POD-(H)DG Method for Incompressible Flow Simulations

A Least Squares Spectral Element Method for Incompressible Flow Simulations

Hybridizable discontinuous Galerkin (HDG) method for Oseen flow

3 The hybridizable discontinuous Galerkin (HDG) formulation 3 3.1 HDG local problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.2 HDG global problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.3 Local post-process of the velocity field . . . . . . . . . . . . . . . . . . . . 5 3.4 Assembly of the matrices . . . . . . . . . . . . . . . . . . . . . . . . ....

Convergence of gauge method for incompressible flow

A new formulation, a gauge formulation of the incompressible Navier-Stokes equations in terms of an auxiliary field a and a gauge variable φ, u = a +∇φ, was proposed recently by E and Liu. This paper provides a theoretical analysis of their formulation and verifies the computational advantages. We discuss the implicit gauge method, which uses backward Euler or Crank-Nicolson in time discretizat...

A Boundary Method for Incompressible Fluid Flow

The animation of fluids is a topic of great interest in the computer animation community. The common familiarity with real-world fluid motion and the difficulty in achieving this motion combines to make the problem exceptionally challenging — everyone knows what fluid should look like, but animating it convincingly by hand is difficult. To achieve realistic fluid motion, researchers have been g...

Analysis of HDG methods for Stokes flow

In this paper, we analyze a hybridizable discontinuous Galerkin method for numerically solving the Stokes equations. The method uses polynomials of degree k for all the components of the approximate solution of the gradient-velocity-pressure formulation. The novelty of the analysis is the use of a new projection tailored to the very structure of the numerical traces of the method. It renders th...