Shape reconstruction for the time-dependent Navier-Stokes flow

Abstract Background Navier-Stokes and continuity equations are utilized to simulate fully developed laminar Dean flow with an oscillating time-dependent pressure gradient. These equations are solved analytically with the appropriate boundary and initial conditions in terms of Laplace domain and inverted to time domain using a numerical inversion technique known as Riemann-Sum Approximation (RSA). The flow is assumed to be triggered by the applied circumferential pressure gradient (azimuthal pressure gradient) and the oscillating time-dependent pressure gradient. The influence of the various flow parameters on the flow formation are depicted graphically. Comparisons with previously established result has been made as a limit case when the frequency of the oscillation is taken as 0 (ω = 0). Results It was revealed that maintaining the frequency of oscillation, the velocity and skin frictions can be made increasing functions of time. An increasing frequency of the oscillating time-dependent pressure gradient and relatively a small amount of time is desirable for a decreasing velocity and skin frictions. The fluid vorticity decreases with further distance towards the outer cylinder as time passes. Conclusion Findings confirm that increasing the frequency of oscillation weakens the fluid velocity and the drag on both walls of the cylinders.

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A Code for Simulating Heat Transfer in Turbulent Channel Flow

Mathematics ◽

10.3390/math9070756 ◽

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.

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The Differentiability of the Drag with Respect to the Variations of a Lipschitz Domain in a Navier--Stokes Flow

SIAM Journal on Control and Optimization ◽

10.1137/s0363012994278213 ◽

1997 ◽

Vol 35 (2) ◽

pp. 626-640 ◽

Cited By ~ 45

Author(s):

Juan Antonio Bello ◽

Enrique Fernández-Cara ◽

Jérôme Lemoine ◽

Jacques Simon

Keyword(s):

Stokes Flow ◽

Lipschitz Domain ◽

Navier Stokes

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