TY - JOUR

T1 - Flow patterns around heart valves

T2 - A numerical method

AU - Peskin, Charles S.

N1 - Funding Information:
This work was supported by the National Institutes of Health (PHS grant #5T5GM1674) and the Atomic Energy Commission [Contract AT(30-l)-14801 and was closely supervised by Professor A. J. Chorin of the Courant Institute of Mathematical Sciences (NYU). The author is deeply indebted to Professor Chorin for his continuing advice and support on this project, and to the Courant Institute generally for making available computer time and office space. The author also wishes to acknowledge the influence of countless discussions with Dr. E. Yellin of the Albert Einstein College of Medicine concerning the physics and the physiology of blood flow around heart valves.

PY - 1972/10

Y1 - 1972/10

N2 - 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.

AB - 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.

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U2 - 10.1016/0021-9991(72)90065-4

DO - 10.1016/0021-9991(72)90065-4

M3 - Article

AN - SCOPUS:49649145203

SN - 0021-9991

VL - 10

SP - 252

EP - 271

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 2

ER -