A stabilized finite element method for incompressible viscous flows using a finite increment calculus formulation

By Eugenio Oñate. 2000

190 citations recorded by the source corpus.

Abstract A stabilized finite element formulation for incompressible viscous flows is derived. The starting point are the modified Navier–Stokes equations incorporating naturally the necessary stabilization terms via a finite increment calculus (FIC) procedure. Application of the standard finite element Galerkin method to the modified differential equations leads to a stabilized discrete system of equations overcoming the numerical instabilities emanating from the advective terms and those due to the lack of compatibility between approximate velocity and pressure fields. The FIC method also provides a natural explanation for the stabilization terms appearing in all equations for both the Navier–Stokes and the simpler Stokes equations. Transient solution schemes with enhanced stabilization properties are also proposed. Finally a procedure for computing the stabilization parameters is presented.

Subfields: Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/11fc7c0fa18f4d4f02769e52dcef9faf82ff0c06

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In Computational Mechanics

Citations in the corpus

A residual correction method based on finite calculus (2003, methodology): “have introduced the concept of finite increment calculus (or finite calculus) method for providing a stabilization which is very effective ( Onate, 1998, 2000”
A Lagrangian meshless finite element method applied to fluid-structure interaction problems (2003, methodology): “Examples of the application of the FIC approach the convection–diffusion problems and incompressible problems in solids and fluid mechanics are presented in [21,22].”
The particle finite element method: a powerful tool to solve incompressible flows with free‐surfaces and breaking waves (2004, methodology): “A simple and effective procedure to derive a stabilized formulation for incompressible flows is based on the so-called Finite Calculus formulations [19–21].”
Finite calculus formulation for incompressible solids using linear triangles and tetrahedra (2004, background): “This equation is typical in incompressible fluid dynamic problems there and arises from the mass continuity conditions [19, 20 ].”
Interaction between an elastic structure and free-surface flows: experimental versus numerical comparisons using the PFEM (2008, methodology): “In our work the stabilization via a finite calculus (FIC) procedure has been chosen [18].”
The particle finite element method. An overview (2004, unknown): “(7)–(10) can be found in [Oñate (1998; 2000); Oñate et al. (2001)].”
To mesh or not to mesh. That is the question (2006, methodology): “A complete description of several stabilizing methods as well as the stabilization used in the examples presented in this paper may be found in [13,24].”
Advances in the particle finite element method for the analysis of fluid-multibody interaction and bed erosion in free surface flows (2008, background): “The new expression for the mass balance equation is [18,26]”