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  • 1
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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
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  • 2
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    Tailoring explicit time-marching schemes to improve convergence characteristics (1990)
    In:  CASI
    Details
    Publication Date: 2013-08-31
    Description: Multi-stage time-stepping schemes, tailored to chosen spatial-differencing operators, are derived and tested. The schemes are constructed to give optimal damping of the high-frequency waves. They are ideal for use with multi-grid acceleration. The concept of characteristic time-stepping, necessary for the extension of the scalar analysis to systems of equations, is presented. The schemes show a marked improvement over Runge-Kutta schemes.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: VKI, Computational Fluid Dynamics, Volume 2; 30 p
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  • 3
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    Towards a genuinely multi-dimensional upwind scheme (1990)
    In:  CASI
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    Publication Date: 2013-08-31
    Description: Methods of incorporating multi-dimensional ideas into algorithms for the solution of Euler equations are presented. Three schemes are developed and tested: a scheme based on a downwind distribution, a scheme based on a rotated Riemann solver and a scheme based on a generalized Riemann solver. The schemes show an improvement over first-order, grid-aligned upwind schemes, but the higher-order performance is less impressive. An outlook for the future of multi-dimensional upwind schemes is given.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: VKI, Computational Fluid Dynamics, Volume 2; 55 p
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  • 4
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    The adaptive, cut-cell Cartesian approach (warts and all) (1995)
    In:  CASI
    Details
    Publication Date: 2013-08-31
    Description: Solution-adaptive methods based on cutting bodies out of Cartesian grids are gaining popularity now that the ways of circumventing the accuracy problems associated with small cut cells have been developed. Researchers are applying Cartesian-based schemes to a broad class of problems now, and, although there is still development work to be done, it is becoming clearer which problems are best suited to the approach (and which are not). The purpose of this paper is to give a candid assessment, based on applying Cartesian schemes to a variety of problems, of the strengths and weaknesses of the approach as it is currently implemented.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: NASA. Langley Research Center, ICASE(LaRC Workshop on Adaptive Grid Methods; p 59-77
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  • 5
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    Adaptive unstructured triangular mesh generation and flow solvers for the Navier-Stokes equations at high Reynolds number (1995)
    In:  CASI
    Details
    Publication Date: 2013-08-31
    Description: A method for generating high quality unstructured triangular grids for high Reynolds number Navier-Stokes calculations about complex geometries is described. Careful attention is paid in the mesh generation process to resolving efficiently the disparate length scales which arise in these flows. First the surface mesh is constructed in a way which ensures that the geometry is faithfully represented. The volume mesh generation then proceeds in two phases thus allowing the viscous and inviscid regions of the flow to be meshed optimally. A solution-adaptive remeshing procedure which allows the mesh to adapt itself to flow features is also described. The procedure for tracking wakes and refinement criteria appropriate for shock detection are described. Although at present it has only been implemented in two dimensions, the grid generation process has been designed with the extension to three dimensions in mind. An implicit, higher-order, upwind method is also presented for computing compressible turbulent flows on these meshes. Two recently developed one-equation turbulence models have been implemented to simulate the effects of the fluid turbulence. Results for flow about a RAE 2822 airfoil and a Douglas three-element airfoil are presented which clearly show the improved resolution obtainable.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: NASA. Langley Research Center, ICASE(LaRC Workshop on Adaptive Grid Methods; p 139-151
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  • 6
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    Adaptive-mesh algorithms for computational fluid dynamics (1993)
    In:  Other Sources
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    Publication Date: 2019-01-25
    Description: The basic goal of adaptive-mesh algorithms is to distribute computational resources wisely by increasing the resolution of 'important' regions of the flow and decreasing the resolution of regions that are less important. While this goal is one that is worthwhile, implementing schemes that have this degree of sophistication remains more of an art than a science. In this paper, the basic pieces of adaptive-mesh algorithms are described and some of the possible ways to implement them are discussed and compared. These basic pieces are the data structure to be used, the generation of an initial mesh, the criterion to be used to adapt the mesh to the solution, and the flow-solver algorithm on the resulting mesh. Each of these is discussed, with particular emphasis on methods suitable for the computation of compressible flows.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: In: Algorithmic trends in computational fluid dynamics; The Institute for Computer Applications in Science and Engineering (ICASE)(LaRC Workshop, NASA Langley Research Center, Hampton, VA, US, Sep. 15; p. 303-337
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  • 7
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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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  • 8
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    A genuinely multi-dimensional upwind cell-vertex scheme for the Euler equations (1989)
    In:  Other Sources
    Details
    Publication Date: 2019-06-28
    Description: A scheme of solving the two-dimensional Euler equations is developed. The scheme is genuinely two-dimensional. At each iteration, the data are locally decomposed into four variables, allowing convection in appropriate directions. This is done via a cell-vertex scheme with a downwind-weighted distribution step. The scheme is conservative and third-order accurate in space. The derivation and stability analysis of the scheme for the convection equation, and the derivation of the extension to the Euler equations are given. Preconditioning techniques based on local values of the convection speeds are discussed. The scheme for the Euler equations is applied to two channel-flow problems. It is shown to converge rapidly to a solution that agrees well with that of a third-order upwind solver.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: AIAA PAPER 89-0095
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  • 9
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    Design of optimally smoothing multistage schemes for the Euler equations (1992)
    In:  Other Sources
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    Publication Date: 2019-07-12
    Description: A recently derived local preconditioning of the Euler equations is shown to be useful in developing multistage schemes suited for multigrid use. The effect of the preconditioning matrix on the spatial Euler operator is to equalize the characteristic speeds. When applied to the discretized Euler equations, the preconditioning has the effect of strongly clustering the operator's eigenvalues in the complex plane. This makes possible the development of explicit marching schemes that effectively damp most high-frequency Fourier modes, as desired in multigrid applications. The technique is the same as developed earlier for scalar convection schemes: placement of the zeros of the amplification factor of the multistage scheme in locations where eigenvalues corresponding to high-frequency modes abound.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Communications in Applied Numerical Methods (ISSN 0748-8025); 8; 10; p. 761-769.
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