2D Navier–Stokes Equations in a Time Dependent Domain with Neumann Type Boundary Conditions

2008 ◽  
Vol 12 (1) ◽  
pp. 1-46 ◽  
Author(s):  
Ján Filo ◽  
Anna Zaušková
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Time Dependent ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Time Dependent Domain ◽  
Neumann Type ◽  
Type Boundary ◽  
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.

AXISYMMETRIC PLUMES IN VISCOUS FLUIDS

2019 ◽  
Vol 61 (02) ◽  
pp. 119-147
Author(s):  
EMMA J. ALLWRIGHT ◽  
L. K. FORBES ◽  
S. J. WALTERS
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Viscous Fluids ◽  
Time Dependent ◽  
Navier Stokes ◽  
Background Flow ◽  
Navier Stokes Equations ◽  
Viscous Boundary ◽  
Channel Bottom ◽  
Evolution With Time

We consider fluid in a channel of finite height. There is a circular hole in the channel bottom, through which fluid of a lower density is injected and rises to form a plume. Viscous boundary layers close to the top and bottom of the channel are assumed to be so thin that the viscous fluid effectively slips along each of these boundaries. The problem is solved using a novel spectral method, in which Hankel transforms are first used to create a steady-state axisymmetric (inviscid) background flow that exactly satisfies the boundary conditions. A viscous correction is then added, so as to satisfy the time-dependent Boussinesq Navier–Stokes equations within the fluid, leaving the boundary conditions intact. Results are presented for the “lazy” plume, in which the fluid rises due only to its own buoyancy, and we study in detail its evolution with time to form an overturning structure. Some results for momentum-driven plumes are also presented, and the effect of the upper wall of the channel on the evolution of the axisymmetric plume is discussed.

Sign in / Sign up

Export Citation Format

Share Document