A 3-D Discontinuous Galerkin Chimera Overset Method

Galbraith, Marshall C.; Orkwis, Paul D.; Benek, John A.

doi:10.2514/6.2014-0776

Cited by 13 publications

(17 citation statements)

References 8 publications

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“…Previous attempts to study the order of accuracy of overset grid schemes have been performed by Galbraith [31], using a Fig. 12 Order of accuracy for inviscid and laminar flow using P 1 , P 2 , and P 3 elements.…”

Section: B Methods Of Manufactured Solutionsmentioning

confidence: 99%

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Petrov–Galerkin Overset Grid Scheme for the Navier–Stokes Equations with Moving Domains

2015

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J053925In terms of mesh resolution requirements, higher order finite element discretization methods offer a more economic means of obtaining accurate simulations and/or to resolve physics at scales not possible with lower order schemes. For simulations that may have large relative motion between multiple bodies, overset grid methods have demonstrated distinct advantages over mesh movement strategies. Combining these approaches offers the ability to accurately resolve the flow phenomena and interaction that may occur during unsteady moving boundary simulations. Additionally, overset grid techniques when used within a finite element setting mitigate many of the difficulties encountered in finite volume implementations. This paper presents the development of an overset grid methodology for use within a streamline/upwind Petrov-Galerkin formulation for unsteady, viscous, moving boundary simulations. Furthermore, a novel hole cutting procedure based on solutions to Poisson equations is introduced and compared with existing techniques. Order of accuracy is examined via the method of manufactured solutions and the extent of the overlapped region is studied. Overset grid results are presented for several steady-state and timedependent moving boundary simulations with linear, quadratic, and cubic elements.

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Section: B Methods Of Manufactured Solutionsmentioning

confidence: 99%

“…This ultimately may slow the convergence of the GMRES. However, this preconditioner has been used successfully by Galbraith [31]. To this end, two modified approaches, which use a mechanism of global communication among all grids, were explored.…”

Section: B Linearization and Solution Proceduresmentioning

confidence: 99%

Petrov–Galerkin Overset Grid Scheme for the Navier–Stokes Equations with Moving Domains

2015

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“…This feature makes the DG technique well-suited for high-order analyses of complex and full-configuration geometries encountered in air vehicle design. Galbraith 1,3,4,5 has developed a flexible DG framework called XDG. XDG is a Chimera overset code, capable of both 2D and 3D solutions.…”

Section: Introductionmentioning

confidence: 99%

“…2,1 The Discontinuous Galerkin (DG) technique has gained popularity in recent years as a high-order method. Unlike finite difference and finite volume techniques, the DG method is able to achieve high-order accuracy without increasing stencil size.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of a Discontinuous Galerkin Implementation of RANS and Spalart Allmaras Turbulence Model

Schrock

Benek

Galbraith

et al. 2015

53rd AIAA Aerospace Sciences Meeting

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This paper presents the results of an initial evaluation of an implementation of the Spalart Allmaras (SA) turbulence model within the Discontinuous Galerkin (DG) solver XDG developed by Galbraith. 1 The model is applied to three 2D test cases of increasing complexity: a zero-pressure gradient flat plate, a bump in a channel flow, and a backward facing step. Solutions are demonstrated on both single block and overset configurations utilizing second, third, and fourth order accurate schemes. The results show good agreement with those published in the NASA Langley Research Center's Turbulence Modeling Resource database for the SA model utilizing standard finite volume solution techniques. Stability of the method was observed to be significantly dependent upon the grid spacing within the boundary layer, particularly in regions of high gradients in eddy viscosity.

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“…A recursive function expression strategy is suitable for binary operations which cannot be efficiently evaluated element-wise, such as linear algebra matrix multiplication operations 24,25 . …”

Section: B Expression Templates Operator Overloadingmentioning

confidence: 99%

A Verification Driven Process for Rapid Development of CFD Software

Galbraith

Allmaras

Darmofal

2015

53rd AIAA Aerospace Sciences Meeting

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Previous work by the authors has demonstrated a high-order fully-automated output-error based mesh adaptation method suitable for solving the Reynolds-Averaged Navier-Stokes equations. The high-order of accuracy is achieved with a discontinuous Galerkin discretization. While the adaptation method has proven to provide significant reduction in computational cost relative to second-order methods, the authors are currently exploring alternate high-order finite element discretizations to further reduce the computational cost. However, the previously developed software framework is not suitable for all discretizations of interest. Hence, a new software framework is being developed with enhanced maintainability and flexibility relative to the previous framework. This paper focuses on strategies employed to accelerate the development of the new software framework. A software development environment that promotes a verification driven process for software development is presented. The development environment encourages developers to incorporate the verification principles of Verification and Validation as part of the software development process to promote maintainability and collaboration. The software development is further accelerated through the use of automatic differentiation, which is used here to automatically compute the linearization of a mathematical model. This paper outlines an implementation of automatic differentiation with minimal computational overhead relative to manually written linearizations.

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A 3-D Discontinuous Galerkin Chimera Overset Method

Cited by 13 publications

References 8 publications

Petrov–Galerkin Overset Grid Scheme for the Navier–Stokes Equations with Moving Domains

Petrov–Galerkin Overset Grid Scheme for the Navier–Stokes Equations with Moving Domains

Evaluation of a Discontinuous Galerkin Implementation of RANS and Spalart Allmaras Turbulence Model

A Verification Driven Process for Rapid Development of CFD Software

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