A stabilized finite element method for the incompressible Navier–Stokes equations using a hierarchical basis

By C. Whiting, Kenneth E. Jansen. 2001

322 citations recorded by the source corpus.

How researchers see this paper

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

Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows (2007, result): “Our exposition is similar to that of Whiting and Jansen [76] and Whiting [75].”
Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries (2006, methodology): “In order to stabilize the Galerkin method, the formulation becomes [24,42]: Find~v 2 Sh and p 2 Ph such that for every ~w 2 W k h and q 2 Ph Bð~w; q;~v; pÞ 1⁄4 0; Bð~w; q;~v; pÞ 1⁄4 BGð~w; q;~v; pÞ þ Xnel”
Adaptive mesh generation for curved domains (2005, methodology): “For this problem the flow is modeled using time dependent, incompressible Navier–Stokes equations and discretized using a stabilized finite element [29].”
A generalized-α method for integrating the filtered Navier–Stokes equations with a stabilized finite element method (2000, background): “This incompressible formulation is completely described in Whiting and Jansen [23], and the details will not be given here.”
Computation of incompressible bubble dynamics with a stabilized finite element level set method (2005, background): “When both phases of the flow can be considered incompressible, and as well as immiscible, the governing equations for the flow are the well known equations of motion represented as (see [24] for more detail on notation): qð _ ui þ ujui;jÞ 1⁄4 p;i þ sij;j þ fi; ð1Þ ui;i 1⁄4 0: ð2Þ”