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Abstract
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.
Highlights
To model the shallow water equations (SWE), various numerical methods such as explicit and implicit finite-difference methods with higher-order compact (HOC) scheme have been used by a number of investigators
We present our results for wet bed and dry bed conditions for downstream of the dam
It can be noticed that the water depth profiles for wet bed and dry bed condition remains same till mid location of the upstream section and subsequently water depth profile of wet bed increases gradually towards downstream direction
Summary
To model the shallow water equations (SWE), various numerical methods such as explicit and implicit finite-difference methods with higher-order compact (HOC) scheme have been used by a number of investigators. Navon and Riphagen [1] developed compact fourth order algorithm by using alternating-direction implicit finite-difference scheme to solve non-linear shallow-water equations, expressed in conservationlaw form. To demonstrate the application of higher order compact scheme, classical dam-break problem is considered to simulate the flood wave in channel transition. The flow is considered to be inviscid and incompressible and the non-linear SWE are expressed as These above equations are described in primitive variable form are obtained from Navier-Stokes (NS) equations by integrating over the depth and by assuming hydrostatic pressure distribution.
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