---
tag: 720QQR553X
kind: concept
name: Immersed boundary method
msc: [65M85, 76D05, 76M20]
sources:
  - url: https://en.wikipedia.org/wiki/Immersed_boundary_method
same_as:
  wikidata: Q11425899
  wikipedia: Immersed boundary method
---

## Summary

The immersed boundary method simulates elastic structures moving in a viscous incompressible fluid on a fixed Cartesian grid.
The fluid is described by the [[Navier–Stokes equations|18KXZHVF4M]] on the grid, and the structure by points that move with the fluid.
The two are coupled by smoothed versions of the [[Dirac delta function|0KPHENZ5S7]].
The structure spreads its elastic forces to the grid and takes its velocity from the grid.
It was introduced by Charles Peskin to model blood flow through the heart.
See the [[definition|E8FQ2R87VX]].

## Explanations

### L1 human

Picture a heart valve, a thin elastic sheet, waving in the blood.
Building a mesh that follows the valve as it moves is hard.
The immersed boundary method keeps a fixed square grid for the blood and treats the valve as a chain of points carried by the flow.
The points push on the nearby fluid with their elastic forces, and the fluid carries the points along.