Computing with hp-ADAPTIVE FINITE ELEMENTS

Demkowicz, Leszek

doi:10.1201/9781420011685

Cited by 245 publications

(168 citation statements)

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“…However, it is hard to imagine a 30-300 million node grid without some severe local flow anomalies. A method that eliminates the problem altogether is to solve on a fine grid which is always a uniform refinement of a coarse grid, see Demkovicz [3]. The fine grid would, of course, be an affordable grid.…”

Section: Issuesmentioning

confidence: 99%

Observations Regarding Algorithms Required for Robust CFD Codes

Johnson

Kamenetskiy

Melvin

et al. 2011

Math. Model. Nat. Phenom.

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Abstract. Over the last three decades Computational Fluid Dynamics (CFD) has gradually joined the wind tunnel and flight test as a primary flow analysis tool for aerodynamic designers. CFD has had its most favorable impact on the aerodynamic design of the high-speed cruise configuration of a transport. This success has raised expectations among aerodynamicists that the applicability of CFD can be extended to the full flight envelope. However, the complex nature of the flows and geometries involved places substantially increased demands on the solution methodology and resources required. Currently most simulations involve Reynolds-Averaged Navier-Stokes (RANS) codes although Large Eddy Simulation (LES) and Detached Eddy Suimulation (DES) codes are occasionally used for component analysis or theoretical studies. Despite simplified underlying assumptions, current RANS turbulence models have been spectacularly successful for analyzing attached, transonic flows. Whether or not these same models are applicable to complex flows with smooth surface separation is an open question. A prerequisite for answering this question is absolute confidence that the CFD codes employed reliably solve the continuous equations involved. Too often, failure to agree with experiment is mistakenly ascribed to the turbulence model rather than inadequate numerics. Grid convergence in three dimensions is rarely achieved. Even residual convergence on a given grid is often inadequate. This paper discusses issues involved in residual and especially grid convergence.

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Section: Issuesmentioning

confidence: 99%

Observations Regarding Algorithms Required for Robust CFD Codes

Johnson

Kamenetskiy

Melvin

et al. 2011

Math. Model. Nat. Phenom.

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“…In view of varying polynomial order and normal continuity of the basis functions we rely on the common edge-cell-based construction, see e.g. [13,2]. Hence, in general, the polynomial degree can vary on each edge and the interior (cell) of the element.…”

Section: The Element Stiffness Matrix On Trianglesmentioning

confidence: 99%

“…In order to allow for globally varying polynomial degree we use as common a face-cellbased construction [2,13] of the basis functions. Again, for ease of notation, we assume a uniform polynomial order p.…”

Section: The Element Stiffness Matrix On Tetrahedramentioning

confidence: 99%

“…For more than twenty years, spectral methods, [20], as well as the p-version and the hp-version of the finite element method, see e.g. [15], [13], [29], [32], and the references therein, have become more and more popular. In the classical (h-version) finite element method, convergence of a piecewise polynomial discrete solution (typically of fixed low degree) to the exact solution is achieved by decreasing the mesh size h. In the p-version of the finite element method the mesh is fixed and convergence is obtained by increasing the polynomial degree p. Combing both ideas, i.e.…”

Section: Introductionmentioning

confidence: 99%

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Sparsity optimized high order finite element functions for H(div) on simplices

Beuchler

Pillwein²,

Zaglmayr³

2012

Numer. Math.

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“…The application of the mixed order finite elements is well established in the mathematical finite element literature [12], [13]. The mixed order elements are also applied in different engineering domains [14], [15].…”

Section: Introductionmentioning

confidence: 99%

Mixed-Order Finite-Element Modeling of Magnetic Material Degradation Due to Cutting

et al. 2018

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As a part of manufacturing of electrical machines, electrical sheets are cut to the desired shape by various cutting techniques such as punching, laser cutting etc. This cutting process degrades the magnetic material near the cut-edge which should be included in the finite element modeling of electrical machines. However, due to the nature of the cutting effects, the existing finite element modeling of the cutting effect results in computationally heavy simulations. This paper investigates the application of mixed order elements to model the cutting effect. The second order nodal triangular elements are used near the cut-edge whereas transition/first order elements are applied in the remaining solution domain. Further, the accuracy of the presented method is analyzed with the traditional method. According to the simulations, the mixed order elements returned accurate results significantly faster than the traditional finite element based approaches. Further, the effect of the cutting on the machine performance is also studied by comparing it's results briefly.

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Computing with hp-ADAPTIVE FINITE ELEMENTS

Cited by 245 publications

References 0 publications

Observations Regarding Algorithms Required for Robust CFD Codes

Observations Regarding Algorithms Required for Robust CFD Codes

Sparsity optimized high order finite element functions for H(div) on simplices

Mixed-Order Finite-Element Modeling of Magnetic Material Degradation Due to Cutting

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