A weighted ENO-flux limiter scheme for hyperbolic conservation laws

被引:9
作者
Peer, A. A. I. [1 ]
Dauhoo, M. Z. [1 ]
Gopaul, A. [1 ]
Bhuruth, M. [1 ]
机构
[1] Univ Mauritius, Dept Math, Reduit, Mauritius
关键词
essentially non-oscillatory methods; MUSCL-type interpolants; UNO limiter; multistep schemes; hyperbolic conservation laws; ESSENTIALLY NONOSCILLATORY SCHEMES; 2-DIMENSIONAL RIEMANN PROBLEMS; SHOCK-CAPTURING SCHEMES; HIGH-ORDER; WENO SCHEMES; EFFICIENT IMPLEMENTATION; GAS-DYNAMICS; POSITIVE SCHEMES; SYSTEMS; MONOTONICITY;
D O I
10.1080/00207160903124934
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We present a new scheme that combines essentially non-oscillatory (ENO) reconstructions together with monotone upwind schemes for scalar conservation laws interpolants. We modify a second-order ENO polynomial by choosing an additional point inside the stencil in order to obtain the highest accuracy when combined with the Harten-Osher reconstruction-evolution method limiter. Numerical experiments are done in order to compare a weighted version of the hybrid scheme to weighted essentially non-oscillatory (WENO) schemes with constant Courant-Friedrichs-Lewy number under relaxed step size restrictions. Our results show that the new scheme reduces smearing near shocks and corners, and in some cases it is more accurate near discontinuities compared with higher-order WENO schemes. The hybrid scheme avoids spurious oscillations while using a simple componentwise extension for solving hyperbolic systems. The new scheme is less damped than WENO schemes of comparable accuracy and less oscillatory than higher-order WENO schemes. Further experiments are done on multi-dimensional problems to show that our scheme remains non-oscillatory while giving good resolution of discontinuities.
引用
收藏
页码:3467 / 3488
页数:22
相关论文
共 41 条
[1]  
[Anonymous], J SCI COMPUT
[2]  
[Anonymous], 1997, 9765 ICASE
[3]   Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy [J].
Balsara, DS ;
Shu, CW .
JOURNAL OF COMPUTATIONAL PHYSICS, 2000, 160 (02) :405-452
[4]   An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws [J].
Borges, Rafael ;
Carmona, Monique ;
Costa, Bruno ;
Don, Wai Sun .
JOURNAL OF COMPUTATIONAL PHYSICS, 2008, 227 (06) :3191-3211
[5]   A FINITE-VOLUME HIGH-ORDER ENO SCHEME FOR 2-DIMENSIONAL HYPERBOLIC SYSTEMS [J].
CASPER, J ;
ATKINS, HL .
JOURNAL OF COMPUTATIONAL PHYSICS, 1993, 106 (01) :62-76
[6]   Total variation diminishing Runge-Kutta schemes [J].
Gottlieb, S ;
Shu, CW .
MATHEMATICS OF COMPUTATION, 1998, 67 (221) :73-85
[7]   Strong stability-preserving high-order time discretization methods [J].
Gottlieb, S ;
Shu, CW ;
Tadmor, E .
SIAM REVIEW, 2001, 43 (01) :89-112
[8]  
HARTEN A, 1987, J COMPUT PHYS, V71, P231, DOI [10.1016/0021-9991(87)90031-3, 10.1006/jcph.1996.5632]
[9]   UNIFORMLY HIGH-ORDER ACCURATE NONOSCILLATORY SCHEMES .1. [J].
HARTEN, A ;
OSHER, S .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1987, 24 (02) :279-309
[10]   Mapped weighted essentially non-oscillatory schemes: Achieving optimal order near critical points [J].
Henrick, AK ;
Aslam, TD ;
Powers, JM .
JOURNAL OF COMPUTATIONAL PHYSICS, 2005, 207 (02) :542-567