Journal ArticleDOI
Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements
TLDR
In this paper, a finite element formulation based on stabilized bilinear and linear equal-order-interpolation velocity-pressure elements is presented for computation of steady and unsteady incompressible flows.Abstract:
Finite element formulations based on stabilized bilinear and linear equal-order-interpolation velocity-pressure elements are presented for computation of steady and unsteady incompressible flows. The stabilization procedure involves a slightly modified Galerkin/least-squares formulation of the steady-state equations. The pressure field is interpolated by continuous functions for both the quadrilateral and triangular elements used. These elements are employed in conjunction with the one-step and multi-step time integration of the Navier-Stokes equations. The three test cases chosen for the performance evaluation of these formulations are the standing vortex problem, the lid-driven cavity flow at Reynolds number 400, and flow past a cylinder at Reynolds number 100.read more
Citations
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Journal ArticleDOI
A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space-time procedure. I: The concept and the preliminary numerical tests
TL;DR: In this paper, a new strategy based on the stabilized space-time finite element formulation is proposed for computations involving moving boundaries and interfaces, where the deformation of the spatial domain with respect to time is taken into account automatically.
Book ChapterDOI
Stabilized Finite Element Formulations for Incompressible Flow Computations
TL;DR: In this article, stabilized finite element formulations for incompressible flow computations are discussed, which involve two main sources of potential numerical instabilities associated with the Galerkin formulation of a problem.
Journal ArticleDOI
A pressure-based method for unstructured meshes
S. R. Mathur,Jayathi Y. Murthy +1 more
TL;DR: A cell-centered equal-order formulation for multidimensional incompressible flows that is applied to benchmark problems using a variety of quadrilateral/hexahedral, triangular/tetrahedral, and hybrid meshes, and is shown to perform satisfactorily.
Journal ArticleDOI
The particle finite element method. An overview
TL;DR: The particle finite element method (PFEM) as mentioned in this paper is a general formulation for the analysis of fluid-structure interaction problems using the Lagrangian description to model the motion of nodes (particles) in both the fluid and the structure domains.
Journal ArticleDOI
Flow past a rotating cylinder
B. Sanjay Mittal,Bhaskar Kumar +1 more
TL;DR: In this article, the stability analysis of flow past a spinning circular cylinder placed in a uniform stream is investigated via two-dimensional computations, and a stabilized finite element method is utilized to solve the incompressible Navier-Stokes equations in the primitive variables formulation.
References
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Journal ArticleDOI
Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
A. N. Brooks,Thomas J. R. Hughes +1 more
TL;DR: In this article, a new finite element formulation for convection dominated flows is developed, based on the streamline upwind concept, which provides an accurate multidimensional generalization of optimal one-dimensional upwind schemes.
Journal ArticleDOI
A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuscka-Brezzi condition: A stable Petrov-Galerkin formulation of
TL;DR: A new Petrov-Galerkin formulation of the Stokes problem is proposed in this paper, which possesses better stability properties than the classical Galerkin/variational method.
Journal ArticleDOI
A new finite element formulation for computational fluid dynamics: VIII. The galerkin/least-squares method for advective-diffusive equations
TL;DR: Galerkin/least-squares finite element methods for advective-diffusive equations are presented in this paper, and a convergence analysis and error estimates are presented.
Journal ArticleDOI
A new finite formulation for computational fluid dynamics: VII. The Stokes problem with various well-posed boundary conditions: symmetric formulations that converge for all velocity/pressure spaces
TL;DR: Symmetric finite element formulations are proposed for the primitive-variables form of the Stokes equations and shown to be convergent for any combination of pressure and velocity interpolations as mentioned in this paper.
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