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Discontinuous Galerkin solutions of the NavierStokes equations using linear multigrid preconditioning. AIAA Paper
, 2007
"... A NewtonKrylov method is developed for the solution of the steady compressible NavierStokes equations using a Discontinuous Galerkin (DG) discretization on unstructured meshes. An element LineJacobi preconditioner is presented which solves a block tridiagonal system along lines of maximum couplin ..."
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Cited by 4 (2 self)
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A NewtonKrylov method is developed for the solution of the steady compressible NavierStokes equations using a Discontinuous Galerkin (DG) discretization on unstructured meshes. An element LineJacobi preconditioner is presented which solves a block tridiagonal system along lines of maximum coupling in the flow. An incomplete blockLU factorization (BlockILU(0)) is also presented as a preconditioner, where the factorization is performed using a reordering of elements based upon the lines of maximum coupling. This reordering is shown to be superior to standard reordering techniques (Nested Dissection, Oneway Dissection, Quotient Minimum Degree, Reverse CuthillMckee) especially for viscous test cases. The BlockILU(0) factorization is performed inplace and a novel algorithm is presented for the application of the linearization which reduces both the memory and CPU time over the traditional dual matrix storage format. A linear pmultigrid algorithm using element LineJacobi and BlockILU(0) smoothing is presented as a preconditioner to GMRES. The linear multigrid preconditioner is shown to significantly improve convergence in terms of the number of linear iterations as well as to reduce the total CPU time required to obtain a converged solution. I.
Review of OutputBased Error Estimation and Mesh Adaptation in Computational Fluid Dynamics
"... Error estimation and control are critical ingredients for improving the reliability of computational simulations. Adjointbased techniques can be used to both estimate the error in chosen solution outputs and to provide local indicators for adaptive refinement. This article reviews recent work on th ..."
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Error estimation and control are critical ingredients for improving the reliability of computational simulations. Adjointbased techniques can be used to both estimate the error in chosen solution outputs and to provide local indicators for adaptive refinement. This article reviews recent work on these techniques for computational fluid dynamics applications in aerospace engineering. The definition of the adjoint as the sensitivity of an output to residual source perturbations is used to derive both the adjoint equation, in fully discrete and variational formulations, and the adjointweighted residual method for error estimation. Assumptions and approximations made in the calculations are discussed. Presentation of the discrete and variational formulations enables a sidebyside comparison of recent work in outputerror estimation using the finite volume method and the finite element method. Techniques for adapting meshes using outputerror indicators are also reviewed. Recent adaptive results from a variety of laminar and Reynoldsaveraged Navierâ€“Stokes applications show the power of outputbased adaptive methods for improving the robustness of computational fluid dynamics computations. However, challenges and areas of additional future research remain, including computable error bounds and robust mesh adaptation mechanics. I.
Petaflops Opportunities for the NASA Fundamental Aeronautics Program
"... The premise of this paper is the observation that the engineering community in general, and the NASA aeronautics program in particular, have not been active participants in the renewed interest in high performance computing at the national level. Advocacy for high performance computing has increasin ..."
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The premise of this paper is the observation that the engineering community in general, and the NASA aeronautics program in particular, have not been active participants in the renewed interest in high performance computing at the national level. Advocacy for high performance computing has increasingly been taken up by the science community with the argument that computational methods are becoming a third pillar of scientific discovery alongside theory and experiment. Computational engineering, on the other hand, has continually been relegated to a set of mature software tools which run on commodity hardware, with the notion that engineering problems are not complex enough to warrant the deployment of stateoftheart hardware on such a vast scale. We argue that engineering practices can benefit equally from an aggressive program in high performance computational methods, and that these problems are at least as important as science problems, particularly with regards to any national competitiveness agenda. Because NASA aeronautics has historically been a principal driver of computational engineering research and development, the current situation represents an opportunity for the NASA aeronautics program to resume its role as a leading advocate for high performance computational engineering at the national level. We outline a sample set of Grand Challenge problems which are used to illustrate the potential benefits a reinvigorated program could produce, and use these examples to identify critical barriers to progress and required areas of investment. We conclude by noting that other communities have spent significant efforts in formulating the case for increased investment in high performance computing activities, and that a similar roadmap will be required for the engineering community. I.
An Automated Reliable Method for TwoDimensional Reynoldsaveraged NavierStokes Simulations
, 2011
"... development of computational fluid dynamics algorithms and increased computational resources have led to the ability to perform complex aerodynamic simulations. Obstacles remain which prevent autonomous and reliable simulations at accuracy levels required for engineering. To consider the solution st ..."
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development of computational fluid dynamics algorithms and increased computational resources have led to the ability to perform complex aerodynamic simulations. Obstacles remain which prevent autonomous and reliable simulations at accuracy levels required for engineering. To consider the solution strategy autonomous and reliable, high quality solutions must be provided without user interaction or detailed previous knowledge about the flow to facilitate either adaptation or solver robustness. One such solution strategy is presented for
A HighOrder, Adaptive, Discontinuous Galerkin Finite . . .
, 2008
"... This thesis presents highorder, discontinuous Galerkin (DG) discretizations of the ReynoldsAveraged NavierStokes (RANS) equations and an outputbased error estimation and mesh adaptation algorithm for these discretizations. In particular, DG discretizations of the RANS equations with the Spalart ..."
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This thesis presents highorder, discontinuous Galerkin (DG) discretizations of the ReynoldsAveraged NavierStokes (RANS) equations and an outputbased error estimation and mesh adaptation algorithm for these discretizations. In particular, DG discretizations of the RANS equations with the SpalartAllmaras (SA) turbulence model are examined. The dual consistency of multiple DG discretizations of the RANSSA system is analyzed. The approach of simply weighting gradient dependent source terms by a test function and integrating is shown to be dual inconsistent. A dual consistency correction for this discretization is derived. The analysis also demonstrates that discretizations based on the popular mixed formulation, where dependence on the state gradient is handled by introducing additional