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Application of a fourth-order relaxation scheme to hyperbolic systems of conservation laws 被引量:7
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作者 Jianzhong Chen Zhongke Shi 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2006年第1期84-92,共9页
A fourth-order relaxation scheme is derived and applied to hyperbolic systems of conservation laws in one and two space dimensions. The scheme is based on a fourthorder central weighted essentially nonoscillatory (CW... A fourth-order relaxation scheme is derived and applied to hyperbolic systems of conservation laws in one and two space dimensions. The scheme is based on a fourthorder central weighted essentially nonoscillatory (CWENO) reconstruction for one-dimensional cases, which is generalized to two-dimensional cases by the dimension-by-dimension approach. The large stability domain Runge-Kutta-type solver ROCK4 is used for time integration. The resulting method requires neither the use of Riemann solvers nor the computation of Jacobians and therefore it enjoys the main advantage of the relaxation schemes. The high accuracy and high-resolution properties of the present method are demonstrated in one- and two-dimensional numerical experiments. 展开更多
关键词 Hyperbolic systems of conservation laws Relaxation schemes cweno reconstruction
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A New Well-Balanced Finite Volume CWENO Scheme for Shallow Water Equations over Bottom Topography
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作者 Wei Guo Ziming Chen +2 位作者 Shouguo Qian Gang Li Qiang Niu 《Advances in Applied Mathematics and Mechanics》 SCIE 2023年第6期1515-1539,共25页
In this article,we develop a new well-balanced finite volume central weighted essentially non-oscillatory(CWENO)scheme for one-and two-dimensional shallow water equations over uneven bottom.The well-balanced property ... In this article,we develop a new well-balanced finite volume central weighted essentially non-oscillatory(CWENO)scheme for one-and two-dimensional shallow water equations over uneven bottom.The well-balanced property is of paramount importance in practical applications,where many studied phenomena can be regarded as small perturbations to the steady state.To achieve the well-balanced property,we construct numerical fluxes by means of a decomposition algorithm based on a novel equilibrium preserving reconstruction procedure and we avoid applying the traditional hydrostatic reconstruction technique accordingly.This decomposition algorithm also helps us realize a simple source term discretization.Both rigorous theoretical analysis and extensive numerical examples all verify that the proposed scheme maintains the well-balanced property exactly.Furthermore,extensive numerical results strongly suggest that the resulting scheme can accurately capture small perturbations to the steady state and keep the genuine high-order accuracy for smooth solutions at the same time. 展开更多
关键词 Shallow water equations source term cweno scheme decomposition algorithm well-balanced property
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A CHARACTERISTIC-BASED FINITE VOLUME SCHEME FOR SHALLOW WATER EQUATIONS 被引量:7
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作者 GUO Yan LIU Ru-xun +1 位作者 DUAN Ya-li LI Yuan 《Journal of Hydrodynamics》 SCIE EI CSCD 2009年第4期531-540,共10页
We propose a new characteristic-based finite volume scheme combined with the method of Central Weighted Essentially Non-Oscillatory (CWENO) reconstruction and characteristics, to solve shallow water equations. We ap... We propose a new characteristic-based finite volume scheme combined with the method of Central Weighted Essentially Non-Oscillatory (CWENO) reconstruction and characteristics, to solve shallow water equations. We apply the scheme to simulate dam-break problems. A number of challenging test cases are considered, such as large depth differences even wet/dry bed. The numerical solutions well agree with the analytical solutions. The results demonstrate the desired accuracy, high-resolution and robustness of the presented scheme. 展开更多
关键词 shallow water equations finite volume method characteristic method Central Weighted Essentially Non-Oscillatory cweno scheme HLLC flux
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