NURBS‐enhanced finite element method (NEFEM)

Sevilla, Rubén; Fernández‐Méndez, Sonia; Huerta, Antonio

doi:10.1002/nme.2311

Cited by 215 publications

(179 citation statements)

References 63 publications

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“…It produces an accurate representation of the flow front but with an inacceptable computational cost. To reduce it, in [5] is combined NURBS-Enhance Finite Element Method (NEFEM) with Discontinuous Galerkin Formulation, FEM. Only the mould contour is defined as a NURBS curve and inside the domain reducing the computational costs.…”

Section: Introductionmentioning

confidence: 99%

An improvement of flow front computation through Bézier shape deformation guaranteeing mass conservation law

et al. 2010

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This paper aims to define the flow front as a continuous curve, in particular a Bézier curve, to reduce the inaccuracies generated by classical Finite Elements (FEM) in the flow front definition. The flow front is used in LCM processes for optimization algorithms, on-line control systems, PPI index and in general for whatever design and correction task. In these algorithms it is commonly used FEM simulation where the flow front is represented as a set of discrete points. This fact introduces an inaccuracy with the real flow front, because is continuous. In addition, the shape of the flow front obtained by FEM simulation differs in a great manner from the smooth shape of the real flow front. This concept was solved in our previous research, [7], where, using a mathematical technique, a Bézier curve is deformed and moved using velocity vectors. This technique is called Bézier Shape Deformation. This work improved the flow front representation but also introduced inaccuracies. In particular, the area enclosed between two Bézier curves, the flow front in different time instants, do not corresponds to the resins amount introduced in this range of time. To solve it, in the present research it is guaranteed the mass conservation law. Hence, it is introduced the required enclosed area in the mathematical technique to guarantee that not only velocity vectors has an influence in the Bézier curve deformation.

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Section: Introductionmentioning

confidence: 99%

An improvement of flow front computation through Bézier shape deformation guaranteeing mass conservation law

et al. 2010

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“…There has been a rising popularity of non-uniform rational B-spline (NURBS) enhanced methods throughout multiple engineering fields (Sevilla et al, 2006;Tan et al, 2015). NURBS have the ability to exactly represent all conic sections and are the standard geometric interpolant used in computer aided design (CAD) software.…”

Section: Introductionmentioning

confidence: 99%

An Application of the Isogeometric Analysis Method to Reservoir Simulation

Lynd

Foster

Nguyen

2016

SPE Europec Featured at 78th EAGE Conference and Exhibition

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The isogeometric analysis method (IGA) has been an emerging technique for exact geometrical discretization and efficient high order approximations in the field of computational engineering. While its potential has been demonstrated in a variety of disciplines, it has yet to be applied extensively to the field of reservoir simulation. This work shows IGA's potential as a useful tool for next generation reservoir simulation, highlighting its ability to exactly capture complex-shaped geometrical features in the reservoir and, consequentially, accurately model the pressure fields. First, an IGA code is validated against the analytic solution for a quarter five-spot pattern as well as a reference solution for a straight line source problem with pressure enforced at the corners of the domain. Next, the numerical efficiency of IGA is compared against a finite element method solution of single phase flow in a 2D representative reservoir containing a centralized ЉS-shapedЉ line source. Results suggest a clear advantage of the IGA method over the classical finite element method, which has lower convergence rates in terms of number of degrees of freedom.

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“…In Kim et al (2010) a trimmed surface based analysis framework has been proposed where the NURBS-enhanced FEM Sevilla et al (2008Sevilla et al ( , 2011 was applied to define a suitable integration domain within the parameter space. Trimming techniques provide a promising alternative for representing complex NURBS domains.…”

Section: Introductionmentioning

confidence: 99%

Isogeometric Methods for Numerical Simulation

Beer¹,

Bordas²

2015

CISM International Centre for Mechanical Sciences

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NURBS‐enhanced finite element method (NEFEM)

Cited by 215 publications

References 63 publications

An improvement of flow front computation through Bézier shape deformation guaranteeing mass conservation law

An improvement of flow front computation through Bézier shape deformation guaranteeing mass conservation law

An Application of the Isogeometric Analysis Method to Reservoir Simulation

Isogeometric Methods for Numerical Simulation

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