Flow patterns around heart valves: A numerical method

Charles Peskin

Research output: Contribution to journalArticle

Abstract

The subject of this paper is the flow of a viscous incompressible fluid in a region containing immersed boundaries which move with the fluid and exert forces on the fluid. An example of such a boundary is the flexible leaflet of a human heart valve. It is the main achievement of the present paper that a method for solving the Navier-Stokes equations on a rectangular domain can now be applied to a problem involving this type of immersed boundary. This is accomplished by replacing the boundary by a field of force which is defined on the mesh points of the rectangular domain and which is calculated from the configuration of the boundary. In order to link the representations of the boundary and fluid, since boundary points and mesh points need not coincide, a semi-discrete analog of the δ function is introduced. Because the boundary forces are of order h-1, and because they are sensitive to small changes in boundary configuration, they tend to produce numerical instability. This difficulty is overcome by an implicit method for calculating the boundary forces, a method which takes into account the displacements that will be produced by the boundary forces themselves. The numerical scheme is applied to the two-dimensional simulation of flow around the natural mitral valve.

Original languageEnglish (US)
Pages (from-to)252-271
Number of pages20
JournalJournal of Computational Physics
Volume10
Issue number2
DOIs
StatePublished - 1972

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heart valves
Flow patterns
Numerical methods
flow distribution
Fluids
Navier Stokes equations
mesh
fluid boundaries
fluids
incompressible fluids
configurations
Navier-Stokes equation

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy(all)

Cite this

Flow patterns around heart valves : A numerical method. / Peskin, Charles.

In: Journal of Computational Physics, Vol. 10, No. 2, 1972, p. 252-271.

Research output: Contribution to journalArticle

Peskin, Charles. / Flow patterns around heart valves : A numerical method. In: Journal of Computational Physics. 1972 ; Vol. 10, No. 2. pp. 252-271.
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