The Finite Element Method for Fluid Dynamics

By O. C. Zienkiewicz, Robert Taylor, Perumal Nithiarasu. 2005

805 citations recorded by the source corpus.

Subfields: Computational Mechanics, Control and Systems Engineering, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/08b56d2b7fe912dbb228a0fe131fbc2b7089f03e

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In Computational Mechanics

In Control and Systems Engineering

In Mechanical Engineering

Citations in the corpus

Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications (2010, background): “The three succeeding volumes [12,219,220] are considered the most important monographs in the field to date.”
Advances in the particle finite element method for the analysis of fluid-multibody interaction and bed erosion in free surface flows (2008, background): “The standard infinitesimal equations for a viscous incompressible fluid can be written in a Lagrangian frame as [17,34].”
Numerical modelling of magma dynamics coupled to tectonic deformation of lithosphere and crust (2013, methodology): “…P E N D I X A : N U M E R I C A L M E T H O D A.1 Implementation of governing equations To find a suitable implementation of the conservation eqs (57)–(59), we follow a similar strategy as is used for implementing variable viscosity Stokes flow in finite-element modelling (Zienkiewicz et al. 2005).”
Hybridizable discontinuous Galerkin p‐adaptivity for wave propagation problems (2013, background): “A “rule of thumb” usually suggests 10 linear elements per wavelength [63, 64] and, obviously, less than 4 linear elements is impossible.”
Isogeometric Collocation: Cost Comparison with Galerkin Methods and Extension to Adaptive Hierarchical NURBS Discretizations (2013, background): “An in-depth discussion of this problem and its exact solution can be found in [128,129].”
FEAP - - A Finite Element Analysis Program (2011, result): “The stream function, ψ, defines the velocities as[9] u1 = − ∂ψ ∂x2 and u2 = ∂ψ ∂x1 (2.”
Possibilities of the particle finite element method for fluid–soil–structure interaction problems (2011, methodology): “An advantage of the Lagrangian formulation is that the convective terms disappear from the fluid equations [11,48].”
Divergence‐free discontinuous Galerkin schemes for the Stokes equations and the MAC scheme (2008, methodology): “While this scheme has been widely used in applications (see for example [15]), it took until [10] to obtain optimal error estimates for the vorticity and pressure.”
Development of a cell centred upwind finite volume algorithm for a new conservation law formulation in structural dynamics (2013, methodology): “14) (2)In fluid dynamics, velocity at the surface vanishes when viscous fluid passes a solid wall [25, 81,83].”