On the use of composite grid schemes in computational aerodynamics

Steger, J. L.; Benek, John A.

doi:10.1016/0045-7825(87)90045-4

Cited by 231 publications

(118 citation statements)

References 2 publications

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“…In order to overcome these problems mentioned above, overset grids (Rai 1986;Steger & Benek 1987;Chesshire & Henshaw 1990;Usmanov 1996;Yoshida & Kageyama 2004;Kageyama & Sato 2004;Kageyama 2005) may be one of the best choices. Among these overset grids, the Yin-Yang grid has been applied successfully in simulations of geoscience (Yoshida & Kageyama 2004;Kageyama & Sato 2004;Kageyama 2005).…”

Section: Introductionmentioning

confidence: 99%

THREE-DIMENSIONAL SOLARWINDMODELING FROM THE SUN TO EARTH BY A SIP-CESE MHD MODEL WITH A SIX-COMPONENT GRID

Feng

Yang

Cui

et al. 2010

ApJ

171

144

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The objective of this paper is to explore the application of a six-component overset grid to solar wind simulation with a three-dimensional (3D) Solar-InterPlanetary Conservation Element/Solution Element MHD model. The essential focus of our numerical model is devoted to dealing with: (1) the singularity and mesh convergence near the poles via the use of the six-component grid system, (2) the ∇ · B constraint error via an easy-to-use cleaning procedure by a fast multigrid Poisson solver, (3) the Courant-Friedrichs-Levy number disparity via the Courant-number insensitive method, (4) the time integration by multiple time stepping, and (5) the time-dependent boundary condition at the subsonic region by limiting the mass flux escaping through the solar surface. In order to produce fast and slow plasma streams of the solar wind, we include the volumetric heating source terms and momentum addition by involving the topological effect of the magnetic field expansion factor f S and the minimum angular distance θ b (at the photosphere) between an open field foot point and its nearest coronal hole boundary. These considerations can help us easily code the existing program, conveniently carry out the parallel implementation, efficiently shorten the computation time, greatly enhance the accuracy of the numerical solution, and reasonably produce the structured solar wind. The numerical study for the 3D steady-state background solar wind during Carrington rotation 1911 from the Sun to Earth is chosen to show the above-mentioned merits. Our numerical results have demonstrated overall good agreements in the solar corona with the Large Angle and Spectrometric Coronagraph on board the Solar and Heliospheric Observatory satellite and at 1 AU with WIND observations.

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Section: Introductionmentioning

confidence: 99%

THREE-DIMENSIONAL SOLARWINDMODELING FROM THE SUN TO EARTH BY A SIP-CESE MHD MODEL WITH A SIX-COMPONENT GRID

Feng

Yang

Cui

et al. 2010

ApJ

171

144

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“…The first use of overlapping grids (called composite grids at the time) appeared in papers by Volkov [4,5], who considered approximations to Poisson's equation in regions with corners. Other pioneering work includes that of Starius [6][7][8], Kreiss [9], and Steger et al [10] who referred to the approach as Chimera grids. Since this early work, the overlapping grid technique has been used successfully to solve a wide variety of problems in high-speed reactive flow [2,3,11], reactive and non-reactive multi-material flow [12,13], combustion [14], aerodynamics [15][16][17][18][19][20][21], blood flow [22], flows around ships [23], visco-elastic flows [24], and flows with deforming boundaries [25][26][27], among others.…”

Section: Introductionmentioning

confidence: 99%

Parallel computation of three-dimensional flows using overlapping grids with adaptive mesh refinement

Henshaw¹,

Schwendeman²

2008

Journal of Computational Physics

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This paper describes an approach for the numerical solution of time-dependent partial differential equations in complex three-dimensional domains. The domains are represented by overlapping structured grids, and block-structured adaptive mesh refinement (AMR) is employed to locally increase the grid resolution. In addition, the numerical method is implemented on parallel distributed-memory computers using a domain-decomposition approach. The implementation is flexible so that each base grid within the overlapping grid structure and its associated refinement grids can be independently partitioned over a chosen set of processors. A modified bin-packing algorithm is used to specify the partition for each grid so that the computational work is evenly distributed amongst the processors. All components of the AMR algorithm such as error estimation, regridding, and interpolation are performed in parallel.The parallel time-stepping algorithm is illustrated for initial-boundary-value problems involving a linear advectiondiffusion equation and the (nonlinear) reactive Euler equations. Numerical results are presented for both equations to demonstrate the accuracy and correctness of the parallel approach. Exact solutions of the advection-diffusion equation are constructed, and these are used to check the corresponding numerical solutions for a variety of tests involving different overlapping grids, different numbers of refinement levels and refinement ratios, and different numbers of processors. The problem of planar shock diffraction by a sphere is considered as an illustration of the numerical approach for the Euler equations, and a problem involving the initiation of a detonation from a hot spot in a T-shaped pipe is considered to demonstrate the numerical approach for the reactive case. For both problems, the solutions are shown to be well resolved on the finest grid. The parallel performance of the approach is examined in detail for the shock diffraction problem.

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“…The Cubed Sphere [31] is a type of multiblock grid that has also been developed for solving PDEs on a spherical surface; in [39], this grid is used with a high-order finite-volume method to solve the shallow-water equations. There is a rich literature on the subjects of mapped and multiblock grids that is too extensive to summarize here; we refer the interested reader to several review articles [35,37,2].…”

Section: Major Radiusmentioning

confidence: 99%

High-order finite-volume methods for hyperbolic conservation laws on mapped multiblock grids

McCorquodale

Dorr

Hittinger

et al. 2015

Journal of Computational Physics

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We present an approach to solving hyperbolic conservation laws by finitevolume methods on mapped multiblock grids, extending the approach of Colella, Dorr, Hittinger, and Martin (2011) for grids with a single mapping. We consider mapped multiblock domains for mappings that are conforming at inter-block boundaries. By using a smooth continuation of the mapping into ghost cells surrounding a block, we reduce the inter-block communication problem to finding an accurate, robust interpolation into these ghost cells from neighboring blocks. We demonstrate fourth-order accuracy for the advection equation for multiblock coordinate systems in two and three dimensions.

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On the use of composite grid schemes in computational aerodynamics

Cited by 231 publications

References 2 publications

THREE-DIMENSIONAL SOLARWINDMODELING FROM THE SUN TO EARTH BY A SIP-CESE MHD MODEL WITH A SIX-COMPONENT GRID

THREE-DIMENSIONAL SOLARWINDMODELING FROM THE SUN TO EARTH BY A SIP-CESE MHD MODEL WITH A SIX-COMPONENT GRID

Parallel computation of three-dimensional flows using overlapping grids with adaptive mesh refinement

High-order finite-volume methods for hyperbolic conservation laws on mapped multiblock grids

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