Approximate boundary-flux calculations

Carey, G. F.; Chow, S. S.; Seager, Mark

doi:10.1016/0045-7825(85)90085-4

Cited by 76 publications

(85 citation statements)

References 3 publications

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“…In an effort to recover the boundary fluxes with higher accuracy, Carey [35] and Carey et al [36] used the FE equations on nodes having Dirichlet boundary conditions to recover the boundary flux. The technique is based on the work of Wheeler [37], which recovers superconvergent derivatives for two-point boundary value problems.…”

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confidence: 99%

Nodal velocity derivatives of finite element solutions: The FiND method for incompressible Navier–Stokes equations

Ilinca

Pelletier

2008

Numerical Meth Engineering

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SUMMARYThis paper presents the development and application of the finite node displacement (FiND) method to the incompressible Navier-Stokes equations. The method computes high-accuracy nodal derivatives of the finite element solutions. The approach imposes a small displacement to individual mesh nodes and solves a very small problem on the patch of elements surrounding the node. The only unknown is the value of the solution (u, p) at the displaced node. A finite difference between the original and the perturbed values provides the directional derivative. Verification by grid refinement studies is shown for two-dimensional problems possessing a closed-form solution: a Poiseuille flow and a flow mimicking a boundary layer. For internal nodes, the method yields accuracy slightly superior to that of the superconvergent patch recovery (SPR) technique of Zienkiewicz and Zhu (ZZ). We also present a variant of the method to treat boundary nodes. The local discretization is enriched by inserting an additional mesh point very close to the boundary node of interest. Computations show that the resulting nodal derivatives are much more accurate than those obtained by the ZZ SPR technique.

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confidence: 99%

Nodal velocity derivatives of finite element solutions: The FiND method for incompressible Navier–Stokes equations

Ilinca

Pelletier

2008

Numerical Meth Engineering

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“…Postprocessing is especially effective in problems where better accuracy is required for derivatives of nodal variables in regions where Dirichlet essential boundary condition is imposed strongly. For Darcy flow analogy with thermal analysis can be exploited and technique already published in [5][6][7][8][9] can be implemented. Nevertheless in our case the problem must be posed differently, as explained in next section, with the help of several numerical examples.…”

Section: Numerical Simulationmentioning

confidence: 99%

“…In the region where Darcy flow is fully developed, normal component velocities on free boundary, where homogenized capillary pressure is imposed, can be recalculated from the following weak formulation [5][6][7][8][9]:…”

Section: Post-processing Of Darcy Flowmentioning

confidence: 99%

“…If only one side of the square would be used for recalculation without the symmetry implementation, then the coefficients in the left hand side matrix in the first and the last line would be h/3 and h/6, and the recalculated solution would exhibit intolerable perturbation in the corners (Figure 3a). Implementing the technique suggested in [7], values in the corners are estimated by zero and the recalculated solution goes back to the previous nice form, but now with the exact value in the corners (Figure 3b). The legend keeps the same rules, "m" expresses that the recalculation technique was modified according to [7].…”

Section: Post-processing Of Darcy Flowmentioning

confidence: 99%

“…This can be overcome by post-processing freeboundary normal velocities yielding superior convergence results. Post-processing a finite element solution is a well-known technique [5][6][7][8][9], which consists in a recalculation of the originally obtained quantities such that the rate of convergence increases without the need for expensive remeshing techniques. Post-processing methods are especially effective in problems where better accuracy is required for derivatives of nodal variables in regions where Dirichlet essential boundary condition is imposed strongly.…”

Section: Introductionmentioning

confidence: 99%

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Post-processing Techniques in Free Boundary Flows during Liquid Composite Moulding Processes

Dimitrovová¹

Proceedings of the Tenth International Conference on Civil, Structural and Environmental Engineering Computing

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Post-processing a finite element solution is a well-known technique, which consists in a recalculation of the originally obtained quantities such that the rate of convergence increases without the need for expensive remeshing techniques. Postprocessing is especially effective in problems where better accuracy is required for derivatives of nodal variables in regions where Dirichlet essential boundary condition is imposed strongly. Consequently such an approach can be exceptionally good in modelling of resin infiltration under quasi steady-state assumption by remeshing techniques and with explicit time integration, because only the free-front normal velocities are necessary to advance the resin front to the next position. The new contribution is the post-processing analysis and implementation of the freeboundary velocities of mesolevel infiltration analysis. Such implementation ensures better accuracy on even coarser meshes, which in consequence reduces the computational time also by the possibility of employing larger time steps.

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Joint elements, stress post-processing and superconvergent extraction with application to Mohr-Coulomb failure

Carey

1999

Commun. Numer. Meth. Engng.

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SUMMARYIn this study we investigate issues related to stress post-processing and superconvergent extraction techniques for ®nite element analysis involving joint elements. The behaviour of joint elements is ®rst compared with more standard ®nite element models and homogenization techniques. Then the interface stress extraction problem is investigated. Finally we extend and apply this idea to Mohr±Coulomb failure. Supporting numerical studies are conducted to demonstrate the ideas and their implications.

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Approximate boundary-flux calculations

Cited by 76 publications

References 3 publications

Nodal velocity derivatives of finite element solutions: The FiND method for incompressible Navier–Stokes equations

Nodal velocity derivatives of finite element solutions: The FiND method for incompressible Navier–Stokes equations

Post-processing Techniques in Free Boundary Flows during Liquid Composite Moulding Processes

Joint elements, stress post-processing and superconvergent extraction with application to Mohr-Coulomb failure

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