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68
The nas parallel benchmarks
- The International Journal of Supercomputer Applications
, 1991
"... A new set of benchmarks has been developed for the performance evaluation of highly parallel supercomputers. These benchmarks consist of ve \parallel kernel " benchmarks and three \simulated application" benchmarks. Together they mimic the computation and data movement characterist ..."
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Cited by 694 (9 self)
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A new set of benchmarks has been developed for the performance evaluation of highly parallel supercomputers. These benchmarks consist of ve \parallel kernel " benchmarks and three \simulated application" benchmarks. Together they mimic the computation and data movement characteristics of large scale computational uid dynamics applications. The principal distinguishing feature of these benchmarks is their \pencil and paper " speci cation | all details of these benchmarks are speci ed only algorithmically. In this way many of the di culties associated with conventional benchmarking approaches on highly parallel systems are avoided. 1
Numerical Solutions of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time-Stepping Schemes
, 1981
"... A new combination of a finite volume discretization in conjunction with carefully designed dissipative terms of third order, and a Runge Kutta time stepping scheme, is shown to yield an effective method for solving the Euler equations in arbitrary geometric domains. The method has been used to deter ..."
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Cited by 517 (78 self)
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A new combination of a finite volume discretization in conjunction with carefully designed dissipative terms of third order, and a Runge Kutta time stepping scheme, is shown to yield an effective method for solving the Euler equations in arbitrary geometric domains. The method has been used to determine the steady transonic flow past an airfoil using an O mesh. Convergence to a steady state is accelerated by the use of a variable time step determined by the local Courant member, and the introduction of a forcing term proportional to the difference between the local total enthalpy and its free stream value.
Analysis and Design of Numerical Schemes for Gas Dynamics 1 Artificial Diffusion, Upwind Biasing, Limiters and Their Effect on Accuracy and Multigrid Convergence
- INTERNATIONAL JOURNAL OF COMPUTATIONAL FLUID DYNAMICS
, 1995
"... The theory of non-oscillatory scalar schemes is developed in this paper in terms of the local extremum diminishing (LED) principle that maxima should not increase and minima should not decrease. This principle can be used for multi-dimensional problems on both structured and unstructured meshes, whi ..."
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Cited by 122 (45 self)
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The theory of non-oscillatory scalar schemes is developed in this paper in terms of the local extremum diminishing (LED) principle that maxima should not increase and minima should not decrease. This principle can be used for multi-dimensional problems on both structured and unstructured meshes, while it is equivalent to the total variation diminishing (TVD) principle for one-dimensional problems. A new formulation of symmetric limited positive (SLIP) schemes is presented, which can be generalized to produce schemes with arbitrary high order of accuracy in regions where the solution contains no extrema, and which can also be implemented on multi-dimensional unstructured meshes. Systems of equations lead to waves traveling with distinct speeds and possibly in opposite directions. Alternative treatments using characteristic splitting and scalar diffusive fluxes are examined, together with a modification of the scalar diffusion through the addition of pressure differences to the momentum equations to produce full upwinding in supersonic flow. This convective upwind and split pressure (CUSP) scheme exhibits very rapid convergence in multigrid calculations of transonic flow, and provides excellent shock resolution at very high Mach numbers.
A Perspective on Computational Algorithms for Aerodynamic Analysis and Design
- Progress in Aerospace Sciences
, 2001
"... This paper exam nes the use of computational fluid dynamics as a tool for aircraft design. It addresses the requirements for effective industrial use, and trade-offs between modeling accuracy and computational costs. Essential elements of algorithm design are discussed in detail, together with a uni ..."
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Cited by 58 (19 self)
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This paper exam nes the use of computational fluid dynamics as a tool for aircraft design. It addresses the requirements for effective industrial use, and trade-offs between modeling accuracy and computational costs. Essential elements of algorithm design are discussed in detail, together with a unified approach to the design of shock capturing schemes. Finally, the paper discusses the use of techniques drawn from control theory to determine optimal aerodynamic shapes. In the future multidisciplinary analysis and optimization should be combined to take account of the trade-offs in the overall performance of the complete system
Multigrid algorithms for compressible flow calculations
- Lecture Notes in Mathematics
, 1985
"... During the last two decades computational methods have transformed the science of aerodynamics. Following the introduction of panel methods for subsonic flow in the sixties [1, 2], and major advances in the simulation of transonic flow by the potential flow approximation in the seventies [3–6], the ..."
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Cited by 48 (24 self)
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During the last two decades computational methods have transformed the science of aerodynamics. Following the introduction of panel methods for subsonic flow in the sixties [1, 2], and major advances in the simulation of transonic flow by the potential flow approximation in the seventies [3–6], the eighties have seen rapid developments in methods for solving the Euler and Navier Stokes equations [7–11]. Multigrid techniques have penetrated this
Positive schemes and shock modelling for compressible flows
- International Journal for Numerical Methods in Fluids
, 1995
"... A unified theory of non-oscillatory finite volume schemes for both structured and unstructured meshes is developed in two parts. In the first part, a theory of local extremum diminishing (LED) and essentially local extremum diminishing (ELED) schemes is developed for scalar conservation laws. This l ..."
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Cited by 37 (2 self)
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A unified theory of non-oscillatory finite volume schemes for both structured and unstructured meshes is developed in two parts. In the first part, a theory of local extremum diminishing (LED) and essentially local extremum diminishing (ELED) schemes is developed for scalar conservation laws. This leads to symmetric and upstream limited positive (SLIP and USLIP) schemes which can be formulated on either structured or unstructured meshes. The second part examines the application of similar ideas to the treatment of systems of conservation laws. An analysis of discrete shock structure leads to conditions on the numerical flux such that stationary discrete shocks can contain a single interior point. The simplest formulation which meets these conditions is a convective upwind and split pressure (CUSP) scheme, in which the coefficient of the pressure differences is fully determined by the coefficient of convective diffusion. Numerical results are presmted which confirm the properties of these schemes. KEY WORDS computational aerodynamics; shock capturing; positive schemes 1.
New Progress in Anisotropic Grid Adaptation for Inviscid and Viscous Flows Simulations
- In 4th Annual Intl. Meshing Roundtable
, 1995
"... Two new ideas for anisotropic adaptation of unstructured triangular grids are presented with particular emphasis to fluid flows computations. The first concept enables a suitable extension of our mesh adaptation to the case of systems of PDE like Navier-Stokes equations and the second makes possible ..."
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Cited by 32 (3 self)
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Two new ideas for anisotropic adaptation of unstructured triangular grids are presented with particular emphasis to fluid flows computations. The first concept enables a suitable extension of our mesh adaptation to the case of systems of PDE like Navier-Stokes equations and the second makes possible a correct boundary layer computation which was until now one of the major weakness of anisotropic adaptations in CFD. KEY WORDS: Mesh, Anisotropic, Adaptation, Delaunay, Metric, CFD. 1 Introduction Three major advantages of unstructured grids over structured ones are the ease for complex geometries to be considered and grid adaptation and general mesh anisotropy concept to be incorporated (see [6], [7], [11]). Of course, the introduction of mesh adaptivity and anisotropy reduces the number of grid elements if the simulated physical phenomena are strongly directional (see [11]) as in the case of shocks and limit layers for fluid flows. However, two major difficulties remain. Firstly, as me...
Articial dissipation models for the Euler equations
- AIAA J
, 1986
"... Various artificial dissipation models that are used with central difference algorithms for the Euler equations are analyzed for their effect on accuracy, stability, and convergence rates. In particular, linear and nonlinear models are investigated using an implicit approximate factorization code (AR ..."
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Cited by 29 (4 self)
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Various artificial dissipation models that are used with central difference algorithms for the Euler equations are analyzed for their effect on accuracy, stability, and convergence rates. In particular, linear and nonlinear models are investigated using an implicit approximate factorization code (ARC2D) for transonic airfoils. Fully implicit application of the dissipation models is shown to improve robustness and convergence rates. The treat-ment of dissipation models at boundaries will be examined. It will be shown that accurate, error free solutions with sharp shocks can be obtained using a central difference algorithm coupled with an appropriate nonlinear artificial dissipation model. I.
