Stationary Navier–Stokes Equation on Lipschitz Domains in Riemannian Manifolds with Nonvanishing Boundary Conditions

2009 ◽  
pp. 135-144
Author(s):  
Martin Dindoš
Keyword(s):  
Boundary Conditions ◽  
Stokes Equation ◽  
Riemannian Manifolds ◽  
Navier Stokes ◽  
Lipschitz Domains ◽  
Navier Stokes Equation

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.

scholarly journals Simulation of J-Solution Solving Process of Navier–Stokes Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Wenjie Wang ◽  
Melkamu Teshome Ayana
Keyword(s):  
Boundary Conditions ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Simulation Analysis ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Fine Grid ◽  
Navier Stokes Equations ◽  
Advantages And Disadvantages ◽  
Original Boundary

To avoid grid degradation, the numerical analysis of the j-solution of the Navier–Stokes equation has been studied. The Navier–Stokes equations describe the motion of viscous fluid substances. On the basis of the advantages and disadvantages of the Navier–Stokes equations, the incompressible terms and the nonlinear terms are separated, and the original boundary conditions satisfying the j-solution of the Navier–Stokes equation are analyzed. Secondly, the development of a computational grid has been introduced; the turbulence model has also been described. The fluid form and the initial value of the j-solution of the Navier–Stokes equation are combined. The original boundary conditions are solved by a computer, and the nonlinear turbulence equations are derived, which control the fluid flow. The simulation of the fine grid is comprehended to analyze the research outcome. Simulation analysis is carried out to generate multiblock-structured grids with high quality. The j-solution on the grid points is the j-solution that can be used with a fewer number of meshes under the same conditions. The proposed work is easy to implement, and it consumes lesser memory. The results obtained are able to avoid mesh degradation skillfully, and the generated mesh exhibits the characteristics of smoothness, orthogonality, and controllability, which eventually improves the calculation accuracy.

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