Hyperbolicity and Optimal Coordinates for the Three-Dimensional Supersonic Euler Equations

Hui, W. H.; He, Yong

doi:10.1137/s0036139995282712

Cited by 16 publications

(15 citation statements)

References 20 publications

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“…is quite similar to (12), but it is only weakly hyperbolic for any h, although the sub-system representing the physical conservation laws and the sub-system representing the geometric conservation laws are each strongly hyperbolic [17].…”

Section: Hyperbolicity Of the 2-d Unsteady Euler Equations In The Unimentioning

confidence: 99%

“…The eigenvalues of (14) can be found using a method similar to [17], and the results are as follows:…”

Section: Hyperbolicity Of the 2-d Unsteady Euler Equations In The Unimentioning

confidence: 99%

“…After a series of studies [10][11][12][13][14][15][16][17] on steady supersonic flow, it was found that the advantages of Lagrangian coordinates arise from computational cells moving in the direction of the fluid particles but not with their speeds. It was also found that literally following fluid particles, as does Lagrangian, not only causes computational cells to deform with the fluid but also renders the governing equations for inviscid supersonic flow not fully hyperbolic, as there is no complete set of eigenvectors, although all eigenvalues are still real.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Unified Coordinate System for Solving the Two-Dimensional Euler Equations

Hui¹,

Li²,

Li³

1999

Journal of Computational Physics

114

103

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Section: Hyperbolicity Of the 2-d Unsteady Euler Equations In The Unimentioning

confidence: 99%

“…The eigenvalues of (14) can be found using a method similar to [17], and the results are as follows:…”

Section: Hyperbolicity Of the 2-d Unsteady Euler Equations In The Unimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Unified Coordinate System for Solving the Two-Dimensional Euler Equations

Hui¹,

Li²,

Li³

1999

Journal of Computational Physics

114

103

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“…We shall use the unsplit finite volume method applying the Godunov upwind fluxes across each intercell boundary with the MUSCL update to higher resolution in space to solve system (4). The computation will be done entirely in the λ-ξ -η-ζ space.…”

Section: Solution Strategiesmentioning

confidence: 99%

A Unified Coordinate System for Solving the Three-Dimensional Euler Equations

Hui¹,

Kudriakov²

2001

Journal of Computational Physics

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Two general coordinate systems have been used extensively in computational fluid dynamics: the Eulerian and the Lagrangian. The Eulerian coordinates cause excessive numerical diffusion across flow discontinuities, slip lines in particular. The Lagrangian coordinates, on the other hand, can resolve slip lines sharply but cause severe grid deformation, resulting in large errors and even breakdown of the computation. Recently, Hui et al. (J. Comput. Phys. 153, 596 (1999)) have introduced a unified coordinate system which moves with velocity hq, q being velocity of the fluid particle. It includes the Eulerian system as a special case when h = 0 and the Lagrangian when h = 1 and was shown to be superior to both Eulerian and Lagrangian systems for the two-dimensional Euler equations of gas dynamics when h is chosen to preserve the grid angles. The main purpose of this paper is to extend the work of Hui et al. to the three-dimensional Euler equations. In this case, the free function h is chosen so as to preserve grid skewness. This results in a coordinate system which avoids the excessive numerical diffusion across slip lines in the Eulerian coordinates and avoids severe grid deformation in the Lagrangian coordinates; yet it retains sharp resolution of slip lines, especially for steady flow.

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“…The existence of an optimal coordinate system is of fundamental importance in the numerical computation of steady gas flow. The computation then marches along the streamlines and w x is thus robust, accurate, and efficient 10,15 . w x On the other hand, in 16 , it has been established recently that there exists a remarkable connection between complex-lamellar hydrodynamic motions and a Heisenberg spin equation which, in a certain reduction, is associated with the nonlinear Schrodinger equation.…”

Section: Introductionmentioning

confidence: 99%

On Complex-Lamellar Motion of a Prim Gas

Rogers

Schief

Hui

2002

Journal of Mathematical Analysis and Applications

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An intrinsic formulation of Prim's canonical equations of gas dynamics is employed to establish a generalization of Crocco's theorem to complex-lamellar motion. This new result is then employed to establish the existence of a Heisenberg spin-type equation in such motion. The optimal coordinate systems in the generalized Lagrangian method which are known to exist only in complex-lamellar motion are then shown by intrinsic geometric methods to correspond to a marching direction along geodesics on generalized Bernoulli surfaces. ᮊ 2002 Elsevier Science

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Hyperbolicity and Optimal Coordinates for the Three-Dimensional Supersonic Euler Equations

Cited by 16 publications

References 20 publications

A Unified Coordinate System for Solving the Two-Dimensional Euler Equations

A Unified Coordinate System for Solving the Two-Dimensional Euler Equations

A Unified Coordinate System for Solving the Three-Dimensional Euler Equations

On Complex-Lamellar Motion of a Prim Gas

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