Immersed boundary method: Difference between revisions

Revision as of 18:24, 26 July 2022

Revision as of 20:17, 28 July 2022

Line 1:

{{More footnotes|date=April 2017}}

In [[computational fluid dynamics]], the '''immersed boundary method''' originally referred to an approach developed by [[Charles S. Peskin|Charles Peskin]] in 1972 to simulate fluid-structure (fiber) interactions.<ref>{{Cite journal|last=Peskin|first=Charles S|date=1972-10-01|title=Flow patterns around heart valves: A numerical method|journal=Journal of Computational Physics|volume=10|issue=2|pages=252–271|doi=10.1016/0021-9991(72)90065-4|issn=0021-9991}}</ref> Treating the coupling of the structure deformations and the fluid flow poses a number of challenging problems for [[Computer simulation|numerical simulations]] (the elastic boundary changes the flow of the fluid and the fluid moves the elastic boundary simultaneously). In the immersed boundary method the fluid is represented onin an [[Lagrangian and Eulerian coordinates|Eulerian coordinate]] system and the structure is represented on ain [[Lagrangian and Eulerian coordinates|Lagrangian coordinatecoordinates]]. For [[Newtonian fluids]] governed by the incompressible [[Navier–Stokes equations]], the fluid equations are

:<math>

Line 9:

</math>

and inif casethe offlow is incompressible fluids (assuming constant density), we have the further condition that

:<math>

Line 15:

</math>

The immersed structures are typically represented as a collection of one-dimensional fibers, denoted by <math> \Gamma </math>. Each fiber can be viewed as a parametric curve <math> X(s,t) </math> where <math> s </math> is the parameterLagrangian coordinate along the fiber and <math>t </math> is time. PhysicsThe physics of the fiber is represented via thea fiber force distribution function <math> F(s,t) </math>. Spring forces, bending resistance or any other type of behavior can be built into this term. The force exerted by the structure on the fluid is then interpolated as a source term in the momentum equation using

:<math>