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Design of optimally smoothing multi-stage schemes for the Euler equations

B. Van Leer

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Design of optimally smoothing multi-stage schemes for the Euler equations

by B. Van Leer

154 Want to read
11 Currently reading

Published 1989 .
Written in English

Edition Notes

ID Numbers
Statement	B. Van Leer.
Series	AIAA 89 1933 CP
Open Library	OL17848073M

After a review of mathematical models of fluid flow, methods for solving the transonic potential flow equation (of mixed type) are examined. The central part of the article discusses the formulation and implementation of shock‐capturing schemes for the Euler and Navier–Stokes equations. An optimal multistage scheme was used for the time integration, and the multistage coefficients were modified by Tai et al., and redefined using the Courant number for multidimensional use. Also, a residual smoothing method was imposed to accelerate convergence and to improve numerical stability. 4. Results and Discussion Initial ConditionsCited by: 2.

ods for ordinary diﬀerential equations. The implicit Euler method and stiﬀ diﬀerential equations A minor-looking change in the method, already considered by Euler in , makes a big diﬀer-ence: taking as the argument of f the new value instead of the previous one yields y n+1 = y n +hf(t n+1,y n+1), from which y n+1 is now File Size: KB. 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.

methods for computing steady solutions of the Euler and Navier-Stokes equations are the multi-stage methods pioneered by Jameson et al. This lecture concerns the design of explicit multi-stage schemes for the Euler equations, for use in a multi-grid strategy. For the Euler equations, it is suggested to instead use a corresponding pressure sensor. Furthermore, ri+1/2 is the scalar diffusion coefﬁcient, given by rj+1/2 = max(rj,rj+1). It approximates the spectral radius and is chosen instead of a matrix valued diffusion as in other versions of this Size: 3MB.

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Design of optimally smoothing multi-stage schemes for the Euler equations by B. Van Leer Download PDF EPUB FB2

Design of Optimally Smoothing Multi-Stage Schemes for the Euler Equations Bram van Leer* Chang-Hsien Tait and Kenneth G. Powell$ The University of Michigan Department of Aerospace Engineering Abstract In this paper, a method is developed for designing multi-stage schemes that give optimal damping of high-Cited by: Design of optimally smoothing multistage schemes for the euler equations Bram van Leer Department of Aerospace Engineering, The University of Michigan Cited by: Design of optimally smoothing multi-stage schemes for the Euler equations.

Weighted compact high-order nonlinear schemes for the Euler equations. Xiaogang Deng, Multi-stage schemes for the Euler and Navier-Stokes equations with optimal smoothing. JOHN LYNN and. [Show full abstract] a method was developed for designing optimally smoothing multi-stage time-marching schemes, given any spatial-differencing operator.

The analysis was extended to the Euler. PDF | A recently derived local preconditioning of the Euler equations is shown to be useful in developing multistage schemes suited for multigrid use. | Find, read and cite all the research you. 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. AIREX: Design of optimally smoothing multi-stage schemes for the Euler equations In this paper, a method is developed for designing multi-stage schemes that give optimal damping of high-frequencies for a given spatial-differencing operator.

The objective of the method is to design schemes that combine well with multi-grid acceleration. smoothing properties of multistage scheme was extended to a two-dimensional scalar convection equation by Catalano and Deconick5 and, more satisfactorily, by Lynn and Van Leer.6 In the latter work, the optimization method is extended to the system of Euler equations, using the local preconditioning of Van Leer et al.7 to.

The objective of the method is to design schemes that combine well with multi-grid acceleration. The schemes are tested on a nonlinear scalar equation, and compared to Runge-Kutta schemes with the maximum stable time-step.

The optimally smoothing schemes perform better than the Runge-Kutta schemes, even on a single grid. Multi-Stage Schemes for the Euler and Navier-Stokes Equations with Optimal Smoothing John F.

Lynn* and Bram van Leert Department of Aerospace Engineering, The University of Michigan, Ann Arbor, MI Abstract there was a local preconditioning matrix that removes the spread among the characteristic speeds as much asCited by: B.

van Leer, C. Tai, and K. Powell, “Design of optimally-smoothing multi-stage schemes for the Euler equations,” in AIAA 9th Computational Fluid Dynamics Conference, Cited by: 1. Design of Optimally-Smoothing Multi-stage Schemes for the Euler Equations () 21 K.

Riemslagh, E. Dick, A multigrid method for steady Euler equations on unstructured adaptive grids, 6th Copper Mountain Conf. on Multigrid Methods, NASA Conference Publication, Cited by: B.

van Leer, C. Tai, and K. Powell, “Design of optimally-smoothing multi-stage schemes for the Euler equations,” AIAA Paper 89–CP, Google ScholarCited by: 6. The scheme is based on the same elements that make up many modern compressible gas dynamics codes: a high-resolution upwinding based on an approximate Riemann solver for MHD and limited reconstruction; an optimally smoothing multi-stage time-stepping scheme; and solution-adaptive refinement and coarsening.

In addition, a method for increasing the accuracy of the scheme by Cited by: An adaptive Cartesian mesh algorithm for the Euler equations in arbitrary geometries.

MARSHA BERGER and; RANDALL LEVEQUE; Design of optimally smoothing multi-stage schemes for the Euler equations. BRAM VA, CHANG-HSIEN TAI and; A central finite volume TVD scheme for the calculation of supersonicand hypersonic flow fields around complex.

Inhe embarked on a very large project, to achieve steady Euler solutions in O(N) operations by a purely explicit methodology. There were three crucial components to this strategy: 1. Optimally smoothing multistage single-grid schemes for advections 2. Local preconditioning of the Euler equations 3.

Semi-coarsened multigrid relaxationDoctoral advisor: Hendrik C. van de Hulst. After having converted the optimal parameters found in previous studies (e.g.

Van Leer, C.H. Tai, K.G. Powell, Design of optimally smoothing multi-stage schemes for the Euler equations, AIAA Paper]) we compare them with those that we obtain when we optimize for an integrated 2-grid V-cycle and show that this results in.

van Leer, C.H. Tai, K.G. Powell, Design of Optimally-Smoothing Multi-stage Schemes for the Euler Equations (). CPRF21 K. Riemslagh, E. Dick, A multigrid method for steady Euler equations on unstructured adaptive grids, 6th Copper Mountain Conf. on Multigrid Methods, NASA Conference Publication, Cited by: Two dimensional optimization of smoothing properties of multistage schemes applied to hyperbolic equations This report provides a numerical technique for optimizing the smoothing properties of multi-stage explicit time integration schemes for à general spatial discretization of the 2D advection equation.

with the Forward Euler scheme Cited by: Smoothing Multi-Stage Schemes for the Euler Equations," Communications in Applied Nu- merical Mathematics, vol.

8, pp. {, [5] E. Mayer and K. Powell, \Viscous and Inviscid Instabilities of a Trailing Vortex,". This solver which combined the adjective upwind splitting method (AUSM) family of low-diffusion flux-splitting scheme with an optimally smoothing multistage scheme and the time-derivative preconditioning is used to solve both the compressible and incompressible Euler and Navier-Stokes by: 4.

Flux Schemes for Solving Nonlinear Systems of Conservation Laws (J M Ghidaglia) A Lax–Wendroff Type Theorem for Residual Schemes (R Abgrall et al.) Kinetic Schemes for Solving Saint–Venant Equations on Unstructured Grids (M O Bristeau & B Perthame) Nonlinear Projection Methods for Multi-Entropies Navier–Stokes Systems (C Berthon & F Coquel).Dispersive smoothing for the Euler-Korteweg model Corentin Audiard Ap Abstract The Euler-Korteweg system consists in a quasi-linear, dispersive perturba-tion of the Euler equations.

The Cauchy problem has been studied in any dimen-sion d 1 by Benzoni-Danchin-Descombes, who obtained local well-posedness.