scholarly journals An h-Adaptive Finite-Element Technique for Constructing 3D Wind Fields

2009 ◽  
Vol 48 (3) ◽  
pp. 580-599 ◽  
Author(s):  
Darrell W. Pepper ◽  
Xiuling Wang
Keyword(s):  
Finite Element ◽  
Large Element ◽  
Error Estimator ◽  
Small Element ◽  
Computational Domain ◽  
Adaptive Finite Element ◽  
Wind Fields ◽  
Adaptive Procedure ◽  
Irregular Terrain ◽  
L2 Norm

Abstract An h-adaptive, mass-consistent finite-element model (FEM) has been developed for constructing 3D wind fields over irregular terrain utilizing sparse meteorological tower data. The element size in the computational domain is dynamically controlled by an a posteriori error estimator based on the L2 norm. In the h-adaptive FEM algorithm, large element sizes are typically associated with smooth flow regions and small errors; small element sizes are attributed to fast-changing flow regions and large errors. The adaptive procedure employed in this model uses mesh refinement–unrefinement to satisfy error criteria. Results are presented for wind fields using sparse data obtained from two regions within Nevada: 1) the Nevada Test Site, located approximately 65 mi (1 mi ≈ 1.6 km) northwest of Las Vegas, and 2) the central region of Nevada, about 100 mi southeast of Reno.

Constructing 3-D Wind Fields for Nellis Dunes in Nevada

2008 ◽  
Author(s):  
Xiuling Wang ◽  
Darrell W. Pepper ◽  
Brenda Buck ◽  
Dirk Goossens
Keyword(s):  
Element Model ◽  
Posteriori Error ◽  
Large Element ◽  
Error Estimator ◽  
Small Element ◽  
Computational Domain ◽  
Wind Fields ◽  
Adaptive Procedure ◽  
Irregular Terrain ◽  
L2 Norm

An h-adaptive, mass consistent finite element model (FEM) is used to construct 3-D wind fields over irregular terrain utilizing sparse meteorological tower data. The element size in the computational domain is dynamically controlled by a–posteriori error estimator based on the L2 norm. In the h-adaptive FEM algorithm, large element sizes are typically associated with computational regions where the flow is smooth and small errors; small element sizes are attributed to fast changing flow regions and large errors. The adaptive procedure uses mesh refinement/unrefinement to satisfy error criteria. The application of a mass consistent approach essentially poses a least-squares problem in the computational domain. Preliminary results are obtained for constructing 3-D wind fields for Nellis Dunes in Nevada.

An H-Adaptive Finite Element Model for Constructing 3-D Wind Fields

2004 ◽  
Author(s):  
Xiuling Wang ◽  
Darrell W. Pepper ◽  
Yitung Chen ◽  
Hsuan-Tsung Hsieh
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Wind Field ◽  
Compressible Flows ◽  
Element Model ◽  
Computational Time ◽  
Individual Element ◽  
Adaptive Finite Element ◽  
Wind Fields ◽  
Irregular Terrain

Calculating wind velocities accurately and efficiently is the key to successfully assessing wind fields over irregular terrain. In the finite element method, decreasing individual element size (increasing the mesh density) and increasing shape function interpolation order are known to improve accuracy. However, computational speed is typically impaired, along with tremendous increases in computational storage. This problem becomes acutely obvious when dealing with atmospheric flows. An h-adaptation scheme, which allows one to start with a coarse mesh that ultimately refines in high gradients regions, can obtain high accuracy at reduced computational time and storage. H-adaptation schemes have been shown to be very effective in compressible flows for capturing shocks [1], but have found limited use in atmospheric wind field simulations [2]. In this paper, an h-adaptive finite element model has been developed that refines and unrefines element regions based upon velocity gradients. An objective analysis technique is applied to generate a mass consistent 3-D flow field utilizing sparse meteorological data. Results obtained from the PSU/NCAR MM5 atmospheric model are used to establish the initial velocity field in lieu of available meteorological tower data. Wind field estimations for the northwest area of Nevada are currently being examined as potential locations for wind turbines.

An HP-Adaptive Finite Element Model for Convective Heat Transfer in an Attic Space

2006 ◽  
Author(s):  
Xiuling Wang ◽  
Darrell W. Pepper
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Natural Convection ◽  
Convection Heat Transfer ◽  
Element Model ◽  
Posteriori Error ◽  
Error Estimator ◽  
Adaptive Finite Element ◽  
Aspect Ratios ◽  
L2 Norm

An hp-adaptive finite element algorithm is used to simulate heat transfer within attic spaces driven by buoyancy forces. The element size (h-) and shape function order (p-) are dynamically controlled by an a-posteriori error estimator based on the L2 norm. A three-step process is used to solve the system of equations. The hp-adaptive algorithm is validated using natural convection heat transfer within a differentially heated enclosure. Application of the model is used to simulate heat transfer within attic spaces subjected to natural convection for Rayleigh numbers ranging from 7.1×102 to 7.1×105. Attic aspect ratios range from 0.2 to 1.0. Heat transfer rates typical of summer days in Las Vegas are considered: roofs (inclined surfaces) of attics are hot; bases (bottom surfaces) are cold and vertical walls are insulated. Results are compared with data in literature when possible; good agreement is generally observed.

scholarly journals Quasi-optimality of an Adaptive Finite Element Method for Cathodic Protection

2019 ◽  
Vol 53 (5) ◽  
pp. 1645-1665
Author(s):  
Guanglian Li ◽  
Yifeng Xu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Cathodic Protection ◽  
Finite Element Approximation ◽  
Adaptive Finite Element Method ◽  
Error Estimator ◽  
Element Approximation ◽  
Adaptive Finite Element ◽  
Energy Error ◽  
Element Method

In this work, we derive a reliable and efficient residual-typed error estimator for the finite element approximation of a 2D cathodic protection problem governed by a steady-state diffusion equation with a nonlinear boundary condition. We propose a standard adaptive finite element method involving the Dörfler marking and a minimal refinement without the interior node property. Furthermore, we establish the contraction property of this adaptive algorithm in terms of the sum of the energy error and the scaled estimator. This essentially allows for a quasi-optimal convergence rate in terms of the number of elements over the underlying triangulation. Numerical experiments are provided to confirm this quasi-optimality.

Adaptive finite element computational fluid dynamics using an anisotropic error estimator

2000 ◽  
Vol 182 (3-4) ◽  
pp. 379-400 ◽  
Author(s):  
Regina C. Almeida ◽  
Raúl A. Feijóo ◽  
Augusto C. Galeão ◽  
Claudio Padra ◽  
Renato S. Silva
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Finite Element ◽  
Error Estimator ◽  
Adaptive Finite Element

Quasi-optimal convergence of AFEM based on separate marking, Part II

2015 ◽  
Vol 23 (2) ◽  
Author(s):  
Hella Rabus
Keyword(s):  
Finite Element ◽  
Solid Mechanics ◽  
Convergence Rates ◽  
Stokes Equations ◽  
Total Error ◽  
Poisson Model ◽  
Error Estimator ◽  
Adaptive Finite Element ◽  
Optimal Convergence ◽  
High Degree

AbstractVarious applications in computational fluid dynamics and solid mechanics motivate the development of reliable and efficient adaptive algorithms for nonstandard finite element methods (FEMs). Standard adaptive finite element algorithms consist of the iterative loop of the basic steps Solve, Estimate, Mark, and Refine. For separate marking strategies, this standard scheme may be universalised. The (total) error estimator is split into a volume term and an error estimator term.Since the volume term is independent of the discrete solution, an appropriate data approximation may be realised by a high degree of local mesh refinement. This observation results in a natural adaptive algorithm based on separate marking. Its quasi-optimal convergence is proven in this second part for the pure displacement problem in linear elasticity and the Stokes equations and nonconforming Crouzeix-Raviart FEM. The proofs follow the same general methodology as for the Poisson model problem in the first part of this series. The numerical experiments confirm the optimal convergence rates and reveal its flexibility.

scholarly journals Quasi-optimality of an Adaptive Finite Element Method for an Optimal Control Problem

2011 ◽  
Vol 11 (2) ◽  
pp. 107-128 ◽  
Author(s):  
Roland Becker ◽  
Shipeng Mao
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Posteriori Error ◽  
Adaptive Finite Element Method ◽  
Error Estimator ◽  
Adaptive Finite Element ◽  
Posteriori Error Estimator ◽  
A Posteriori Error ◽  
Data Approximation ◽  
Element Algorithm

Abstract We prove quasi-optimality of an adaptive finite element algorithm for a model problem of optimal control including control constraints. The quasi-optimility expresses the fact that the decrease of error with respect to the number of mesh cells is optimal up to a constant. The considered algorithm is based on an adaptive marking strategy which compares a standard residualtype a posteriori error estimator with a data approximation term in each step of the algorithm in order to adapt the marking of cells.

Convergent Adaptive Finite Element Method Based on Centroidal Voronoi Tessellations and Superconvergence

2011 ◽  
Vol 10 (2) ◽  
pp. 339-370 ◽  
Author(s):  
Yunqing Huang ◽  
Hengfeng Qin ◽  
Desheng Wang ◽  
Qiang Du
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Voronoi Tessellation ◽  
Posteriori Error ◽  
Adaptive Finite Element Method ◽  
Adaptive Finite Element ◽  
Adaptive Procedure ◽  
Seamless Integration ◽  
Practical Applications ◽  
Element Method

AbstractWe present a novel adaptive finite element method (AFEM) for elliptic equations which is based upon the Centroidal Voronoi Tessellation (CVT) and superconvergent gradient recovery. The constructions of CVT and its dual Centroidal Voronoi Delaunay Triangulation (CVDT) are facilitated by a localized Lloyd iteration to produce almost equilateral two dimensional meshes. Working with finite element solutions on such high quality triangulations, superconvergent recovery methods become particularly effective so that asymptotically exact a posteriori error estimations can be obtained. Through a seamless integration of these techniques, a convergent adaptive procedure is developed. As demonstrated by the numerical examples, the new AFEM is capable of solving a variety of model problems and has great potential in practical applications.

scholarly journals Residual-based a posteriori error estimation for hp-adaptive finite element methods for the Stokes equations

2019 ◽  
Vol 27 (4) ◽  
pp. 237-252
Author(s):  
Arezou Ghesmati ◽  
Wolfgang Bangerth ◽  
Bruno Turcksin
Keyword(s):  
Finite Element ◽  
Error Estimation ◽  
Posteriori Error ◽  
Error Estimator ◽  
Adaptive Finite Element ◽  
A Posteriori ◽  
Posteriori Error Estimation ◽  
A Posteriori Error Estimator ◽  
Posteriori Error Estimator ◽  
A Posteriori Error

AbstractWe derive a residual-based a posteriori error estimator for the conforminghp-Adaptive Finite Element Method (hp-AFEM) for the steady state Stokes problem describing the slow motion of an incompressible fluid. This error estimator is obtained by extending the idea of a posteriori error estimation for the classicalh-version of AFEM. We also establish the reliability and efficiency of the error estimator. The proofs are based on the well-known Clément-type interpolation operator introduced in [27] in the context of thehp-AFEM. Numerical experiments show the performance of an adaptivehp-FEM algorithm using the proposed a posteriori error estimator.

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