Stokes equations in spectral spaceturbulent energy, scales of random motion ‐ of passing interestenergy cascade, kinetic energy flow ‐ from largescale eddies ‐ to small‐scale eddiestriad interactions in homogeneous turbulenceKolmogoroff's inertial‐range theory ‐ dominant interactions in inertial ...
This chapter provides an introductory review to the fundamentals of the RANS approach and the major classes of turbulence models used to approximate the Reynolds stresses – the correlations of turbulent velocity fluctuations that arise upon Reynolds-averaging of the Navier–Stokes equations. The ...
We discretize the incompressible Navier–Stokes equations on a polytopal mesh by using mimetic reconstruction operators. The resulting method conserves discrete mass, momentum, and kinetic energy in the inviscid limit, and determines the vorticity such that the global vorticity is consistent with the ...
Navier–Stokes equationsEnd-point regularity criterionBy taking full advantage of the regularity of the vertical velocity component, we could be able to show a regularity criterion in terms of the vertical velocity component, and the vertical derivative of the horizontal velocity components, which ...
Stokes equationsDeforming domainsWe introduce a space–time discontinuous Galerkin (DG) finite element method for the incompressible Navier–Stokes equations. Our formulation can be made arbitrarily high-order accurate in both space and time and can be directly applied to deforming domains. Different ...
O. Ladyzhenskaya, Initial-boundary problem for Navier-Stokes equations in domains with time-varing boundaries, in Boundary Value Problems of Mathematical Physics and Related Aspects of Function Theory III, edited by O. Ladyzhenskaya, Consultants Bureau, New York, 1970, 35-46. Original in Russian...
Time-dependent Navier–Stokes equationsnoncompact domainstime-dependent Poiseuille flowglobal existenceThe time-dependent Navier–Stokes system is studied in a two-dimensional domain with strip-like outlets to infinity in weighted Sobolev function spaces. It is proved that under natural compatibility ...
Non-linear Petrov-Galerkin methods for reduced order modelling of the Navier- Stokes equations using a mixed finite element pair. Comput. Methods Appl. Mech. Eng. 255, 147-157.D. Xiao, F. Fang, J. Du, C.C. Pain, I.M. Navon, A.G. Buchan, A.H. ElSheikh, and G. Hu. Non- ...
Stokes equationsvelocity–In the present work, an indirect boundary integral method for the numerical solution of Navier–Stokes equations formulated in velocity–vorticity dependent variables is proposed. This wholly integral approach, based on Helmholtz's decomposition, deals directly with the vorticity ...