A 2 exp n tree based automated viscous Cartesian grid methodology for feature capturing

Wang, Z.; Chen, R.; Hariharan, Nathan S.; Przekwas, Andrzej; Grove, Darren

doi:10.2514/6.1999-3300

Cited by 24 publications

(12 citation statements)

References 25 publications

(27 reference statements)

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“…The grid has an inherent capability to treat a complicated geometry because of its non-body-fitted property, which is different from other commonly used grids. [1][2][3][4][5] Although its applications to the problem of a stationary body have gained popularity, some factors remain to be solved for the problem of a moving body. The Cartesian grid has a unique property; that is, the grid itself remains stationary as a body moves across it.…”

Section: Introductionmentioning

confidence: 99%

Flow Calculation of Moving Body on Cartesian Grid by Using New Cell-Merging Method.

Lahur

Nakamura

2001

Trans. Japan Soc. Aero. S Sci.

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Flow simulation around a moving body is a challenging problem, especially when there is more than one body moving relative to each other. To tackle this problem, a Cartesian grid is used in this paper, where its non-body-fitted property allows the grid to stay stationary while the bodies move across it. As a result, it requires only local grid modification in the vicinity of body surface, which may lead to a significant saving of computational cost. On the other hand, the body-fitted grids such as structured and tetrahedral-based unstructured grids move with the body; thus global grid modification is necessary during the movement. In the present study we devised a new implementation procedure for an existing two-dimensional cell-merging method to overcome the problem of conservation regarding gas dynamic properties, a problem caused by body movement across a grid. The present method may have a better potential for extension to 3D. It is based on our previous algorithm developed for a 3D unstructured Cartesian grid and was successfully applied to several test cases in this study. In particular, the efficiency of the method is greatly improved by employing a tree-based data structure to reduce the time to find body panels during computation of the cell's geometrical properties.

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Section: Introductionmentioning

confidence: 99%

Flow Calculation of Moving Body on Cartesian Grid by Using New Cell-Merging Method.

Lahur

Nakamura

2001

Trans. Japan Soc. Aero. S Sci.

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“…While the octree structure is often applied, its main drawback consists in its isotropy. In order to avoid this drawback, Wang et al 11 improved the octree method by elaborating an anisotropic mesh generation, the 2 n tree. Use of the 2 n tree data structure allows for variations in the size of mesh elements, which can result in considerable efficiency gains when adaptations of anisotropic mesh help to resolve flow characteristics.…”

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confidence: 99%

“…Use of the 2 n tree data structure allows for variations in the size of mesh elements, which can result in considerable efficiency gains when adaptations of anisotropic mesh help to resolve flow characteristics. For example, Wang et al 11 made a comparison between an octree and a 2 n tree mesh on F-16 aircraft geometry with the maximum refinement criteria set at level 5 for the 2 n tree case. The difference in the number of cells involved with the 2 n tree versus the octree method is larger than 6.…”

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confidence: 99%

Toward a CFD/6 DOF Coupled Model Enhancing Projectile Trajectory Prediction

Luu

Grignon²,

Plourde

2013

21st AIAA Computational Fluid Dynamics Conference

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This article describes a new advanced coupled computational fluid dynamics/flight mechanics designed to compute the flight trajectory of the projectile. A first test has been carried out to compute the unsteady aerodynamics associated with free flight of the finned projectile at supersonic speed. Computed positions and orientations of the projectile have been compared with literature results and close agreements have been underlined. Predicted aerodynamic forces and moments are extracted and have been compared.Nomenclature C = Aerodynamics coefficient vector δ = Total angle attack C p = Specific heat mass at constant pressure η = Azimuth angle C v = Specific heat mass at constant volume κ = Thermal conductivity C d, C I , C S = Smargorinsky coefficient λ i = Quaternion component Cor = Coriolis force μ = Dynamic viscosity d ref = Refinement reference distance μ 0 = Reference dynamic viscosity ds = Surface unit μ T = Turbulent viscosity E = Total energy of mass unit ρ = Volume density f = Function vector of flight mechanics σ ij = Viscous tensor g = Gravity acceleration φ = Roll angle G = Projectile gravity center ψ = precession angle H = Projectile kinetic moment τ = Shear stress I 1 = Projectile longitudinal inertia τ ij = Sub-grid shear tress tensor I 2 , I 3 = Projectile transversal inertia θ = elevation angle J = Projectile inertia matrix ω i = Projectile rotation velocity m = Projectile mass t  = Time step     M  = Transfer matrix between two reference Pr = Prandtl number Pr t = Turbulent Prandtl number q j = Energy sub-grid tensor Q = Quaternion S ij = Deformation tensor u i = Velocity component U = State parameter vector v abs = Projectile absolute velocity x,y,z = Projectile position 1 Doctor, Researcher, FTC Department, Thermal Branch, van-thuan.luu@ensma.fr 2 Doctor, CNRS senior scientist, FTC Department, Thermal Branch, frederic.plource@ensma.fr 3 Doctor, DGA ballistics expert, christophe.grignon@dga.defense.gouv.fr 1 Downloaded by CARLETON UNIVERSITY LIBRARY on March 16, 2015 | http://arc.aiaa.org | I. IntroductionIn the framework of ballistics, the computational study of complete projectile behavior during flight is a challenging problem because of the very complex and multi-coupled physics. The computational fluid dynamic remains difficult to address due to the broad turbulence scales used for depiction of unsteady flow behaviors, especially in the wake of the projectile. The flow field structure obviously depends on the flow regime, i.e. subsonic, transonic and supersonic regime providing specific aerodynamic loads on the projectile due to the multiple physical mechanisms involved: shock waves, detachment/reattachment flows, shear-layer and turbulent wakes. Rotation of gyrostabilized projectiles also significantly contributes to the overall flight trajectory. Significant changes in aerodynamic loads on the projectile will change its relative position in time, thereby directly impinging upon aerodynamic performance. A full Computational Fluid Dynamic (CFD) 1 and a 6 DOF flight mechanics (three ...

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“…Cartesian mesh with a projected boundary layer technique was proposed by Wang et al [15,16] that uses a 2 n [15,16] tree data structure, permitting both anisotropic and isotropic refinements.…”

Section: Anisotropic Amr Techniquesmentioning

confidence: 99%

Parallel Anisotropic Block-Based Adaptive Mesh Refinement Algorithm For Three-Dimensional Flows

Williamschen

Groth

2013

21st AIAA Computational Fluid Dynamics Conference

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A 2 exp n tree based automated viscous Cartesian grid methodology for feature capturing

Cited by 24 publications

References 25 publications

Flow Calculation of Moving Body on Cartesian Grid by Using New Cell-Merging Method.

Flow Calculation of Moving Body on Cartesian Grid by Using New Cell-Merging Method.

Toward a CFD/6 DOF Coupled Model Enhancing Projectile Trajectory Prediction

Parallel Anisotropic Block-Based Adaptive Mesh Refinement Algorithm For Three-Dimensional Flows

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