| | |
Summary: Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.
SIAM J. SCI. COMPUT. c 2007 Society for Industrial and Applied Mathematics
Vol. 29, No. 6, pp. 26072620
IMPLICIT SCHEME FOR HYPERBOLIC CONSERVATION LAWS
USING NONOSCILLATORY RECONSTRUCTION IN SPACE AND
TIME
KARTHIKEYAN DURAISAMY AND JAMES D. BAEDER
Abstract. The efficiency of high order accurate schemes for the solution of unsteady hyper-
bolic conservation laws is adversely affected by time-step restrictions that arise from monotonicity
requirements. When applied to the solution of problems involving discontinuities, these restrictions
render conventional high order implicit time integration schemes impractical. In the present study,
a new single step second order implicit scheme that uses nonoscillatory reconstruction in space and
time is presented. Both the spatial and temporal limiters are dependent on the evolving solution,
and this nonlinearity allows for a circumvention of total variation diminishing bounds. Numerical
results on model scalar and vector hyperbolic equations suggest that the scheme holds promise in
achieving accurate and unconditionally nonoscillatory solutions.
Key words. high resolution schemes, implicit schemes, time limiting
AMS subject classifications. 65M06, 35L65
DOI. 10.1137/070683271
1. Introduction. The present study is concerned with the solution of hyperbolic
|
