%

Novel quadratic Bézier triangular and tetrahedral elements using existing mesh generators: Applications to linear nearly incompressible elastostatics and implicit and explicit elastodynamics

Kadapa

2018

Numerical Meth Engineering

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In this paper, we present novel techniques of using quadratic Bézier triangular and tetrahedral elements for elastostatic and implicit/explicit elastodynamic simulations involving nearly incompressible linear elastic materials. A simple linear mapping is proposed for developing finite element meshes with quadratic Bézier triangular/tetrahedral elements from the corresponding quadratic Lagrange elements that can be easily generated using the existing mesh generators. Numerical issues arising in the case of nearly incompressible materials are addressed using the consistent B-bar formulation, thus reducing the finite element formulation to one consisting only of displacements. The higher-order spatial discretization and the nonnegative nature of Bernstein polynomials are shown to yield significant computational benefits. The optimal spatial convergence of the B-bar formulation for the quadratic triangular and tetrahedral elements is demonstrated by computing error norms in displacement and stresses.The applicability and computational efficiency of the proposed elements for elastodynamic simulations are demonstrated by studying several numerical examples involving real-world geometries with complex features. Numerical results obtained with the standard linear triangular and tetrahedral elements are also presented for comparison. 544KADAPA of finite elements, triangular/tetrahedral elements are often the favorable choice because of the ease of mesh generation, even for complicated industrial geometries, and the availability of numerous commercial and open-source mesh generation software suites. In the past few decades, a plethora of numerical techniques has been developed for performing simulations using triangular and tetrahedral elements, as the task of mesh generation with triangular and tetrahedral elements is well established.Nevertheless, in spite of the tremendous amount of research work that has gone into the development of numerical techniques for obtaining accurate numerical solutions using triangular/tetrahedral elements, robust and efficient techniques for performing simulations using these elements are still lacking, especially for explicit elastodynamic simulations involving nearly incompressible material models that are commonly encountered in soils, a majority of polymeric materials, and biological tissues. This lack of development is due to the fact that triangular/tetrahedral Lagrange elements suffer from quite a few disadvantages that limit their applicability to explicit elastodynamic simulations consisting of nearly incompressible elastic and elastoplastic material models. The important disadvantages of triangular/tetrahedral Lagrange elements that motivated the present research work are as follows.• Due to the approximation of constant strain across the element, linear triangular/tetrahedral Lagrange elements with pure displacement formulation exhibit a very stiff behavior when compared with the linear quadrilateral/hexahedral Lagrange elements. 1 Therefore, to obtain numerical results of suffici...

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Section: Element Design Mesh Generation and Application Of Dirichlementioning

confidence: 87%

Novel quadratic Bézier triangular and tetrahedral elements using existing mesh generators: Applications to linear nearly incompressible elastostatics and implicit and explicit elastodynamics

Kadapa

2018

Numerical Meth Engineering

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“…To the best of our knowledge, the sole available approaches are the splitting methods introduced in 5,22,23,24 for the immersed boundary or fictitious domain methods, and in 18,19,25,26 for unfitted Nitsche based methods. The loosely coupled schemes reported in 5,18,19,25,23 are known to enforce severe time-step restrictions for stability/accuracy or to be sensitive to the amount of added-mass effect. In the case of the coupling with thin-walled solids, these issues are circumvented by the semi-implicit and loosely coupled schemes reported in 22,19,26 and in 24 , respectively.…”

Section: Introductionmentioning

confidence: 99%

An unfitted mesh semi‐implicit coupling scheme for fluid‐structure interaction with immersed solids

Fernández

Gerosa

2020

Numerical Meth Engineering

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Unfitted mesh finite element approximations of immersed incompressible fluidstructure interaction problems which efficiently avoid strong coupling without compromising stability and accuracy are rare in the literature. Moreover, most of the existing approaches introduce additional unknowns or are limited by penalty terms which yield ill conditioning issues. In this paper, we introduce a new unfitted mesh semi-implicit coupling scheme which avoids these issues. To this purpose, we provide a consistent generalization of the projection based semi-implicit coupling paradigm of [Int.

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“…In the last decade, the use of spline functions, such as B-splines, non-uniform rational B-splines (NURBS), analysis-suitable T-splines (ASTS), and hierarchical B-splines, has become widespread in computational mechanics thanks to isogeometric analysis (IGA) [51,54]. In the field of immersed methods for FSI, IGA has already been used to perform NURBS-based and ASTS-based generalizations of the IB method [15,16], develop the immersogeometric method [38,55,39], couple shells with Stokes flows using the boundary integral method [56,57], solve air-blast problems [58], develop a fictitious domain approach [59], and a stabilized cut-cell immersed framework [60].…”

Section: Introductionmentioning

confidence: 99%

Non-body-fitted fluid–structure interaction: Divergence-conforming B-splines, fully-implicit dynamics, and variational formulation

Casquero

Zhang

Bona-Casas

et al. 2018

Journal of Computational Physics

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Immersed boundary (IB) methods deal with incompressible visco-elastic solids interacting with incompressible viscous fluids. A long-standing issue of IB methods is the challenge of accurately imposing the incompressibility constraint at the discrete level. We present the divergence-conforming immersed boundary (DCIB) method to tackle this issue. The DCIB method leads to completely negligible incompressibility errors at the Eulerian level and various orders of magnitude of increased accuracy at the Lagrangian level compared to other IB methods. Furthermore, second-order convergence of the incompressibility error at the Lagrangian level is obtained as the discretization is refined. In the DCIB method, the Eulerian velocitypressure pair is discretized using divergence-conforming B-splines, leading to inf-sup stable and pointwise divergence-free Eulerian solutions. The Lagrangian displacement is discretized using non-uniform rational B-splines, which enables to robustly handle large mesh distortions. The data transfer needed between the Eulerian and Lagrangian descriptions is performed at the quadrature level using the same spline basis functions that define the computational meshes. This conduces to a fully variational formulation, sharp treatment of the fluid-solid interface, and a 0.5 increase in the convergence rate of the Eulerian velocity and the Lagrangian displacement measured in L 2 norm in comparison with using discretized Dirac delta functions for the data transfer. By combining the generalized-α method and a block-iterative solution strategy, the DCIB method results in a fully-implicit discretization, which enables to take larger time steps. Various two-and three-dimensional problems are solved to show all the aforementioned properties of the DCIB method along with mesh-independence studies, verification of the numerical method by comparison with the literature, and measurement of convergence rates.

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A stabilised immersed framework on hierarchical b-spline grids for fluid-flexible structure interaction with solid–solid contact

Abstract: A stabilised immersed framework on hierarchical b-spline grids for fluidflexible structure interaction with solid-solid contact. Computer Methods in Applied Mechanics and Engineering

Cited by 54 publications

References 39 publications

Novel quadratic Bézier triangular and tetrahedral elements using existing mesh generators: Applications to linear nearly incompressible elastostatics and implicit and explicit elastodynamics

Novel quadratic Bézier triangular and tetrahedral elements using existing mesh generators: Applications to linear nearly incompressible elastostatics and implicit and explicit elastodynamics

An unfitted mesh semi‐implicit coupling scheme for fluid‐structure interaction with immersed solids

Non-body-fitted fluid–structure interaction: Divergence-conforming B-splines, fully-implicit dynamics, and variational formulation

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