On the Construction, Comparison, and Local Characteristic Decomposition for High-Order Central WENO Schemes

Qiu, Jianxian; Shu, Chi‐Wang

doi:10.1006/jcph.2002.7191

Cited by 233 publications

(190 citation statements)

References 31 publications

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“…In particular, it appears to become successively less satisfactory as the order of accuracy of the reconstruction is increased. See [7] for a detailed discussion with respect to central WENO schemes, for instance.…”

Section: Reconstructionmentioning

confidence: 44%

WENOCLAW: A Higher Order Wave Propagation Method

Ketcheson¹,

LeVeque²

2008

Hyperbolic Problems: Theory, Numerics, Applications

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Section: Reconstructionmentioning

confidence: 44%

WENOCLAW: A Higher Order Wave Propagation Method

Ketcheson¹,

LeVeque²

2008

Hyperbolic Problems: Theory, Numerics, Applications

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“…Moreover, HR does not use local characteristic decomposition and thus is convenient for unstructured meshes. Note that the traditional ENO/WENO reconstruction should be performed on characteristic variables (e.g., [7,8,19]) when the order of accuracy of the scheme gets higher, otherwise spurious oscillations may occur beyond third order accuracy.…”

Section: Introductionmentioning

confidence: 48%

Point-wise hierarchical reconstruction for discontinuous Galerkin and finite volume methods for solving conservation laws

Liu

Lin

et al. 2011

Journal of Computational Physics

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We develop a new hierarchical reconstruction (HR) method [17,28] for limiting solutions of the discontinuous Galerkin and finite volume methods up to fourth order of accuracy without local characteristic decomposition for solving hyperbolic nonlinear conservation laws on triangular meshes. The new HR utilizes a set of point values when evaluating polynomials and remainders on neighboring cells, extending the technique introduced in Hu, Li and Tang [9]. The point-wise HR simplifies the implementation of the previous HR method which requires integration over neighboring cells and makes HR easier to extend to arbitrary meshes. We prove that the new point-wise HR method keeps the order of accuracy of the approximation polynomials. Numerical computations for scalar and system of nonlinear hyperbolic equations are performed on two-dimensional triangular meshes. We demonstrate that the new hierarchical reconstruction generates essentially non-oscillatory solutions for schemes up to fourth order on triangular meshes. ‡

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“…In the case k = 1, u g =ũ g holds due to the coupling conditions (16). For the step k − 1 → k we first look at the generalized Riemann problem at the 2-junction.…”

Section: Proof (Proof Of Theorem 2) the Proof Is By Induction Over Ksupporting

confidence: 41%

“…In the past decades high order accurate numerical methods for hyperbolic conservation laws have been developed, such as WENO- [14,15,16] or ADER-schemes [17,18,19,20]. These methods have proven their efficiency in many challenging applications [21,22].…”

Section: Introductionsupporting

confidence: 40%

ADER schemes and high order coupling on networks of hyperbolic conservation laws

Borsche

Kall

2014

Journal of Computational Physics

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In this article we present a method to extend high order finite volume schemes to networks of hyperbolic conservation laws with algebraic coupling conditions. This method is based on an ADER approach in time to solve the generalized Riemann problem at the junction. Additionally to the high order accuracy, this approach maintains an exact conservation of quantities if stated by the coupling conditions. Several numerical examples confirm the benefits of a high order coupling procedure for high order accuracy and stable shock capturing.

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On the Construction, Comparison, and Local Characteristic Decomposition for High-Order Central WENO Schemes

Cited by 233 publications

References 31 publications

WENOCLAW: A Higher Order Wave Propagation Method

WENOCLAW: A Higher Order Wave Propagation Method

Point-wise hierarchical reconstruction for discontinuous Galerkin and finite volume methods for solving conservation laws

ADER schemes and high order coupling on networks of hyperbolic conservation laws

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