Pressure Stability in Fractional Step Finite Element Methods for Incompressible Flows

By Ramon Codina. 2001

294 citations recorded by the source corpus.

Abstract The objective of this paper is to analyze the pressure stability of fractional step finite element methods for incompressible flows that use a pressure Poisson equation. For the classical first-order projection method, it is shown that there is a pressure control which depends on the time step size, and therefore there is a lower bound for this time step for stability reasons. The situation is much worse for a second-order scheme in which part of the pressure gradient is kept in the momentum equation. The pressure stability in this case is extremely weak. To overcome these shortcomings, a stabilized fractional step finite element method is also considered, and its stability is analyzed. Some simple numerical examples are presented to support the theoretical results.

Subfields: Computational Mechanics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/a3a5e057d7a7591b334d4dce57366c6321eff279

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Citations in the corpus

To mesh or not to mesh. That is the question (2006, methodology): “The fractional-step method will be used for the solution in time [23].”
An Object-oriented Environment for Developing Finite Element Codes for Multi-disciplinary Applications (2010, methodology): “[ 18 ] using equal order pressure-velocity elements stabilized by Orthogonal SubScales (OSS) [19], or Finite Increment Calculus (FIC) [63].”
The immersed boundary method: A projection approach (2007, unknown): “While remedies are offered in [18,9], we have not utilized them here since a much larger Dt is usually selected based on the CFL constraint.”
A coupled PFEM–Eulerian approach for the solution of porous FSI problems (2012, methodology): “Following the analysis of Codina [6], and considering the additional presence of the Darcy term, τ is defined as τi = ( α t + 4ν f i h2i + 2|u f i | hi + (E1 + E2|uf i”
The particle finite element method: a powerful tool to solve incompressible flows with free‐surfaces and breaking waves (2004, methodology): “In this work, the mesh is generated using the so-called extended Delaunay tesselation (EDT) presented in Reference [14].”
A Lagrangian meshless finite element method applied to fluid-structure interaction problems (2003, methodology): “To overcome these difficulties, a fractional step method has been proposed [18] which consists in splitting each time step in 2 steps as follows.”