Energy absorbing boundary conditions for the Navier-Stokes equation

2006 ◽  
pp. 505-510
Author(s):  
Jan Nordström
Keyword(s):  
Boundary Conditions ◽  
Stokes Equation ◽  
Absorbing Boundary Conditions ◽  
Navier Stokes ◽  
Absorbing Boundary ◽  
Navier Stokes Equation ◽  
Energy Absorbing

On the Navier-Stokes equation with boundary conditions based on vorticity

2004 ◽  
Vol 269-270 (1) ◽  
pp. 59-72 ◽  
Author(s):  
Hamid Bellout ◽  
Jiří Neustupa ◽  
Patrick Penel
Keyword(s):  
Boundary Conditions ◽  
Stokes Equation ◽  
Navier Stokes ◽  
Navier Stokes Equation

scholarly journals Mathematical problems in modeling artificial heart

1995 ◽  
Vol 1 (3) ◽  
pp. 245-254 ◽  
Author(s):  
N. U. Ahmed
Keyword(s):  
Blood Flow ◽  
Boundary Conditions ◽  
Stokes Equation ◽  
Artificial Heart ◽  
Moving Boundary ◽  
Hyperbolic Type ◽  
The Other ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Heart Chamber

In this paper we discuss some problems arising in mathematical modeling of artificial hearts. The hydrodynamics of blood flow in an artificial heart chamber is governed by the Navier-Stokes equation, coupled with an equation of hyperbolic type subject to moving boundary conditions. The flow is induced by the motion of a diaphragm (membrane) inside the heart chamber attached to a part of the boundary and driven by a compressor (pusher plate). On one side of the diaphragm is the blood and on the other side is the compressor fluid. For a complete mathematical model it is necessary to write the equation of motion of the diaphragm and all the dynamic couplings that exist between its position, velocity and the blood flow in the heart chamber. This gives rise to a system of coupled nonlinear partial differential equations; the Navier-Stokes equation being of parabolic type and the equation for the membrane being of hyperbolic type. The system is completed by introducing all the necessary static and dynamic boundary conditions. The ultimate objective is to control the flow pattern so as to minimize hemolysis (damage to red blood cells) by optimal choice of geometry, and by optimal control of the membrane for a given geometry. The other clinical problems, such as compatibility of the material used in the construction of the heart chamber, and the membrane, are not considered in this paper. Also the dynamics of the valve is not considered here, though it is also an important element in the overall design of an artificial heart. We hope to model the valve dynamics in later paper.

CFD Simulations of a Semi-Submersible With Absorbing Boundary Conditions

2009 ◽  
Author(s):  
Peter R. Wellens ◽  
Roel Luppes ◽  
Arthur E. P. Veldman ◽  
Mart J. A. Borsboom
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Computing Time ◽  
Height Function ◽  
Absorbing Boundary Conditions ◽  
Navier Stokes ◽  
Two Phase ◽  
Absorbing Boundary ◽  
Wide Range ◽  
Grid Points

The CFD tool ComFLOW is suitable for simulations of two-phase flows in offshore applications. ComFLOW solves the Navier-Stokes equations in both water and (compressible) air. The water surface is advected through a Volume-of-Fluid method, with a height-function approach for improved accuracy. By employing Absorbing Boundary Conditions (ABC), boundaries can be located relatively close to an object, without influencing outgoing waves or generating numerical reflections that affect the waves inside the flow domain. Traditionally, boundaries are located far from the obstacle to avoid reflections; even when numerical damping zones are used. Hence, with the ABC approach less grid points are required for the same accuracy, which reduces the computing time considerably. Simulations of a semi-submersible model are compared to measurements. The overall agreement is reasonably good, for a wide range of wave conditions. The ABC performs well; numerical reflections are almost absent. Moreover, computing times reduce with a factor four compared to damping zone techniques.

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