Analysis of Viscous Fluid Flows: An Approach by Evolution Equations

2020 ◽  
pp. 1-146 ◽  
Author(s):  
Matthias Hieber
Keyword(s):  
Viscous Fluid ◽  
Evolution Equations ◽  
Fluid Flows

scholarly journals Obtaining Expressions for Time-Dependent Functions That Describe the Unsteady Properties of Swirling Jets of Viscous Fluid

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1860
Author(s):  
Eugene Talygin ◽  
Alexander Gorodkov
Keyword(s):  
Blood Flow ◽  
Viscous Fluid ◽  
Swirling Flow ◽  
Fluid Flows ◽  
Theoretical Method ◽  
Flow Channel ◽  
Navier Stokes ◽  
Swirling Jets ◽  
Continuity Equations ◽  
Dynamic Velocity

Previously, it has been shown that the dynamic geometric configuration of the flow channel of the left heart and aorta corresponds to the direction of the streamlines of swirling flow, which can be described using the exact solution of the Navier–Stokes and continuity equations for the class of centripetal swirling viscous fluid flows. In this paper, analytical expressions were obtained. They describe the functions C0t and Г0t, included in the solutions, for the velocity components of such a flow. These expressions make it possible to relate the values of these functions to dynamic changes in the geometry of the flow channel in which the swirling flow evolves. The obtained expressions allow the reconstruction of the dynamic velocity field of an unsteady potential swirling flow in a flow channel of arbitrary geometry. The proposed approach can be used as a theoretical method for correct numerical modeling of the blood flow in the heart chambers and large arteries, as well as for developing a mathematical model of blood circulation, considering the swirling structure of the blood flow.

Optimal boundary control of nonlinear-viscous fluid flows

2020 ◽  
Vol 211 (4) ◽  
pp. 505-520 ◽  
Author(s):  
E. S. Baranovskii
Keyword(s):  
Viscous Fluid ◽  
Boundary Control ◽  
Fluid Flows ◽  
Optimal Boundary ◽  
Optimal Boundary Control

scholarly journals David J. Benney: Nonlinear Wave and Instability Processes in Fluid Flows

2020 ◽  
Vol 52 (1) ◽  
pp. 21-36 ◽  
Author(s):  
T.R. Akylas
Keyword(s):  
Nonlinear Wave ◽  
Evolution Equations ◽  
Flow Instability ◽  
Three Dimensional ◽  
Fluid Flows ◽  
Nonlinear Evolution Equations ◽  
Nonlinear Phenomena ◽  
New Paradigm ◽  
Applied Mathematician ◽  
Modulated Wave Trains

David J. Benney (1930–2015) was an applied mathematician and fluid dynamicist whose highly original work has shaped our understanding of nonlinear wave and instability processes in fluid flows. This article discusses the new paradigm he pioneered in the study of nonlinear phenomena, which transcends fluid mechanics, and it highlights the common threads of his research contributions, namely, resonant nonlinear wave interactions; the derivation of nonlinear evolution equations, including the celebrated nonlinear Schrödinger equation for modulated wave trains; and the significance of three-dimensional disturbances in shear flow instability and transition.

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