Element residual error estimate for the finite volume method

Jasak, Hrvoje; Gosman, A. D.

doi:10.1016/s0045-7930(02)00004-x

Cited by 88 publications

(100 citation statements)

References 27 publications

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“…These difficulties are mainly a consequence of the integral form of the equations found in finite volume discretization method. Methods that have been proposed rely on a-posteriori error estimates which require solutions on meshes with different spacing [65] or on methods that treat the finite volume as a particular case of finite element and exploit the weak formulation [66]. In regard to the reduced order level, efficient and reliable a-posteriori error bounds are required.…”

Section: Discussionmentioning

confidence: 99%

Parametric POD-Galerkin Model Order Reduction for Unsteady-State Heat Transfer Problems

Georgaka¹

2020

CiCP

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A parametric reduced order model based on proper orthogonal decomposition with Galerkin projection has been developed and applied for the modeling of heat transport in T-junction pipes which are widely found in nuclear power reactor cooling systems. Thermal mixing of different temperature coolants in T-junction pipes leads to temperature fluctuations and this could potentially cause thermal fatigue in the pipe walls. The novelty of this paper is the development of a parametric ROM considering the three dimensional, incompressible, unsteady Navier-Stokes equations coupled with the heat transport equation in a finite volume regime. Two different parametric cases are presented in this paper: parametrization of the inlet temperatures and parametrization of the kinematic viscosity. Different training spaces are considered and the results are compared against the full order model. The first test case results to a computational speed-up factor of 374 while the second test case to one of 211.

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Section: Discussionmentioning

confidence: 99%

Parametric POD-Galerkin Model Order Reduction for Unsteady-State Heat Transfer Problems

Georgaka¹

2020

CiCP

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“…Residual error has been widely used as an a posteriori error estimator in adaptive FEM [62], the finite volume method (FVM) [63], and boundary element method (BEM) [64]. It can be shown that the error of the approximate solution is bounded from above and below by the residual error with some constant multiplication factors independent of the solution [65].…”

Section: Optimization Of the Shape Parametermentioning

confidence: 99%

Exponential convergence and H‐c multiquadric collocation method for partial differential equations

Cheng

Golberg²,

Kansa

et al. 2003

Numerical Methods Partial

329

173

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The radial basis function (RBF) collocation method uses global shape functions to interpolate and collocate the approximate solution of PDEs. It is a truly meshless method as compared to some of the so-called meshless or element-free finite element methods. For the multiquadric and Gaussian RBFs, there are two ways to make the solution converge-either by refining the mesh size h, or by increasing the shape parameter c. While the h-scheme requires the increase of computational cost, the c-scheme is performed without extra effort. In this paper we establish by numerical experiment the exponential error estimate ⑀ ϳ O( ͌c/h ), where 0 Ͻ Ͻ 1. We also propose the use of residual error as an error indicator to optimize the selection of c.

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“…Significant work has been done in adjoint-based error estimation for hp-adaptivity in PDEs using finite element discretizations [28,6,6,179,201,17,80,53,141,211,29,167,4,21,89,90,106,122]. Additional work has been done on finite-volume methods [221,130]. For a detailed review of the history and recent developments see [29,90].…”

Section: Adjoints For Error Estimation Uncertainty Quantificationmentioning

confidence: 99%