An interior penalty discontinuous Galerkin approach for 3D incompressible Navier-Stokes equation for permeability estimation of porous media

  title={An interior penalty discontinuous Galerkin approach for 3D incompressible Navier-Stokes equation for permeability estimation of porous media},
  author={Chen Liu and Florian Frank and Faruk Omer Alpak and B{\'e}atrice M. Rivi{\`e}re},
  journal={J. Comput. Phys.},

Improved a priori error estimates for a discontinuous Galerkin pressure correction scheme for the Navier-Stokes equations

The pressure correction scheme is combined with interior penalty discontinuous Galerkin method to solve the time-dependent Navier-Stokes equations. Optimal error estimates are derived for the

Convergence of a Decoupled Splitting Scheme for the Cahn-Hilliard-Navier-Stokes System

. This paper is devoted to the analysis of an energy-stable discontinuous Galerkin algo- rithm for solving the Cahn–Hilliard–Navier–Stokes equations within a decoupled splitting framework. We show

Optimal Error Estimates of a Discontinuous Galerkin Method for the Navier-Stokes Equations

The estiablished semi-discrete error estimates related to the L(L)-norm of velocity and L (L-norm of pressure are optimal and sharper than those derived in the earlier articles.

A Priori Error Estimates of a Discontinuous Galerkin Finite Element Method for the Kelvin-Voigt Viscoelastic Fluid Motion Equations

This paper applies a discontinuous Galerkin finite element method to the Kelvin-Voigt viscoelastic fluid motion equations when the forcing function is in L(L)-space. Optimal a priori error estimates

Estimating permeability of 3D micro-CT images by physics-informed CNNs based on DNS

A novel methodology for permeability prediction from micro-CT scans of geological rock samples by solving the stationary Stokes equation in an efficient and distributed-parallel manner and thereby improving the generality and accuracy of the training data set.

An Electrodiffusion Model Coupled with Fluid-Flow Effects for an On-Chip Electromembrane Extraction System

This paper proposes the first computational modeling of a miniaturized version of an electromembrane extraction (EME) setup to a chip format, where the donor solution is delivered by a syringe pump



A discontinuous Galerkin method with nonoverlapping domain decomposition for the Stokes and Navier-Stokes problems

A family of discontinuous Galerkin finite element methods is formulated and analyzed for Stokes and Navier-Stokes problems and it is shown that the method can treat a finite number of nonoverlapping domains with nonmatching grids at interfaces.

Finite Element Methods for the Incompressible Navier-Stokes Equations

These notes are based on lectures given in a Short Course on Theoretical and Numerical Fluid Mechanics in Vancouver, British Columbia, Canada, July 27–28, 1996, and at several other places since

A finite volume / discontinuous Galerkin method for the advective Cahn–Hilliard equation with degenerate mobility on porous domains stemming from micro-CT imaging

A numerical method is formulated for the solution of the advective Cahn–Hilliard (CH) equation with constant and degenerate mobility in three-dimensional porous media with non-vanishing velocity on

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,


Fluid dynamical problems are often conceptualized in unbounded domains. However, most methods of numerical simulation then require a truncation of the conceptual domain to a bounded one, thereby

Estimation of penalty parameters for symmetric interior penalty Galerkin methods

Discontinuous Galerkin methods for solving elliptic and parabolic equations - theory and implementation

  • B. Rivière
  • Computer Science
    Frontiers in applied mathematics
  • 2008
Discontinuous Galerkin methods for solving partial differential equations, developed in the late 1990s, have become popular among computational scientists and engineers who work in fluid dynamics and solid mechanics and want to use DG methods for their numerical results.