scholarly journals Existence and periodicity of weak solutions of the Navier-Stokes equations in a time dependent domain

1982 ◽  
Vol 12 (3) ◽  
pp. 513-528 ◽  
Author(s):  
Tetsuro Miyakawa ◽  
Yoshiaki Teramoto
Keyword(s):  
Weak Solutions ◽  
Stokes Equations ◽  
Time Dependent ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Time Dependent Domain ◽  
Dependent Domain

VORTICES IN BIOLOGICAL FLOWS

2013 ◽  
Vol 13 (05) ◽  
pp. 1340001
Author(s):  
TIN-KAN HUNG
Keyword(s):  
Da Vinci ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Leonardo Da Vinci ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Time Dependent Domain ◽  
Tacoma Narrows Bridge ◽  
Solid Motion ◽  
Dependent Domain

Vortices in flow past a heart valve, in streams and behind an arrow were realized, sketched and discussed by Leonardo da Vinci. The forced resonance and collapse of the Tacoma Narrows Bridge under 64 km/h. wind in 1940 and the Kármán vortex street are classic examples of dynamic interaction between fluid flow and solid motion. There are similar and dissimilar characteristics of vortices between biological and physical flow processes. They can be analyzed by numerical solutions of the Navier–Stokes equations with moving boundaries. One approach is to transform the time-dependent domain to a fixed domain with the geometric, kinematic and dynamic parameters as forcing functions in the Navier–Stokes equations.

scholarly journals A Code for Simulating Heat Transfer in Turbulent Channel Flow

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 756
Author(s):  
Federico Lluesma-Rodríguez ◽  
Francisco Álcantara-Ávila ◽  
María Jezabel Pérez-Quiles ◽  
Sergio Hoyas
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Turbulent Channel Flow ◽  
Passive Scalar ◽  
Direct Numerical Simulations ◽  
Time Dependent ◽  
Navier Stokes ◽  
Thermal Flow ◽  
Navier Stokes Equations

One numerical method was designed to solve the time-dependent, three-dimensional, incompressible Navier–Stokes equations in turbulent thermal channel flows. Its originality lies in the use of several well-known methods to discretize the problem and its parallel nature. Vorticy-Laplacian of velocity formulation has been used, so pressure has been removed from the system. Heat is modeled as a passive scalar. Any other quantity modeled as passive scalar can be very easily studied, including several of them at the same time. These methods have been successfully used for extensive direct numerical simulations of passive thermal flow for several boundary conditions.

A finite element method for the Navier-Stokes equations in moving domain with application to hemodynamics of the left ventricle

2017 ◽  
Vol 32 (4) ◽  
Author(s):  
Alexander Danilov ◽  
Alexander Lozovskiy ◽  
Maxim Olshanskii ◽  
Yuri Vassilevski
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Left Ventricle ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Computed Tomography Images ◽  
Time Dependent Domain ◽  
Element Method

AbstractThe paper introduces a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method is based on a quasi-Lagrangian formulation of the problem and handling the geometry in a time-explicit way. We prove that numerical solution satisfies a discrete analogue of the fundamental energy estimate. This stability estimate does not require a CFL time-step restriction. The method is further applied to simulation of a flow in a model of the left ventricle of a human heart, where the ventricle wall dynamics is reconstructed from a sequence of contrast enhanced Computed Tomography images.

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