Tri-periodic fully three-dimensional analytic solutions for the Navier–Stokes equations

@article{Antuono2020TriperiodicFT,
  title={Tri-periodic fully three-dimensional analytic solutions for the Navier–Stokes equations},
  author={Matteo Antuono},
  journal={Journal of Fluid Mechanics},
  year={2020},
  volume={890}
}
  • M. Antuono
  • Published 17 March 2020
  • Physics
  • Journal of Fluid Mechanics
In this paper we derive unsteady tri-periodic laminar solutions of the Navier–Stokes equations. In particular, these represent fully three-dimensional (3-D) flows, since all the velocity components depend non-trivially on all three coordinate directions. We show that they belong to the class of Beltrami flows and can be gathered in two distinct solutions characterized by positive and negative helicity. These can be regarded as an extension in three dimensions of the bi-periodic vortex solution… 
Smoothed particle hydrodynamics method from a large eddy simulation perspective. Generalization to a quasi-Lagrangian model
The present work deals with some recent developments regarding the inclusion of the Large-Eddy Simulation (LES) in the weakly compressible Smoothed Particle Hydrodynamics (SPH) framework. Previously
Three-dimensional decaying magnetic field belonging to Beltrami flow
In this study, we analysed a three-dimensional Taylor decaying vortex under an applied magnetic field as a benchmark test problem to verify the calculation method of an electromagnetic fluid flow and
How to train your solver: A method of manufactured solutions for weakly-compressible SPH
TLDR
This paper introduces the method of manufactured solutions (MMS) to comprehensively test aWCSPH-based solver in a robust and efficient manner and shows how the method can be applied in the context of Lagrangian WCSPH solvers to test the convergence and accuracy of the solver.
Objective barriers to the transport of dynamically active vector fields
Abstract We derive a theory for material surfaces that maximally inhibit the diffusive transport of a dynamically active vector field, such as the linear momentum, the angular momentum or the
Large Eddy Simulations of bubbly flows and breaking waves with Smoothed Particle Hydrodynamics
For turbulent bubbly flows, multi-phase simulations resolving both the liquid and bubbles are prohibitively expensive in the context of different natural phenomena. One example is breaking waves, where

References

SHOWING 1-10 OF 20 REFERENCES
Non-linear instability analysis of the two-dimensional Navier-Stokes equation: The Taylor-Green vortex problem
An enstrophy-based non-linear instability analysis of the Navier-Stokes equation for two-dimensional (2D) flows is presented here, using the Taylor-Green vortex (TGV) problem as an example. This
Exact fully 3D Navier–Stokes solutions for benchmarking
SUMMARY Unsteady analytical solutions to the incompressible Navier-Stokes equations are presented. They are fully three-dimensional vector solutions involving all three Cartesian velocity components,
Vorticity dynamics of the three-dimensional Taylor-Green vortex problem
The three-dimensional (3D) Taylor-Green Vortex (TGV) flow problem has been used to study turbulence from genesis to eventual decay governed by the 3D Navier-Stokes equation. The evolution of the TGV
Exact Solutions of the Unsteady Navier-Stokes Equations
The unsteady Navier-Stokes equations are a set of nonlinear partial differential equations with very few exact solutions. This paper attempts to classify and review the existing unsteady exact
A note on the decay of vortices in a viscous fluid
In this short note, we extend a result due to Taylor (1923) concerning eddies in the plane flow of an incompressible Navier–Stokes fluid, each of which is rotating in the opposite sense to four of
Small-scale structure of the Taylor–Green vortex
The dynamics of both the inviscid and viscous Taylor–Green (TG) three-dimensional vortex flows are investigated. This flow is perhaps the simplest system in which one can study the generation of
Simulation of transition and turbulence decay in the Taylor–Green vortex
Conventional large-eddy simulation (LES) and monotone integrated LES (MILES) are tested in emulating the dynamics of transition to turbulence in the Taylor–Green vortex (TGV). A variety of subgrid
Slow Viscous Flow
Many of the problems already presented dealt with situations where inertia forces were cither zero (parallel flow) or could be neglected because of some peculiarities, for example, flow in thin
Smoothed particle hydrodynamics method from a large eddy simulation perspective
The Smoothed Particle Hydrodynamics (SPH) method, often used for the modelling of the Navier–Stokes equations by a meshless Lagrangian approach, is revisited from the point of view of Large Eddy
...
...