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作者:Jun Zhu , Jianxian Qiu
来源:[J].Journal of Scientific Computing(IF 1.71), 2017, Vol.73 (2-3), pp.1338-1359
摘要:A new type of finite difference weighted essentially non-oscillatory (WENO) schemes for hyperbolic conservation laws was designed in Zhu and Qiu (J Comput Phys 318:110–121, 2016 ), in this continuing paper, we extend such methods to finite volume version in multi-dimensions....
作者:Zhanjing Tao , Jianxian Qiu
来源:[J].Advances in Computational Mathematics(IF 1.468), 2017, Vol.43 (5), pp.1023-1058
摘要:In this paper, a class of high-order central Hermite WENO (HWENO) schemes based on finite volume framework and staggered meshes is proposed for directly solving one- and two-dimensional Hamilton-Jacobi (HJ) equations. The methods involve the Lax-Wendroff type discretizations...
作者:Hongqiang Zhu , Jianxian Qiu , Jing-Mei Qiu
来源:[J].Journal of Scientific Computing(IF 1.71), 2017, Vol.73 (2-3), pp.1316-1337
摘要:In this paper, we generalize an h -adaptive Runge–Kutta discontinuous Galerkin scheme developed earlier in Zhu et al. (J Sci Comput 69:1346–1365, 2016 ) for the 1D Vlasov–Poisson system to the guiding center Vlasov model and the 2D time dependent incompressible Euler eq...
作者:Jun Zhu , Jianxian Qiu , Chi-Wang Shu
来源:[J].Journal of Computational Physics(IF 2.138), 2020, Vol.404
摘要:Abstract(#br)In this paper, a new type of multi-resolution weighted essentially non-oscillatory (WENO) limiters for high-order Runge-Kutta discontinuous Galerkin (RKDG) methods is designed. This type of multi-resolution WENO limiters is an extension of the multi-resolution WENO f...
作者:Zhuang Zhao , Yibing Chen , Jianxian Qiu
来源:[J].Journal of Computational Physics(IF 2.138), 2020, Vol.405
摘要:Abstract(#br)In this paper, we propose a hybrid finite volume Hermite weighted essentially non-oscillatory (HWENO) scheme for solving one and two dimensional hyperbolic conservation laws, which would be the fifth order accuracy in the one dimensional case, while is the fourth ord...
作者:Hongqiang Zhu , Jianxian Qiu , Jun Zhu
来源:[J].Computers and Mathematics with Applications(IF 2.069), 2020, Vol.79 (2), pp.317-336
摘要:Abstract(#br)In this paper, a new limiter using weighted essentially non-oscillatory (WENO) methodology is investigated for the Runge–Kutta discontinuous Galerkin (RKDG) methods for solving hyperbolic conservation laws. The idea is to use the high-order DG solution polynomia...
作者:Jun Zhu , Jianxian Qiu
来源:[J].Journal of Computational Physics(IF 2.138), 2017, Vol.349, pp.220-232
摘要:Abstract(#br)In this paper a third order finite volume weighted essentially non-oscillatory scheme is designed for solving hyperbolic conservation laws on tetrahedral meshes. Comparing with other finite volume WENO schemes designed on tetrahedral meshes, the crucial advantag...
作者:Feng Zheng , Chi-Wang Shu , Jianxian Qiu
来源:[J].Journal of Computational Physics(IF 2.138), 2017, Vol.337, pp.27-41
摘要:Abstract(#br)In this paper, a new type of finite difference Hermite weighted essentially non-oscillatory (HWENO) schemes are constructed for solving Hamilton–Jacobi (HJ) equations. Point values of both the solution and its first derivatives are used in the HWENO reconstructi...
作者:Min Zhang , Juan Cheng , Jianxian Qiu
来源:[J].Journal of Computational Physics(IF 2.138), 2019, Vol.397
摘要:Abstract(#br)It is an important and challenging issue for the numerical solution of radiative transfer equations to maintain both high order accuracy and positivity. For the two-dimensional radiative transfer equations, Ling et al. give a counterexample (Ling et al. (2018) [13]) ...

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