A nodal immersed finite element-finite difference method.
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| Title: | A nodal immersed finite element-finite difference method. |
|---|---|
| Authors: | Wells, David R.1 (AUTHOR) drwells@email.unc.edu, Vadala-Roth, Ben1,2 (AUTHOR), Lee, Jae H.1,3 (AUTHOR), Griffith, Boyce E.1,4,5,6,7 (AUTHOR) boyceg@email.unc.edu |
| Source: | Journal of Computational Physics. Mar2023, Vol. 477, pN.PAG-N.PAG. 1p. |
| Subjects: | Finite difference method, Bioprosthetic heart valves, Structural mechanics, Solid mechanics, Fluid-structure interaction, Spectral element method |
| Abstract: | The immersed finite element-finite difference (IFED) method is a computational approach to modeling interactions between a fluid and an immersed structure. The IFED method uses a finite element (FE) method to approximate the stresses, forces, and structural deformations on a structural mesh and a finite difference (FD) method to approximate the momentum and enforce the incompressibility of the entire fluid-structure system on a Cartesian grid. The fundamental approach used by this method follows the immersed boundary framework for modeling fluid-structure interaction (FSI), in which a force spreading operator prolongs structural forces to a Cartesian grid, and a velocity interpolation operator restricts a velocity field defined on that grid back onto the structural mesh. With an FE structural mechanics framework, force spreading first requires that the force itself be projected onto the finite element space. Similarly, velocity interpolation requires projecting velocity data onto the FE basis functions. Consequently, evaluating either coupling operator requires solving a matrix equation at every time step. Mass lumping, in which the projection matrices are replaced by diagonal approximations, has the potential to accelerate this method considerably. This paper provides both numerical and computational analyses of the effects of this replacement for evaluating the force projection and for the IFED coupling operators. Constructing the coupling operators also requires determining the locations on the structure mesh where the forces and velocities are sampled. Here we show that sampling the forces and velocities at the nodes of the structural mesh is equivalent to using lumped mass matrices in the IFED coupling operators. A key theoretical result of our analysis is that if both of these approaches are used together, the IFED method permits the use of lumped mass matrices derived from nodal quadrature rules for any standard interpolatory element. This is different from standard FE methods, which require specialized treatments to accommodate mass lumping with higher-order shape functions. Our theoretical results are confirmed by numerical benchmarks, including standard solid mechanics tests and examination of a dynamic model of a bioprosthetic heart valve. • Nodal coupling is a more efficient method for IB fluid-structure simulations. • The nodal IFED method combines finite element and finite difference methods. • Nodal coupling requires mass lumping in the finite element discretization. • Nodal and elemental coupling have similar accuracy for a heart valve simulator. • In 3D nodal coupling requires about 5-10x fewer interaction points than elemental. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Computational Physics is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 161693406 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: A nodal immersed finite element-finite difference method. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Wells%2C+David+R%2E%22">Wells, David R.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> drwells@email.unc.edu</i><br /><searchLink fieldCode="AR" term="%22Vadala-Roth%2C+Ben%22">Vadala-Roth, Ben</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Lee%2C+Jae+H%2E%22">Lee, Jae H.</searchLink><relatesTo>1,3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Griffith%2C+Boyce+E%2E%22">Griffith, Boyce E.</searchLink><relatesTo>1,4,5,6,7</relatesTo> (AUTHOR)<i> boyceg@email.unc.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Computational+Physics%22">Journal of Computational Physics</searchLink>. Mar2023, Vol. 477, pN.PAG-N.PAG. 1p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Finite+difference+method%22">Finite difference method</searchLink><br /><searchLink fieldCode="DE" term="%22Bioprosthetic+heart+valves%22">Bioprosthetic heart valves</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+mechanics%22">Structural mechanics</searchLink><br /><searchLink fieldCode="DE" term="%22Solid+mechanics%22">Solid mechanics</searchLink><br /><searchLink fieldCode="DE" term="%22Fluid-structure+interaction%22">Fluid-structure interaction</searchLink><br /><searchLink fieldCode="DE" term="%22Spectral+element+method%22">Spectral element method</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The immersed finite element-finite difference (IFED) method is a computational approach to modeling interactions between a fluid and an immersed structure. The IFED method uses a finite element (FE) method to approximate the stresses, forces, and structural deformations on a structural mesh and a finite difference (FD) method to approximate the momentum and enforce the incompressibility of the entire fluid-structure system on a Cartesian grid. The fundamental approach used by this method follows the immersed boundary framework for modeling fluid-structure interaction (FSI), in which a force spreading operator prolongs structural forces to a Cartesian grid, and a velocity interpolation operator restricts a velocity field defined on that grid back onto the structural mesh. With an FE structural mechanics framework, force spreading first requires that the force itself be projected onto the finite element space. Similarly, velocity interpolation requires projecting velocity data onto the FE basis functions. Consequently, evaluating either coupling operator requires solving a matrix equation at every time step. Mass lumping, in which the projection matrices are replaced by diagonal approximations, has the potential to accelerate this method considerably. This paper provides both numerical and computational analyses of the effects of this replacement for evaluating the force projection and for the IFED coupling operators. Constructing the coupling operators also requires determining the locations on the structure mesh where the forces and velocities are sampled. Here we show that sampling the forces and velocities at the nodes of the structural mesh is equivalent to using lumped mass matrices in the IFED coupling operators. A key theoretical result of our analysis is that if both of these approaches are used together, the IFED method permits the use of lumped mass matrices derived from nodal quadrature rules for any standard interpolatory element. This is different from standard FE methods, which require specialized treatments to accommodate mass lumping with higher-order shape functions. Our theoretical results are confirmed by numerical benchmarks, including standard solid mechanics tests and examination of a dynamic model of a bioprosthetic heart valve. • Nodal coupling is a more efficient method for IB fluid-structure simulations. • The nodal IFED method combines finite element and finite difference methods. • Nodal coupling requires mass lumping in the finite element discretization. • Nodal and elemental coupling have similar accuracy for a heart valve simulator. • In 3D nodal coupling requires about 5-10x fewer interaction points than elemental. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Computational Physics is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.jcp.2022.111890 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 1 StartPage: N.PAG Subjects: – SubjectFull: Finite difference method Type: general – SubjectFull: Bioprosthetic heart valves Type: general – SubjectFull: Structural mechanics Type: general – SubjectFull: Solid mechanics Type: general – SubjectFull: Fluid-structure interaction Type: general – SubjectFull: Spectral element method Type: general Titles: – TitleFull: A nodal immersed finite element-finite difference method. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Wells, David R. – PersonEntity: Name: NameFull: Vadala-Roth, Ben – PersonEntity: Name: NameFull: Lee, Jae H. – PersonEntity: Name: NameFull: Griffith, Boyce E. IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 03 Text: Mar2023 Type: published Y: 2023 Identifiers: – Type: issn-print Value: 00219991 Numbering: – Type: volume Value: 477 Titles: – TitleFull: Journal of Computational Physics Type: main |
| ResultId | 1 |
