Immersed boundary method: Difference between revisions

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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>

Since the original development of this method by Peskin, a variety of approaches have been developed to simulate flow over complicated immersed bodies on grids that do not conform to the surface of the body. These include methods such as the immersed interface method, the Cartesian grid method, the ghost fluid method and the cut-cell method. Mittal and Iaccarino<ref>{{harvnb|Mittal|Iaccarino|2005}}.</ref> refer to all these (and other related) methods as Immersed Boundary Methods and provide various categorizations of these methods. From the point of view of implementation, they categorize immersed boundary methods into ''continuous forcing'' and ''discrete forcing'' methods. In the former, a force term is added to the continuous Navier-Stokes equations before discretization, whereas in the latter, the forcing is applied (explicitly or implicitly) to the discretized equations. Under this taxonomy, Peskin's original method is a ''continuous forcing'' method whereas Cartesian grid, cut-cell and the ghost-fluid methods are ''discrete forcing'' methods.

For simulations of viscoelastic fluids, curved fluid interfaces, microscopic biophysical systems (proteins in lipid bilayer membranes), and engineered devices, further variants of the immersed boundary method also have been developed, such as the Stochastic Immersed Boundary Methods of Atzberger, Kramer, and Peskin

<ref>

{{Cite journal

| last = Atzberger

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| bibcode = 2011JCoPh.230.2821A

| s2cid = 6067032

}}.

</ref> <ref>

{{Citation

and Stochastic Eulerian Lagrangian Methods of Atzberger

| last1=Atzberger

<ref>{{Cite journal

| first1=Paul

| title=Incorporating Shear into Stochastic Eulerian Lagrangian Methods for Rheological Studies of Complex Fluids and Soft Materials

| journal=Physica D

| volume=265

| pages=57–70

| year=2013

| doi=10.1016/j.physd.2013.09.002

| arxiv = 2212.10651

}}

</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.

|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 |pages=169–187

|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>

<ref>{{Cite journal

| last = Atzberger

| first = Paul J.

| title = Stochastic Eulerian Lagrangian Methods for Fluid Structure Interactions with Thermal Fluctuations

| journal = Journal of Computational Physics

| volume = 230

| issue = 8

| pages = 2821–2837

| year = 2011

| doi = 10.1016/j.jcp.2010.12.028

| arxiv = 1009.5648

| bibcode = 2011JCoPh.230.2821A

| s2cid = 6067032

}}

</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>

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

| last = Atzberger

| first = Paul J.

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| s2cid = 6067032

}}

</ref><ref>

{{Citation

<ref>

{{Cite

| last1=Atzberger

| first1=Paul

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| journal=Physica D

| volume=265

| pages=57-7057–70

| year=2013

| doi=10.1016/j.physd.2013.09.002

| arxiv = 2212.10651

}}

</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 |issue=32 |pages=6685-67076685–6707 |doi=10.1039/C6SM00194G |pmid=27373277 | arxiv=18031601.0759406461}}

</ref>

</ref> Massed Immersed Boundary Methods of Mori,<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=1803.07594}}

{{Cite journal

</ref>.

| last1 = Mori

| first1 = Yoichiro

| last2 = Peskin

| first2 = Charles S.

| title = Implicit Second-Order Immersed Boundary Methods with Boundary Mass

| journal = Computer Methods in Applied Mechanics and Engineering

| volume = 197

| issue = 25–28

| pages = 2049–2067

| year = 2008

| doi = 10.1016/j.cma.2007.05.028

| bibcode = 2008CMAME.197.2049M

}}

</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 |pages=169–187

|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.

== See also ==

*[[Stochastic Eulerian Lagrangian method]]s

*[[Stokesian dynamics]]

*[[Volume of fluid method]]

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*{{CiteCitation

| last1=Atzberger

| first1=Paul

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| journal=Physica D

| volume=265

| pages=57-7057–70

| year=2013

| doi=10.1016/j.physd.2013.09.002

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| doi = 10.4271/2007-01-0109

}}.

* {{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 |issue=32 |pages=6685-67076685–6707 |doi=10.1039/C6SM00194G |pmid=27373277 | arxiv=18031601.0759406461}}.

*{{Cite journal

| last1 = Kim

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| bibcode = 2001JCoPh.171..132K

}}

*{{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}}

*{{Cite journal

| last1 = Mittal

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}}

*{{Cite journal

| last1 = MoriaMori

| first1 = Yoichiro

| last2 = Peskin