Higher order numerical simulation of unsteady viscous incompressible flows using kinetically reduced local Navier–Stokes equations on a GPU

2015 ◽  
Vol 110 ◽  
pp. 108-113 ◽  
Author(s):  
T. Hashimoto ◽  
I. Tanno ◽  
T. Yasuda ◽  
Y. Tanaka ◽  
K. Morinishi ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Higher Order ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Viscous Incompressible Flows

Finite element solution of the Navier—Stokes equations

Acta Numerica ◽  
1993 ◽  
Vol 2 ◽  
pp. 239-284 ◽  
Author(s):  
Michel Fortin
Keyword(s):  
Compressible Flows ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Molten Metals ◽  
Complex Flows ◽  
Navier Stokes Equations ◽  
Viscous Incompressible Flows ◽  
High Reynolds

Viscous incompressible flows are of considerable interest for applications. Let us mention, for example, the design of hydraulic turbines or rheologically complex flows appearing in many processes involving plastics or molten metals. Their simulation raises a number of difficulties, some of which are likely to remain while others are now resolved. Among the latter are those related to incompressibility which are also present in the simulation of incompressible or nearly incompressible elastic materials. Among the still unresolved are those associated with high Reynolds numbers which are also met in compressible flows. They involve the formation of boundary layers and turbulence, an ever present phenomenon in fluid mechanics, implying that we have to simulate unsteady, highly unstable phenomena.

Numerical solution of the reduced Navier-Stokes equations for internal incompressible flows

AIAA Journal ◽  
2000 ◽  
Vol 38 ◽  
pp. 1603-1614
Author(s):  
Martin Scholtysik ◽  
Bernhard Mueller ◽  
Torstein K. Fannelop
Keyword(s):  
Numerical Solution ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations

On Direct Numerical Simulation of Turbulent Flows

2011 ◽  
Vol 64 (2) ◽  
Author(s):  
Giancarlo Alfonsi
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
High Performance Computing ◽  
Turbulent Flows ◽  
High Performance ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Shear ◽  
Navier Stokes Equations ◽  
Performance Computing

The direct numerical simulation of turbulence (DNS) has become a method of outmost importance for the investigation of turbulence physics, and its relevance is constantly growing due to the increasing popularity of high-performance-computing techniques. In the present work, the DNS approach is discussed mainly with regard to turbulent shear flows of incompressible fluids with constant properties. A body of literature is reviewed, dealing with the numerical integration of the Navier-Stokes equations, results obtained from the simulations, and appropriate use of the numerical databases for a better understanding of turbulence physics. Overall, it appears that high-performance computing is the only way to advance in turbulence research through the front of the direct numerical simulation.

scholarly journals Numerical stability analysis of a vortex ring with swirl

2019 ◽  
Vol 878 ◽  
pp. 5-36 ◽  
Author(s):  
Yuji Hattori ◽  
Francisco J. Blanco-Rodríguez ◽  
Stéphane Le Dizès
Keyword(s):  
Numerical Simulation ◽  
Growth Rate ◽  
Direct Numerical Simulation ◽  
Vortex Ring ◽  
Stokes Equations ◽  
Base Flow ◽  
Critical Layer ◽  
Navier Stokes ◽  
Instability Mode ◽  
Navier Stokes Equations

The linear instability of a vortex ring with swirl with Gaussian distributions of azimuthal vorticity and velocity in its core is studied by direct numerical simulation. The numerical study is carried out in two steps: first, an axisymmetric simulation of the Navier–Stokes equations is performed to obtain the quasi-steady state that forms a base flow; then, the equations are linearized around this base flow and integrated for a sufficiently long time to obtain the characteristics of the most unstable mode. It is shown that the vortex rings are subjected to curvature instability as predicted analytically by Blanco-Rodríguez & Le Dizès (J. Fluid Mech., vol. 814, 2017, pp. 397–415). Both the structure and the growth rate of the unstable modes obtained numerically are in good agreement with the analytical results. However, a small overestimation (e.g. 22 % for a curvature instability mode) by the theory of the numerical growth rate is found for some instability modes. This is most likely due to evaluation of the critical layer damping which is performed for the waves on axisymmetric line vortices in the analysis. The actual position of the critical layer is affected by deformation of the core due to the curvature effect; as a result, the damping rate changes since it is sensitive to the position of the critical layer. Competition between the curvature and elliptic instabilities is also investigated. Without swirl, only the elliptic instability is observed in agreement with previous numerical and experimental results. In the presence of swirl, sharp bands of both curvature and elliptic instabilities are obtained for $\unicode[STIX]{x1D700}=a/R=0.1$, where $a$ is the vortex core radius and $R$ the ring radius, while the elliptic instability dominates for $\unicode[STIX]{x1D700}=0.18$. New types of instability mode are also obtained: a special curvature mode composed of three waves is observed and spiral modes that do not seem to be related to any wave resonance. The curvature instability is also confirmed by direct numerical simulation of the full Navier–Stokes equations. Weakly nonlinear saturation and subsequent decay of the curvature instability are also observed.

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