A comparison of hybridized and standard DG methods for target-based hp-adaptive simulation of compressible flow

Woopen, Michael; Balan, Aravind; May, Georg; Schütz, Jochen

doi:10.1016/j.compfluid.2014.03.023

Cited by 63 publications

(59 citation statements)

References 35 publications

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“…1,2,3,4,5,6,7,8 This paper shall address first and foremost details on the structure and implementation of our framework. Employing techniques from both generic 9 and object-oriented 10 programming, the framework is designed with efficiency and extensibility in mind.…”

Section: Introductionmentioning

confidence: 99%

A Unifying Computational Framework for Adaptive High-Order Finite Element Methods

Woopen

Balan

May

2015

22nd AIAA Computational Fluid Dynamics Conference

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We present a comprehensive overview of our computational framework for adaptive high-order finite element methods, including discontinuous Galerkin (DG) methods and their hybridized counterparts (HDG). Besides covering the numerical methods, we grant their actual implementation a prominent position in this paper. Finally, we apply our framework to a variety of flow problems, including laminar, and turbulent flow in both two-and three-dimensional domains.

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Section: Introductionmentioning

confidence: 99%

A Unifying Computational Framework for Adaptive High-Order Finite Element Methods

Woopen

Balan

May

2015

22nd AIAA Computational Fluid Dynamics Conference

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“…Much work has been done in this area for steady problems with finite volume and finite element methods, [13][14][15][16][17][18][19] and recently with HDG discretizations. [20][21][22] Unsteady problems pose additional challenges and computational costs, namely in the unsteady adjoint solution, yet output-based adaptive methods have also been explored, with various modes of adaptation, including static-mesh, dynamic-mesh, space-only, and combined space-time. [23][24][25][26][27][28][29][30][31] In this work, we extend unsteady output-based adaptation techniques to high-order compressible Navier-Stokes simulations on deforming domains, discretized with HDG.…”

Section: Introductionmentioning

confidence: 99%

An Output-Based Adaptive Hybridized Discontinuous Galerkin Method on Deforming Domains

Fidkowski

2015

22nd AIAA Computational Fluid Dynamics Conference

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In this paper we present an output-based adaptive method for unsteady simulations of convection-dominated flows on deformable domains. The target discretization is the hybridized discontinuous Galerkin method (HDG), which offers potential computational savings at high order compared to the discontinuous Galerkin (DG) method. Mesh deformation is achieved through an arbitrary Lagrangian-Eulerian transformation with an analytical mapping. We present details of this transformation applied to the HDG system of equations, with focus on the auxiliary gradient equation, viscous stabilization, and output calculation. The temporal discretization for adaptive runs is DG in time, which lends itself to rigorous a posteriori error estimation using a fine-space discrete adjoint solution. We present modifications to the approximate factorization technique that enables an efficient DG-in-time solution for HDG. Space-time error estimates drive metric-based static spatial refinement on unstructured spatial meshes and slab-based temporal nodalizations. We show accuracy and cost comparisons between adaptive DG and HDG simulations of two-dimensional flows governed by the compressible Navier-Stokes equations on deforming domains.

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“…For this purpose, additional unknowns on the edges of elements are introduced that take over the global coupling from the element unknowns. In most cases this method leads to significant savings in terms of memory requirements and computing time [7]. The possibly nonlinear system of equations is solved using Newton's method.…”

Section: Methodsmentioning

confidence: 99%

An efficient linear solver for the hybridized discontinuous Galerkin method

Jaust

Schütz

Aizinger

2016

Proc Appl Math and Mech

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Discretizing partial differential equations by an implicit solving technique ultimately leads to a linear system of equations that has to be solved. The number of globally coupled unknowns is especially large for discontinuous Galerkin (DG) methods. It can be reduced by using hybridized discontinuous Galerkin (HDG) methods, but still efficient linear solvers are needed. It has been shown that, if hierarchical basis functions are used, a hierarchical scale separation (HSS) ansatz can be an efficient solver. In this work, we couple the HDG method with an HSS solver to solve a scalar nonlinear problem. It is validated by comparing the results with results obtained by GMRES with ILU(3) preconditioning as linear solver.

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A comparison of hybridized and standard DG methods for target-based hp-adaptive simulation of compressible flow

Cited by 63 publications

References 35 publications

A Unifying Computational Framework for Adaptive High-Order Finite Element Methods

A Unifying Computational Framework for Adaptive High-Order Finite Element Methods

An Output-Based Adaptive Hybridized Discontinuous Galerkin Method on Deforming Domains

An efficient linear solver for the hybridized discontinuous Galerkin method

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