High–Order hp–Adaptive Discontinuous Galerkin Finite Element Methods for Compressible Fluid Flows

Giani, Stefano; Houston, Paul

doi:10.1007/978-3-642-03707-8_28

Cited by 12 publications

(10 citation statements)

References 12 publications

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“…DGFE space discretization uses a (higher order) piecewise polynomial discontinuous approximation on arbitrary meshes. DGFE methods were employed in many papers for the discretization of compressible fluid flow problems; let us cite the pioneering works [1][2][3][4] and some recent papers [5][6][7][8][9][10][11] and the references cited therein. Recent progress of the use of the DGFE method for compressible flow simulations can be found in [12].…”

Section: Introductionmentioning

confidence: 99%

A design of residual error estimates for a high order BDF‐DGFE method applied to compressible flows

Dolejší

2013

Numerical Methods in Fluids

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SUMMARY We deal with the numerical solution of the non‐stationary compressible Navier–Stokes equations with the aid of the backward difference formula – discontinuous Galerkin finite element method. This scheme is sufficiently stable, efficient and accurate with respect to the space as well as time coordinates. The nonlinear algebraic systems arising from the backward difference formula – discontinuous Galerkin finite element discretization are solved by an iterative Newton‐like method. The main benefit of this paper are residual error estimates that are able to identify the computational errors following from the space and time discretizations and from the inexact solution of the nonlinear algebraic systems. Thus, we propose an efficient algorithm where the algebraic, spatial and temporal errors are balanced. The computational performance of the proposed method is demonstrated by a list of numerical experiments. Copyright © 2013 John Wiley & Sons, Ltd.

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Section: Introductionmentioning

confidence: 99%

A design of residual error estimates for a high order BDF‐DGFE method applied to compressible flows

Dolejší

2013

Numerical Methods in Fluids

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“…More precisely, the (half) geometry is given by the following expression cf. [23]. This geometry is considered at laminar conditions with inflow Mach number equal to 0.5, at an angle of attack a = 1°, and Reynolds number Re = 5000 with adiabatic no-slip wall boundary condition imposed.…”

Section: Laminar Flow Around a Streamlined Bodymentioning

confidence: 99%

Domain Decomposition Preconditioners for Discontinuous Galerkin Discretizations of Compressible Fluid Flows

Houston¹

2014

NMTMA

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In this article we consider the application of Schwarz-type domain de composition preconditioners to the discontinuous Galerkin finite element approx imation of the compressible Navier-Stokes equations. To discretize this system of conservation laws, we exploit the (adjoint consistent) symmetric version of the inte rior penalty discontinuous Galerkin finite element method. To define the necessary coarse-level solver required for the definition of the proposed preconditioner, we ex ploit ideas from composite finite element methods, which allow for the definition of finite element schemes on general meshes consisting of polygonal (agglomerated) el ements. The practical performance of the proposed preconditioner is demonstrated for a series of viscous test cases in both two-and three-dimensions.

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“…For this reason DWR has been already used in many fields. For example in [22] DWR has been used to accurately compute the lift and drag of wing profile, moreover in [23,24] DWR has been used to accurately compute eigenvalues of eigenvalue problems from different areas of physics.…”

Section: Dual Weighted Residual a Posteriori Error Estimatormentioning

confidence: 99%

High-order/ $$hp$$ -adaptive discontinuous Galerkin finite element methods for acoustic problems

Giani

2012

Computing

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Further information on publisher's website:http://dx.doi.org/10.1007/s00607-012-0253-5Publisher's copyright statement:The nal publication is available at Springer via http://dx.doi.org/10.1007/s00607-012-0253-5Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. High-order/hp-adaptive discontinuous Galerkin finite element methods for acoustic problems. Stefano GianiAbstract In this paper we present two different kinds of error estimators for acoustic problems: a residual-based and a dual weighted residual one. The former error estimator is explicit and cheap to compute. The latter is based on a duality argument and it is capable of computing accurate and reliable estimations of quantities of interest, which can be safely used for finite element analysis and model validation. The error estimators presented in this work are designed to work with a hp-adaptive discontinuous Galerkin (DG) methods.

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High–Order hp–Adaptive Discontinuous Galerkin Finite Element Methods for Compressible Fluid Flows

Cited by 12 publications

References 12 publications

A design of residual error estimates for a high order BDF‐DGFE method applied to compressible flows

A design of residual error estimates for a high order BDF‐DGFE method applied to compressible flows

Domain Decomposition Preconditioners for Discontinuous Galerkin Discretizations of Compressible Fluid Flows

High-order/ $$hp$$ -adaptive discontinuous Galerkin finite element methods for acoustic problems

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