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  • 1995-1999  (6)
  • 1
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    An Accuracy Assessment of Cartesian-Mesh Approaches for the Euler Equations (1995)
    Elsevier
    Details
    Publication Date: 1995-03-01
    Print ISSN: 0021-9991
    Electronic ISSN: 1090-2716
    Topics: Computer Science , Physics
    Published by Elsevier
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    PAPER CURRENT
  • 2
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    A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations (1995)
    In:  CASI
    Details
    Publication Date: 2013-08-31
    Description: A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells are created using polygon-clipping algorithms. The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded: A gradient-limited, linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The more robust of a series of viscous flux functions is used to provide the viscous fluxes at the cell interfaces. Adaptively-refined solutions of the Navier-Stokes equations using the Cartesian, cell-based approach are obtained and compared to theory, experiment and other accepted computational results for a series of low and moderate Reynolds number flows.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Surface Modeling, Grid Generation, and Related Issues in Computational Fluid Dynamic (CFD) Solutions; p 207-224
    Format: application/pdf
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    NASA TECHNICAL REPORTS
  • 3
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    Adaptively Refined Euler and Navier-Stokes Solutions with a Cartesian-Cell Based Scheme (1995)
    In:  CASI
    Details
    Publication Date: 2014-10-15
    Description: A Cartesian-cell based scheme with adaptive mesh refinement for solving the Euler and Navier-Stokes equations in two dimensions has been developed and tested. Grids about geometrically complicated bodies were generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells were created using polygon-clipping algorithms. The grid was stored in a binary-tree data structure which provided a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations were solved on the resulting grids using an upwind, finite-volume formulation. The inviscid fluxes were found in an upwinded manner using a linear reconstruction of the cell primitives, providing the input states to an approximate Riemann solver. The viscous fluxes were formed using a Green-Gauss type of reconstruction upon a co-volume surrounding the cell interface. Data at the vertices of this co-volume were found in a linearly K-exact manner, which ensured linear K-exactness of the gradients. Adaptively-refined solutions for the inviscid flow about a four-element airfoil (test case 3) were compared to theory. Laminar, adaptively-refined solutions were compared to accepted computational, experimental and theoretical results.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: NASA. Langley Research Center, ICASE(LaRC Workshop on Adaptive Grid Methods; p 153-161
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    NASA TECHNICAL REPORTS
  • 4
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    Solution-Adaptive Cartesian Cell Approach for Viscous and Inviscid Flows (1996)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: A Cartesian cell-based approach for adaptively refined solutions of the Euler and Navier-Stokes equations in two dimensions is presented. Grids about geometrically complicated bodies are generated automatically, by the recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal cut cells are created using modified polygon-clipping algorithms. The grid is stored in a binary tree data structure that provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite volume formulation. The convective terms are upwinded: A linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The results of a study comparing the accuracy and positivity of two classes of cell-centered, viscous gradient reconstruction procedures is briefly summarized. Adaptively refined solutions of the Navier-Stokes equations are shown using the more robust of these gradient reconstruction procedures, where the results computed by the Cartesian approach are compared to theory, experiment, and other accepted computational results for a series of low and moderate Reynolds number flows.
    Keywords: Fluid Mechanics and Heat Transfer
    Type: NASA-TM-112891 , NAS 1.15:112891 , AIAA Journal; 34; 5; 938-945
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    NASA TECHNICAL REPORTS
  • 5
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    A mixed volume grid approach for the Euler and Navier-Stokes equations (1996)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: An approach for solving the compressible Euler and Navier-Stokes equations upon meshes composed of nearly arbitrary polyhedra is described. Each polyhedron is constructed from an arbitrary number of triangular and quadrilateral face elements, allowing the unified treatment of tetrahedral, prismatic, pyramidal, and hexahedral cells, as well the general cut cells produced by Cartesian mesh approaches. The basics behind the numerical approach and the resulting data structures are described. The accuracy of the mixed volume grid approach is assessed by performing a grid refinement study upon a series of hexahedral, tetrahedral, prismatic, and Cartesian meshes for an analytic inviscid problem. A series of laminar validation cases are made, comparing the results upon differing grid topologies to each other, to theory, and experimental data. A computation upon a prismatic/tetrahedral mesh is made simulating the laminar flow over a wall/cylinder combination.
    Keywords: AERODYNAMICS
    Type: NASA-TM-107135 , NAS 1.15:107135 , AIAA PAPER 96-0762 , E-10065 , NIPS-96-07909 , Aerospace Sciences Meeting and Exhibit; Jan 15, 1996 - Jan 18, 1996; Reno, NV; United States
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    NASA TECHNICAL REPORTS
  • 6
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    An accuracy assessment of Cartesian-mesh approaches for the Euler equations (1995)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: A critical assessment of the accuracy of Cartesian-mesh approaches for steady, transonic solutions of the Euler equations of gas dynamics is made. An exact solution of the Euler equations (Ringleb's flow) is used not only to infer the order of the truncation error of the Cartesian-mesh approaches, but also to compare the magnitude of the discrete error directly to that obtained with a structured mesh approach. Uniformly and adaptively refined solutions using a Cartesian-mesh approach are obtained and compared to each other and to uniformly refined structured mesh results. The effect of cell merging is investigated as well as the use of two different K-exact reconstruction procedures. The solution methodology of the schemes is explained and tabulated results are presented to compare the solution accuracies.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-TM-111200 , NAS 1.15:111200 , NIPS-96-07173 , (ISSN 0021-9991)
    Format: application/pdf
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