Error estimation and mesh adaptivity in incompressible viscous flows using a residual power approach

Aquesta és una còpia de la versió author's final draft d'un article publicat a la revista Computational mechanics. Abstract. An a-posteriori error estimate with application to inviscid compressible flow problems is presented. The estimate is a surrogate measure of the discretization error, obtained from an approximation to the truncation terms of the governing equations. This approximation is calculated from the discrete nodal differential residuals using a reconstructed solution field on a modified stencil of points. Both the error estimation methodology and the flow solution scheme are implemented using the Finite Point Method, a meshless technique enabling higher-order approximations and reconstruction procedures on general unstructured discretizations. The performance of the proposed error indicator is studied and applications to adaptive grid refinement are presented.

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“…In this respect, methods based on numerical imbalance arguments suggest interesting alternatives, e.g. [9,11]. …”

Section: Discussionmentioning

confidence: 99%

“…in kinetic energy, momentum, etc.) have proven useful in guiding automatic grid adaptation and also as surrogate indicators for errors in derived output quantities; see for instance [9,10] and more recently [11], where power forms of mass and momentum residuals are used to guide mesh adaptivity in incompressible flow problems.…”

Section: /26mentioning

confidence: 99%

A-posteriori error estimation for the finite point method with applications to compressible flow

et al. 2017

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“…Oñate et al [20] have used the FIC method for formulating a residual-based error estimation technique and the corresponding mesh adaption scheme for analysis of incompressible flows with the FEM.…”

Section: Error Estimation and Mesh Adaption Procedures Via Ficmentioning

confidence: 99%

Finite increment calculus (FIC): a framework for deriving enhanced computational methods in mechanics

Oñate

2016

Adv. Model. and Simul. in Eng. Sci.

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In this paper we present an overview of the possibilities of the finite increment calculus (FIC) approach for deriving computational methods in mechanics with improved numerical properties for stability and accuracy. The basic concepts of the FIC procedure are presented in its application to problems of advection-diffusion-reaction, fluid mechanics and fluid-structure interaction solved with the finite element method (FEM). Examples of the good features of the FIC/FEM technique for solving some of these problems are given. A brief outline of the possibilities of the FIC/FEM approach for error estimation and mesh adaptivity is given.

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“…On one hand, despite the existing vast literature on adaptive algorithms, see for instance [1,[3][4][5]7], degree adaptive techniques have not received the attention they deserve, probably due to its cumbersome implementation in the context of continuous approximations. Nevertheless, degree adaptive algorithms, usually in combination with mesh size adaptation, have proved to be clearly suited for CFD computations, specially in the context of discontinuous approximations [3,10].…”

Section: Introductionmentioning

confidence: 99%

“…The importance of adaptive simulations in the field of computational fluid dynamics (CFD) has been pointed out by various authors in the last years [1][2][3][4][5][6][7][8][9]. Non-uniform discretizations, adapted to local flow features, are necessary to capture strong variations in the solution, shocks, sharp fronts or boundary layers, while keeping a coarser mesh where it is possible.…”

Section: Introductionmentioning

confidence: 99%

Hybridizable Discontinuous Galerkin with degree adaptivity for the incompressible Navier–Stokes equations

2014

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A degree adaptive Hybridizable Discontinuous Galerkin (HDG) method for the solution of the incompressible Navier-Stokes equations is presented. The key ingredient is an accurate and computationally inexpensive a posteriori error estimator based on the super-convergence properties of HDG. The error estimator drives the local modification of approximation degree in the elements and faces of the mesh, aimed at obtaining a uniform error distribution below a user-given tolerance in a given are of interest. Three 2D numerical examples are presented. High efficiency of the proposed error estimator is found, and an important reduction of the computational effort is shown with respect to non-adaptive computations, both for steady state and transient simulations.

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Error estimation and mesh adaptivity in incompressible viscous flows using a residual power approach

Cited by 19 publications

References 22 publications

A-posteriori error estimation for the finite point method with applications to compressible flow

A-posteriori error estimation for the finite point method with applications to compressible flow

Finite increment calculus (FIC): a framework for deriving enhanced computational methods in mechanics

Hybridizable Discontinuous Galerkin with degree adaptivity for the incompressible Navier–Stokes equations

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