Immersed boundary method: Difference between revisions

Revision as of 03:16, 19 September 2024

Revision as of 05:28, 28 September 2024

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Variants of this basic approach have been applied to simulate a wide variety of mechanical systems involving elastic structures which interact with fluid flows.

Since the original development of this method by Peskin, a variety of approaches have been developed. These include stochastic formulations for microscopic systems, viscoelastic soft materials, complex fluids, such as the Stochastic Immersed Boundary Methods of Atzberger, Kramer, and Peskin,<ref>

<ref>

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</ref> <ref>

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</ref>, methods for simulating flows over complicated immersed solid bodies on grids that do not conform to the surface of the body Mittal and Iaccarino,<ref>{{harvnb|Mittal|Iaccarino|2005}}.</ref>, and other approaches that incorporate mass and rotational degrees of freedom Olson, Lim, Cortez.<ref>{{Cite journal |last1=Olson |first1=S.

<ref>{{Cite journal |last1=Olson |first1=S.

|last2=Lim |first2=S. |last3=Cortez |first3=R.

|title=Modeling the dynamics of an elastic rod with intrinsic curvature and twist using a regularized Stokes formulation |journal=Journal of Computational Physics |date=2013 |volume=238 |doi=10.1016/j.jcp.2012.12.026}}</ref>. Methods for complicated body shapes include the immersed interface method, the Cartesian grid method, the ghost fluid method and the cut-cell methods categorizing immersed boundary methods into ''continuous forcing'' and ''discrete forcing'' methods. Methods have been developed for simulations of viscoelastic fluids, curved fluid interfaces, microscopic biophysical systems (proteins in lipid bilayer membranes, swimmers), and engineered devices, such as the Stochastic Immersed Boundary Methods of Atzberger, Kramer, and Peskin,<ref>

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</ref><ref>{{cite journal |last1=Rower |first1=David A. |last2=Padidar |first2=Misha |last3=Atzberger |first3=Paul J. |title=Surface fluctuating hydrodynamics methods for the drift-diffusion dynamics of particles and microstructures within curved fluid interfaces |journal=Journal of Computational Physics |date=April 2022 |volume=455 |pages=110994 |doi=10.1016/j.jcp.2022.110994 |arxiv=1906.01146}}</ref>

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Stochastic Eulerian Lagrangian Methods of Atzberger,<ref>{{Cite journal

<ref>{{cite journal |last1=Rower |first1=David A. |last2=Padidar |first2=Misha |last3=Atzberger |first3=Paul J. |title=Surface fluctuating hydrodynamics methods for the drift-diffusion dynamics of particles and microstructures within curved fluid interfaces |journal=Journal of Computational Physics |date=April 2022 |volume=455 |pages=110994 |doi=10.1016/j.jcp.2022.110994 |arxiv=1906.01146}}</ref>

,

Stochastic Eulerian Lagrangian Methods of Atzberger

<ref>{{Cite journal

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| first = Paul J.

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</ref><ref>

<ref>

{{Cite

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</ref><ref>{{cite journal |last1=Atzberger |first1=Paul |title=Hydrodynamic Coupling of Particle Inclusions Embedded in Curved Lipid Bilayer Membranes |journal=Soft Matter, The Royal Society of Chemistry |date=2016 |volume=12 |pages=6685-6707 |doi=10.1039/C6SM00194G | arxiv=1601.06461}}

</ref>

</ref>, Massed Immersed Boundary Methods of Moria,<ref>

<ref>{{cite journal |last1=Atzberger |first1=Paul |title=Hydrodynamic Coupling of Particle Inclusions Embedded in Curved Lipid Bilayer Membranes |journal=Soft Matter, The Royal Society of Chemistry |date=2016 |volume=12 |pages=6685-6707 |doi=10.1039/C6SM00194G | arxiv=1601.06461}}

</ref>, Massed Immersed Boundary Methods of Moria

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| bibcode = 2008CMAME.197.2049M

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,</ref> and Rotational Immersed Boundary Methods of Olson, Lim, Cortez.<ref>{{Cite journal |last1=Olson |first1=S.

</ref>

, and Rotational Immersed Boundary Methods of Olson, Lim, Cortez

<ref>{{Cite journal |last1=Olson |first1=S.

|last2=Lim |first2=S. |last3=Cortez |first3=R.

|title=Modeling the dynamics of an elastic rod with intrinsic curvature and twist using a regularized Stokes formulation |journal=Journal of Computational Physics |date=2013 |volume=238 |doi=10.1016/j.jcp.2012.12.026}}</ref>.

In general, for immersed boundary methods and related variants, there is an active research community that is still developing new techniques and related software implementations and incorporating related techniques into simulation packages and CAD engineering software. For more details see below.