The Pseudo-Direct Numerical Simulation method for multi-scale problems in mechanics

[1]  T. Hughes,et al.  The variational multiscale method—a paradigm for computational mechanics , 1998 .

[2]  T. Hughes,et al.  Large Eddy Simulation and the variational multiscale method , 2000 .

[3]  R. Codina Stabilized finite element approximation of transient incompressible flows using orthogonal subscales , 2002 .

[4]  T. Hughes,et al.  Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows , 2007 .

[5]  R. Müller,et al.  A multiscale approach for modeling progressive damage of composite materials using fast Fourier transforms , 2014 .

[6]  Franco Brezzi,et al.  $b=\int g$ , 1997 .

[7]  B. Ganapathisubramani,et al.  Concurrent Scale Interactions in the Far-Field of a Turbulent Mixing Layer , 2014 .

[8]  L. Richardson The Approximate Arithmetical Solution by Finite Differences of Physical Problems Involving Differential Equations, with an Application to the Stresses in a Masonry Dam , 1911 .

[9]  Arif Masud,et al.  A variational multiscale stabilized formulation for the incompressible Navier–Stokes equations , 2009 .

[10]  T. Hughes Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods , 1995 .

[11]  Volker Gravemeier,et al.  Recent Developments in Variational Multiscale Methods for Large-Eddy Simulation of Turbulent Flow , 2018 .

[12]  W. Horton,et al.  Drift wave turbulence in a low‐order k space , 1983 .

[13]  Rémi Abgrall,et al.  High‐order CFD methods: current status and perspective , 2013 .

[14]  Axel E. Larreteguy,et al.  A pseudo-DNS method for the simulation of incompressible fluid flows with instabilities at different scales , 2020 .

[15]  F. Browand,et al.  Vortex pairing : the mechanism of turbulent mixing-layer growth at moderate Reynolds number , 1974, Journal of Fluid Mechanics.

[16]  Axel E. Larreteguy,et al.  Advances in the Pseudo-DNS Methodology: Database Construction for the Averaged Inertial Stresses on the Internal RVE , 2019 .

[17]  E. Oñate,et al.  FIC–FEM formulation for the multidimensional transient advection–diffusion–absorption equation , 2020, Computer Methods in Applied Mechanics and Engineering.

[18]  C. Rhie,et al.  Numerical Study of the Turbulent Flow Past an Airfoil with Trailing Edge Separation , 1983 .

[19]  L. Richardson,et al.  The Deferred Approach to the Limit. Part I. Single Lattice. Part II. Interpenetrating Lattices , 1927 .

[20]  Guangtao Duan,et al.  Large Eddy Simulation by particle method coupled with Sub-Particle-Scale model and application to mixing layer flow , 2015 .

[21]  Thomas J. R. Hughes,et al.  Multiscale and Stabilized Methods , 2007 .

[22]  E. Oñate,et al.  Nodally exact Ritz discretizations of 1D diffusion–absorption and Helmholtz equations by variational FIC and modified equation methods , 2006 .

[23]  Felix Fritzen,et al.  The finite element square reduced (FE2R) method with GPU acceleration: towards three‐dimensional two‐scale simulations , 2016 .

[24]  Eugenio Oñate,et al.  A general procedure for deriving stabilized space–time finite element methods for advective–diffusive problems , 1999 .

[25]  E. Oñate,et al.  An accurate FIC-FEM formulation for the 1D advection–diffusion–reaction equation , 2016 .

[26]  J. Chaboche,et al.  FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials , 2000 .

[27]  Charbel Farhat,et al.  A Variational Multiscale Method for the Large Eddy Simulation of Compressible Turbulent Flows on Unstructured Meshes - Application to vortex shedding , 2004 .

[28]  Srinivas Sriramula,et al.  Development of an ABAQUS plugin tool for periodic RVE homogenisation , 2019, Engineering with Computers.

[29]  R. Codina Stabilization of incompressibility and convection through orthogonal sub-scales in finite element methods , 2000 .

[30]  Somnath Ghosh Adaptive Hierarchical-Concurrent Multiscale Modeling of Ductile Failure in Heterogeneous Metallic Materials , 2014, JOM.

[31]  Wing Kam Liu,et al.  Multiscale Simulations of Material with Heterogeneous Structures Based on Representative Volume Element Techniques , 2018 .

[32]  M. Pietrzyk,et al.  Concurrent and upscaling methods in multi scale modelling - case studies , 2008 .

[33]  F. Brezzi,et al.  A relationship between stabilized finite element methods and the Galerkin method with bubble functions , 1992 .

[34]  G. Taylor,et al.  Mechanism of the production of small eddies from large ones , 1937 .

[35]  I. Celik,et al.  Limitations of Richardson Extrapolation and Some Possible Remedies , 2005 .

[36]  T. Hughes,et al.  Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations , 1990 .

[37]  I. Wygnanski,et al.  The forced mixing layer between parallel streams , 1982, Journal of Fluid Mechanics.