Topic

# External flow

About: External flow is a research topic. Over the lifetime, 3949 publications have been published within this topic receiving 78061 citations.

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TL;DR: In this paper, the Navier-Stokes equations on a rectangular domain are applied to the simulation of flow around the natural mitral valve of a human heart valve, where 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.

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.

2,517 citations

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DuPont

^{1}TL;DR: In this article, the boundary-layer behavior on continuous surfaces is examined, and the basic differential and integral momentum equations of boundary layer theory are derived for such surfaces, for both laminar and turbulent flow in the boundary layer.

Abstract: This study deals with boundary-layer flow on continuous solid surfaces. Flow of this type represents a new class of boundary-layer problems, with solutions substantially different from those for boundary-layer flow on surfaces of finite length. In this paper the boundary-layer behavior on continuous surfaces is examined, and the basic differential and integral momentum equations of boundary-layer theory are derived for such surfaces. In subsequent papers these equations will be solved for the boundary layer on a moving continuous flat surface and a moving continuous cylindrical surface, for both laminar and turbulent flow in the boundary layer.

2,061 citations

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TL;DR: In this article, the authors propose a method for customizing a page view by dragging and re-positioning the boxes below the boxes. But this method is limited to a single page view.

Abstract: Related Content Customize your page view by dragging and repositioning the boxes below. Related Journal Articles

1,229 citations

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TL;DR: In this paper, the Navier-Stokes equations permit the presence of an externally imposed body force that may vary in space and time, and the velocity is used to iteratively determine the desired value.

Abstract: A novel technique related to Peskin's immersed boundary approach is used to introduce solid surfaces into a simulated flow field. The Navier-Stokes equations permit the presence of an externally imposed body force that may vary in space and time. Forces are chosen to lie along a desired surface and to have a magnitude and direction opposing the local flow such that the flow is brought to rest on an element of the surface. For unsteady viscous flow the direct calculation of the needed force is facilitated by a feedback scheme in which the velocity is used to iteratively determine the desired value. In particular, we determine the surface body force from the relation f(x 5 , t ) = α ∫ t 0 U(x 5 , t′ ) dt′ + βU(x 5 , t ) for surface points x 5 , velocity U, time t , and negative constants α and β. Examples are presented which include 2D flow around cylinders, 3D turbulent channel flow where one boundary is simulated with a force field, and turbulent channel flow over a riblet-covered surface. While the new method may be applied to complex geometries on a non-Cartesian mesh, we have chosen to use a simple Cartesian grid. All simulations are done with a spectral code in a single computational domain without any mapping of the mesh.

1,119 citations