Modeling of Shallow-Water Equations by Using Implicit Higher-Order Compact Scheme with Application to Dam-Break ProblemJafar Bagheri1 and Samir K Das2*
- *Corresponding Author:
- Samir K Das
Defence Institute of Advanced Technology
Girinagar, Pune-411025, India
E-mail: [email protected] / [email protected]
Received May 24, 2013; Accepted June 22, 2013; Published July 07, 2013
Citation: Bagheri J, Das SK (2013) Modeling of Shallow-Water Equations by Using Implicit Higher-Order Compact Scheme with Application to Dam-Break Problem. J Appl Computat Math 2:132. doi: 10.4172/2168-9679.1000132
Copyright: © 2013 Bagheri J, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
The paper deals with the unsteady two-dimensional (2D) non-linear shallow-water equations (SWE) in conservation-law form to capture the fluid flow in transition. Numerical simulations of dam-break flood wave in channel transitions have been performed for inviscid and incompressible flow by using two new implicit higher-order compact (HOC) schemes. The algorithm is second order accurate in time and fourth order accurate in space, on the nine-point stencil using third order non-centered difference at the wall boundaries. To solve the algebraic system, bi-conjugate gradient stabilized method (BiCGStab) with preconditioning has been employed. Although, both the schemes are able to capture both transient and steady state solution of shallow water equations, the scheme expressed in conservative law form is unconditionally stable. The model results have been validated for dam-break problem and compared with the experimental data for dry and wet bed conditions. The model results are found to be in good agreement with the experimental observations. The proposed scheme is useful to solve to capture flow transition with minimal number of nodal points, particularly for hyperbolic system.