Grad–div stabilization and subgrid pressure models for the incompressible Navier–Stokes equations

By Maxim A. Olshanskii, Gert Lube, Timo Heister, J. Löwe. 2009

198 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/86a3d6215dffa318719b35109361627b855e5c7e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biomedical Engineering

In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

On the convergence rate of grad-div stabilized Taylor–Hood to Scott–Vogelius solutions for incompressible flow problems (2011, background): “Yet, in general, the improvement in physical fidelity is limited because grad-div stabilization with γ > O(1) can overstabilize [16, 2].”
A discontinuous skeletal method for the viscosity-dependent Stokes problem (2015, unknown): “This difficuly is traditionally tempered, but not cured, by adding grad-div stabilization [37, 36, 22, 5].”
On the role of the Helmholtz decomposition in mixed methods for incompressible flows and a new variational crime (2014, methodology): “But although poor mass conservation has accompanied the development of mixed methods for incompressible flows for several decades, surprisingly only in recent years research on poor mass conservation began to receive a broader attention and a better understanding of it started [40, 39, 9, 35, 36, 25”
On the Divergence Constraint in Mixed Finite Element Methods for Incompressible Flows (2015, background): “It is now well known that it penalizes for lack of mass conservation, can improve solution accuracy for simulations of Stokes and Navier–Stokes equations by reducing the effect of the pressure on the velocity error [41, 53, 54, 55], and it can improve conditioning of discrete systems [31] and conver”
Efficient augmented Lagrangian‐type preconditioning for the Oseen problem using Grad‐Div stabilization (2013, methodology): “Fortunately, most of the real life problems need additional stabilization, see [23].”