An adaptive mesh method for 1D hyperbolic conservation laws

Hu, Fuxing1; Wang, Rong2; Chen, Xueyong3; Feng, Hui4

2015-05

10.1016/j.apnum.2014.10.008

APPLIED NUMERICAL MATHEMATICS   影响因子和分区

0168-9274

1873-5460

An adaptive method is developed for solving one-dimensional systems of hyperbolic conservation laws, which combines the rezoning approach with the finite volume weighted essentially non-oscillatory (WENO) scheme. An a posteriori error estimate, used to equidistribute the mesh, is obtained from the differences between respective numerical solutions of 5th-order WENO (WENO5) and 3rd-order ENO (ENO3) schemes. The number of grids can be adaptively readjusted based on the solution structure. For higher efficiency, mesh readjustment is performed every few time steps rather than every time step. In addition, a high order conservative interpolation is used to compute the physical solutions on the new mesh from old mesh based on the finite volume ENO reconstruction. Extensive examples suggest that this adaptive method exhibits more accurate resolution of discontinuities for a similar level of computational time comparing with that on a uniform mesh. (C) 2014 IMACS. Published by Elsevier B.V. All rights reserved.

Adaptive method Finite volume WENO methods Hyperbolic conservation laws

SCI ; EI

英语

其他

Doctoral Scientific Research Project of Huizhou University[C5120201]

Mathematics

Mathematics, Applied

WOS:000350705400002

ELSEVIER SCIENCE BV

20150300423634

Error analysis ; One dimensional ; Physical properties

Computer Applications:723.5 ; Physical Properties of Gases, Liquids and Solids:931.2

MATHEMATICS

Web of Science

1.Huizhou Univ, Dept Math, Huizhou 516007, Guangdong, Peoples R China
2.South Univ Sci & Technol China, Dept Gen Educ, Shenzhen 518055, Guangdong, Peoples R China
3.Xuthang Univ, Fac Math & Stat, Xuchang 461000, Henan, Peoples R China
4.Wuhan Univ, Fac Math & Stat, Wuhan 430072, Hubei, Peoples R China

Hu, Fuxing,Wang, Rong,Chen, Xueyong,et al. An adaptive mesh method for 1D hyperbolic conservation laws[J]. APPLIED NUMERICAL MATHEMATICS,2015,91:11-25.

Hu, Fuxing,Wang, Rong,Chen, Xueyong,&Feng, Hui.(2015).An adaptive mesh method for 1D hyperbolic conservation laws.APPLIED NUMERICAL MATHEMATICS,91,11-25.

Hu, Fuxing,et al."An adaptive mesh method for 1D hyperbolic conservation laws".APPLIED NUMERICAL MATHEMATICS 91(2015):11-25.