A locally refined rectangular grid finite element method: Application to computational fluid dynamics and computational physics

Young, David P.; Melvin, Robin G.; Bieterman, Michael B.; Johnson, F. T.; Samant, S. S.; Bussoletti, John E.

doi:10.1016/0021-9991(91)90291-r

Cited by 164 publications

(102 citation statements)

References 12 publications

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“…Usually the finer grids are all constructed using the same rules of thumb, so that seriously inadequate local gridding will remain inadequate. One notable exception to solving on fixed grids is the full potential/integral boundary layer code TRANAIR ( [15], [2]), which from its inception in 1985 was intended to be a solution adaptive grid code. Its success (well over a million complex geometry cases run to date) has inspired the authors to seek a similar capability for solving the Reynolds Averaged Navier-Stokes equations about complex geometries in the corners of the flight envelope.…”

Section: Grid Convergencementioning

confidence: 99%

Observations Regarding Algorithms Required for Robust CFD Codes

Johnson

Kamenetskiy

Melvin

et al. 2011

Math. Model. Nat. Phenom.

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Abstract. Over the last three decades Computational Fluid Dynamics (CFD) has gradually joined the wind tunnel and flight test as a primary flow analysis tool for aerodynamic designers. CFD has had its most favorable impact on the aerodynamic design of the high-speed cruise configuration of a transport. This success has raised expectations among aerodynamicists that the applicability of CFD can be extended to the full flight envelope. However, the complex nature of the flows and geometries involved places substantially increased demands on the solution methodology and resources required. Currently most simulations involve Reynolds-Averaged Navier-Stokes (RANS) codes although Large Eddy Simulation (LES) and Detached Eddy Suimulation (DES) codes are occasionally used for component analysis or theoretical studies. Despite simplified underlying assumptions, current RANS turbulence models have been spectacularly successful for analyzing attached, transonic flows. Whether or not these same models are applicable to complex flows with smooth surface separation is an open question. A prerequisite for answering this question is absolute confidence that the CFD codes employed reliably solve the continuous equations involved. Too often, failure to agree with experiment is mistakenly ascribed to the turbulence model rather than inadequate numerics. Grid convergence in three dimensions is rarely achieved. Even residual convergence on a given grid is often inadequate. This paper discusses issues involved in residual and especially grid convergence.

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Section: Grid Convergencementioning

confidence: 99%

Observations Regarding Algorithms Required for Robust CFD Codes

Johnson

Kamenetskiy

Melvin

et al. 2011

Math. Model. Nat. Phenom.

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“…This cut-cell approach allows the grid to arbitrarily intersect the boundary and the CFD code is modified to account for this arbitrarily intersection. Cartesian cut-cell methods have been very successful for Euler simulations [31][32][33][34] and some viscous simulations. 35,36 This cut cell method has also been applied to simplex meshes.…”

Section: -14mentioning

confidence: 99%

Parallel Anisotropic Tetrahedral Adaptation

Park¹,

Darmofal

2008

46th AIAA Aerospace Sciences Meeting and Exhibit

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An adaptive method that robustly produces high aspect ratio tetrahedra to a general 3D metric specification without introducing hybrid semi-structured regions is presented. The elemental operators and higher-level logic is described with their respective domaindecomposed parallelizations. An anisotropic tetrahedral grid adaptation scheme is demonstrated for 1000-1 stretching for a simple cube geometry. This form of adaptation is applicable to more complex domain boundaries via a cut-cell approach as demonstrated by a parallel 3D supersonic simulation of a complex fighter aircraft. To avoid the assumptions and approximations required to form a metric to specify adaptation, an approach is introduced that directly evaluates interpolation error. The grid is adapted to reduce and equidistribute this interpolation error calculation without the use of an intervening anisotropic metric. Direct interpolation error adaptation is illustrated for 1D and 3D domains.

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“…These techniques have been very successful in solving complicated engineering problems (e.g. [2,3]). The basic idea behind fictitious-domain techniques is to extend domains of complicated shapes to those of simpler shapes for which the generation of meshes is simple and well-established efficient numerical solvers can be applied.…”

Section: Introductionmentioning

confidence: 99%

An integral‐collocation‐based fictitious‐domain technique for solving elliptic problems

Mai‐Duy

See

Tran-Cong

2007

Commun. Numer. Meth. Engng.

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SUMMARYThis paper presents a new fictitious-domain technique for numerically solving elliptic second-order partial-differential equations (PDEs) in complex geometries. The proposed technique is based on the use of integral collocation schemes and Chebyshev polynomials. The boundary conditions on the actual boundary are implemented by means of integration constants. The method works for both Dirichlet and Neumann boundary conditions. Several test problems are considered to verify the technique. Numerical results show that the present method yields spectral accuracy for smooth (analytic) problems.

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A locally refined rectangular grid finite element method: Application to computational fluid dynamics and computational physics

Cited by 164 publications

References 12 publications

Observations Regarding Algorithms Required for Robust CFD Codes

Observations Regarding Algorithms Required for Robust CFD Codes

Parallel Anisotropic Tetrahedral Adaptation

An integral‐collocation‐based fictitious‐domain technique for solving elliptic problems

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