The Experts below are selected from a list of 9132 Experts worldwide ranked by ideXlab platform
Jianxian Qiu - One of the best experts on this subject based on the ideXlab platform.
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runge kutta discontinuous galerkin method with a simple and compact hermite weno limiter
Communications in Computational Physics, 2016Co-Authors: Jun Zhu, Chiwang Shu, Xinghui Zhong, Jianxian QiuAbstract:In this paper, we propose a new type of weighted essentially non-oscillatory (WENO) limiter, which belongs to the class of Hermite WENO (HWENO) Limiters, for the Runge-Kutta discontinuous Galerkin (RKDG) methods solving hyperbolic conservation laws. This new HWENO limiter is a modification of the simple WENO limiter proposed recently by Zhong and Shu [29]. Both Limiters use information of the DG solutions only from the target cell and its immediate neighboring cells, thus maintaining the original compactness of the DG scheme. The goal of both Limiters is to obtain high order accuracy and non-oscillatory properties simultaneously. The main novelty of the new HWENO limiter in this paper is to reconstruct the polynomial on the target cell in a least square fashion [8] while the simple WENO limiter [29] is to use the entire polynomial of the original DG solutions in the neighboring cells with an addition of a constant for conservation. The modification in this paper improves the robustness in the computation of problems with strong shocks or contact discontinuities, without changing the compact stencil of the DG scheme. Numerical results for both one and two dimensional equations including Euler equations of compressible gas dynamics are provided to illustrate the viability of this modified limiter.
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runge kutta discontinuous galerkin method using a new type of weno Limiters on unstructured meshes
Journal of Computational Physics, 2013Co-Authors: Jun Zhu, Chiwang Shu, Xinghui Zhong, Jianxian QiuAbstract:In this paper we generalize a new type of Limiters based on the weighted essentially non-oscillatory (WENO) finite volume methodology for the Runge–Kutta discontinuous Galerkin (RKDG) methods solving nonlinear hyperbolic conservation laws, which were recently developed in [32] for structured meshes, to two-dimensional unstructured triangular meshes. The key idea of such Limiters is to use the entire polynomials of the DG solutions from the troubled cell and its immediate neighboring cells, and then apply the classical WENO procedure to form a convex combination of these polynomials based on smoothness indicators and nonlinear weights, with suitable adjustments to guarantee conservation. The main advantage of this new limiter is its simplicity in implementation, especially for the unstructured meshes considered in this paper, as only information from immediate neighbors is needed and the usage of complicated geometric information of the meshes is largely avoided. Numerical results for both scalar equations and Euler systems of compressible gas dynamics are provided to illustrate the good performance of this procedure.
Chiwang Shu - One of the best experts on this subject based on the ideXlab platform.
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runge kutta discontinuous galerkin method with a simple and compact hermite weno limiter
Communications in Computational Physics, 2016Co-Authors: Jun Zhu, Chiwang Shu, Xinghui Zhong, Jianxian QiuAbstract:In this paper, we propose a new type of weighted essentially non-oscillatory (WENO) limiter, which belongs to the class of Hermite WENO (HWENO) Limiters, for the Runge-Kutta discontinuous Galerkin (RKDG) methods solving hyperbolic conservation laws. This new HWENO limiter is a modification of the simple WENO limiter proposed recently by Zhong and Shu [29]. Both Limiters use information of the DG solutions only from the target cell and its immediate neighboring cells, thus maintaining the original compactness of the DG scheme. The goal of both Limiters is to obtain high order accuracy and non-oscillatory properties simultaneously. The main novelty of the new HWENO limiter in this paper is to reconstruct the polynomial on the target cell in a least square fashion [8] while the simple WENO limiter [29] is to use the entire polynomial of the original DG solutions in the neighboring cells with an addition of a constant for conservation. The modification in this paper improves the robustness in the computation of problems with strong shocks or contact discontinuities, without changing the compact stencil of the DG scheme. Numerical results for both one and two dimensional equations including Euler equations of compressible gas dynamics are provided to illustrate the viability of this modified limiter.
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a simple weighted essentially non oscillatory limiter for the correction procedure via reconstruction cpr framework
Applied Numerical Mathematics, 2015Co-Authors: Chiwang Shu, Mengping ZhangAbstract:In this paper, we adapt a simple weighted essentially non-oscillatory (WENO) limiter, originally designed for discontinuous Galerkin (DG) schemes 45], to the correction procedure via reconstruction (CPR) framework for solving conservation laws. The objective of this simple WENO limiter is to simultaneously maintain uniform high order accuracy of the CPR framework in smooth regions and control spurious numerical oscillations near discontinuities. The WENO limiter we adopt in this paper is particularly simple to implement and will not harm the conservativeness of the CPR framework. Also, it uses information only from the target cell and its immediate neighbors, and thus can maintain the compactness of the CPR framework. Since the CPR framework with the WENO limiter does not in general preserve positivity of the solution, we also extend the positivity-preserving Limiters in 43,44,42] to the CPR framework. Numerical results in one and two dimensions are provided to illustrate the good behavior of this procedure.
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a simple weighted essentially non oscillatory limiter for the correction procedure via reconstruction cpr framework on unstructured meshes
Applied Numerical Mathematics, 2015Co-Authors: Chiwang Shu, Mengping ZhangAbstract:In this paper, we adapt a simple weighted essentially non-oscillatory (WENO) limiter, originally designed for discontinuous Galerkin (DG) schemes on two-dimensional unstructured triangular meshes [39], to the correction procedure via reconstruction (CPR) framework for solving nonlinear hyperbolic conservation laws on two-dimensional unstructured triangular meshes with straight or curved edges. This is an extension of our earlier work [4] in which the WENO limiter was designed for the CPR framework on regular meshes. The objective of this simple WENO limiter is to simultaneously maintain uniform high order accuracy of the CPR framework in smooth regions and control spurious numerical oscillations near discontinuities. The WENO limiter we adopt in this paper uses information only from the target cell and its immediate neighbors. Hence, it is particularly simple to implement and will not harm the conservativeness and compactness of the CPR framework. Since the CPR framework with this WENO limiter does not in general satisfy the positivity preserving property, we also extend the positivity-preserving Limiters [36,33] to the CPR framework. Numerical results for both scalar equations and Euler systems of compressible gas dynamics are provided to illustrate the good behavior of this procedure.
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runge kutta discontinuous galerkin method using a new type of weno Limiters on unstructured meshes
Journal of Computational Physics, 2013Co-Authors: Jun Zhu, Chiwang Shu, Xinghui Zhong, Jianxian QiuAbstract:In this paper we generalize a new type of Limiters based on the weighted essentially non-oscillatory (WENO) finite volume methodology for the Runge–Kutta discontinuous Galerkin (RKDG) methods solving nonlinear hyperbolic conservation laws, which were recently developed in [32] for structured meshes, to two-dimensional unstructured triangular meshes. The key idea of such Limiters is to use the entire polynomials of the DG solutions from the troubled cell and its immediate neighboring cells, and then apply the classical WENO procedure to form a convex combination of these polynomials based on smoothness indicators and nonlinear weights, with suitable adjustments to guarantee conservation. The main advantage of this new limiter is its simplicity in implementation, especially for the unstructured meshes considered in this paper, as only information from immediate neighbors is needed and the usage of complicated geometric information of the meshes is largely avoided. Numerical results for both scalar equations and Euler systems of compressible gas dynamics are provided to illustrate the good performance of this procedure.
Jun Zhu - One of the best experts on this subject based on the ideXlab platform.
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runge kutta discontinuous galerkin method with a simple and compact hermite weno limiter
Communications in Computational Physics, 2016Co-Authors: Jun Zhu, Chiwang Shu, Xinghui Zhong, Jianxian QiuAbstract:In this paper, we propose a new type of weighted essentially non-oscillatory (WENO) limiter, which belongs to the class of Hermite WENO (HWENO) Limiters, for the Runge-Kutta discontinuous Galerkin (RKDG) methods solving hyperbolic conservation laws. This new HWENO limiter is a modification of the simple WENO limiter proposed recently by Zhong and Shu [29]. Both Limiters use information of the DG solutions only from the target cell and its immediate neighboring cells, thus maintaining the original compactness of the DG scheme. The goal of both Limiters is to obtain high order accuracy and non-oscillatory properties simultaneously. The main novelty of the new HWENO limiter in this paper is to reconstruct the polynomial on the target cell in a least square fashion [8] while the simple WENO limiter [29] is to use the entire polynomial of the original DG solutions in the neighboring cells with an addition of a constant for conservation. The modification in this paper improves the robustness in the computation of problems with strong shocks or contact discontinuities, without changing the compact stencil of the DG scheme. Numerical results for both one and two dimensional equations including Euler equations of compressible gas dynamics are provided to illustrate the viability of this modified limiter.
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runge kutta discontinuous galerkin method using a new type of weno Limiters on unstructured meshes
Journal of Computational Physics, 2013Co-Authors: Jun Zhu, Chiwang Shu, Xinghui Zhong, Jianxian QiuAbstract:In this paper we generalize a new type of Limiters based on the weighted essentially non-oscillatory (WENO) finite volume methodology for the Runge–Kutta discontinuous Galerkin (RKDG) methods solving nonlinear hyperbolic conservation laws, which were recently developed in [32] for structured meshes, to two-dimensional unstructured triangular meshes. The key idea of such Limiters is to use the entire polynomials of the DG solutions from the troubled cell and its immediate neighboring cells, and then apply the classical WENO procedure to form a convex combination of these polynomials based on smoothness indicators and nonlinear weights, with suitable adjustments to guarantee conservation. The main advantage of this new limiter is its simplicity in implementation, especially for the unstructured meshes considered in this paper, as only information from immediate neighbors is needed and the usage of complicated geometric information of the meshes is largely avoided. Numerical results for both scalar equations and Euler systems of compressible gas dynamics are provided to illustrate the good performance of this procedure.
T. Kruger - One of the best experts on this subject based on the ideXlab platform.
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First commercial medium voltage superconducting fault-current Limiters: Production, test and installation
Superconductor Science and Technology, 2010Co-Authors: R. Dommerque, H. Piereder, D. Klaus, Joachim Bock, Achim Hobl, M Bludau, Reinhard Böhm, S Kramer, A. Wilson, T. KrugerAbstract:In 2008/09 Nexans SuperConductors GmbH made the step from R&D activities to the production of the first non-publicly funded fault-current limiter units. In close cooperation with two customers, Applied Superconductor Limited (ASL, UK) and Vattenfall (Germany), Nexans was able to design, produce and deliver two resistive superconducting limiter devices. Both devices are designed for the medium voltage grid and were tested at the high voltage and high power lab IPH in Berlin. The superconducting components of both Limiters, coils of bulk MCP BSCCO-2212, have been designed and produced by Nexans.
Xinghui Zhong - One of the best experts on this subject based on the ideXlab platform.
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runge kutta discontinuous galerkin method with a simple and compact hermite weno limiter
Communications in Computational Physics, 2016Co-Authors: Jun Zhu, Chiwang Shu, Xinghui Zhong, Jianxian QiuAbstract:In this paper, we propose a new type of weighted essentially non-oscillatory (WENO) limiter, which belongs to the class of Hermite WENO (HWENO) Limiters, for the Runge-Kutta discontinuous Galerkin (RKDG) methods solving hyperbolic conservation laws. This new HWENO limiter is a modification of the simple WENO limiter proposed recently by Zhong and Shu [29]. Both Limiters use information of the DG solutions only from the target cell and its immediate neighboring cells, thus maintaining the original compactness of the DG scheme. The goal of both Limiters is to obtain high order accuracy and non-oscillatory properties simultaneously. The main novelty of the new HWENO limiter in this paper is to reconstruct the polynomial on the target cell in a least square fashion [8] while the simple WENO limiter [29] is to use the entire polynomial of the original DG solutions in the neighboring cells with an addition of a constant for conservation. The modification in this paper improves the robustness in the computation of problems with strong shocks or contact discontinuities, without changing the compact stencil of the DG scheme. Numerical results for both one and two dimensional equations including Euler equations of compressible gas dynamics are provided to illustrate the viability of this modified limiter.
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runge kutta discontinuous galerkin method using a new type of weno Limiters on unstructured meshes
Journal of Computational Physics, 2013Co-Authors: Jun Zhu, Chiwang Shu, Xinghui Zhong, Jianxian QiuAbstract:In this paper we generalize a new type of Limiters based on the weighted essentially non-oscillatory (WENO) finite volume methodology for the Runge–Kutta discontinuous Galerkin (RKDG) methods solving nonlinear hyperbolic conservation laws, which were recently developed in [32] for structured meshes, to two-dimensional unstructured triangular meshes. The key idea of such Limiters is to use the entire polynomials of the DG solutions from the troubled cell and its immediate neighboring cells, and then apply the classical WENO procedure to form a convex combination of these polynomials based on smoothness indicators and nonlinear weights, with suitable adjustments to guarantee conservation. The main advantage of this new limiter is its simplicity in implementation, especially for the unstructured meshes considered in this paper, as only information from immediate neighbors is needed and the usage of complicated geometric information of the meshes is largely avoided. Numerical results for both scalar equations and Euler systems of compressible gas dynamics are provided to illustrate the good performance of this procedure.
