Abstract
We derive a second-order semidiscrete central-upwind scheme for one- and two-dimensional systems of two-layer shallow water equations. We prove that the presented scheme is well-balanced in the sense that stationary steady-state solutions are exactly preserved by the scheme and positivity preserving; that is, the depth of each fluid layer is guaranteed to be nonnegative. We also propose a new technique for the treatment of the nonconservative products describing the momentum exchange between the layers. The performance of the proposed method is illustrated on a number of numerical examples, in which we successfully capture (quasi) steady-state solutions and propagating interfaces. © 2009 Society for Industrial and Applied Mathematics.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1742-1773 |
| Number of pages | 32 |
| Journal | SIAM Journal on Scientific Computing |
| Volume | 31 |
| Issue number | 3 |
| DOIs | |
| State | Published - Jan 2009 |
| Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: The work of this author was supported in part by NSF grant DMS-0610430. Department of Mathematics, Texas A & M University, College Station, TX 77843 ( [email protected]). The work of this author was supported in part by NSF grants DMS-0505501 and DMS-0810869 and by award KUS-C1-016-04 made by King Abdullah University of Science and Technology ( KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.