A Finite-Volume High-Order ENO Scheme for Two-Dimensional Hyperbolic Systems

Casper, Jay; Atkins, Harold L.

doi:10.1006/jcph.1993.1091

Cited by 123 publications

(98 citation statements)

References 4 publications

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“…Until now, very few attempts have been made to adapt these ideas to multidimensional flows (see for example [9,11]), to smoothly varying grids, or especially to unstructured grids.…”

Section: Introductionmentioning

confidence: 99%

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On Essentially Non-oscillatory Schemes on Unstructured Meshes: Analysis and Implementation

Abgrall

1994

Journal of Computational Physics

371

175

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A few years ago, the class of Essentially Non-Oscillatory Schemes for the numerical simulation of hyperbolic equations and systems was constructed. Since then, some extensions have been made to multidimensional simulations of compressible flows, mainly in the context of very regular structured meshes. In this paper, we first recall and improve the results of an earlier paper about non-oscillatory reconstruction on unstructured meshes, emphasising the effective calculation of the reconstruction. Then we describe a class of numerical schemes on unstructured meshes and give some applications for its third order version. This demonstrates that a higher order of accuracy is indeed obtained, even on very irregular meshes. Accesion ForUfLirL"i Li46PEZTED 5NTIS CRA&I

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“…Until now, very few attempts have been made to adapt these ideas to multidimensional flows (see for example [9,11]), to smoothly varying grids, or especially to unstructured grids.…”

Section: Introductionmentioning

confidence: 99%

“…Atkins & Casper [11] have used a tensor product of ID-reconstructions to derive their numerical scheme. This is possible because they assume a regular transformation between a Cartesian mesh of [0, 1] x [0, 1] and their computational grid.…”

Section: Introductionmentioning

confidence: 99%

On Essentially Non-oscillatory Schemes on Unstructured Meshes: Analysis and Implementation

Abgrall

1994

Journal of Computational Physics

371

175

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“…In this case, the reconstruction operator is applied to a set of volume-weighted averages {i Ui}, and therefore sufficient smoothness in a spatial transformation is required. 5 However, another option exists for the ENO-FV algorithm. The polynomial approximation can be performed in physical space, which releases such burdensome restrictions on grid smoothness.…”

Section: Discrete Formulationsmentioning

confidence: 99%

“…7 , 8 However, the multidimensional, finite-volume TR operator can be readily implemented because it is defined as a product of one-dimensional operators. 5 When required, the finite-volume algorithms will be distinguished as ENO-FV-TR and ENO-FV-PR.…”

Section: Discrete Formulationsmentioning

confidence: 99%

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Comparison of two formulations for high-order accurate essentially nonoscillatory schemes

1994

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Practical aspects of higher-order numerical schemes for wave propagation phenomena

Gaitonde

Shang

Young

1999

Int. J. Numer. Meth. Engng.

166

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This paper examines practical issues related to the use of compact-di erence-based fourth-and sixth-order schemes for wave propagation phenomena with focus on Maxwell's equations of electromagnetics. An outline of the formulation and scheme optimization is followed by an assessment of the error accruing from application on stretched meshes with two approaches: transformed plane method and physical space di erencing. In the ÿrst technique, the truncation error expansion for the sixth-order compact scheme conÿrms that the order of accuracy is preserved if a consistent mesh reÿnement strategy is followed and further that metrics should be evaluated numerically even if analytic expressions are available. Physical space-di erencing formulas are derived for the ÿve-point stencil by expressing the coe cients in terms of local spacing ratios. The order of accuracy of the reconstruction operator is then veriÿed with a numerical experiment on stretched meshes. To ensure stability for a broad range of problems, Fourier analysis is employed to develop a single-parameter family of up to tenth-order tridiagonal-based spatial ÿlters. The implementation of these ÿlters is discussed in terms of their e ect on the interior scheme as well as in a 1-D cavity where they are employed to suppress a late-time instability. The paper concludes after demonstrating the application of the scheme to several 3-D canonical problems utilizing Cartesian as well as curvilinear meshes.

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A Finite-Volume High-Order ENO Scheme for Two-Dimensional Hyperbolic Systems

Cited by 123 publications

References 4 publications

On Essentially Non-oscillatory Schemes on Unstructured Meshes: Analysis and Implementation

On Essentially Non-oscillatory Schemes on Unstructured Meshes: Analysis and Implementation

Comparison of two formulations for high-order accurate essentially nonoscillatory schemes

Practical aspects of higher-order numerical schemes for wave propagation phenomena

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