1D Numerical modelling of dam break using finite element method

Abstract

In numerical modeling, dam break is one case that has its own challenges, because shock wave is found in the dam break modeling that usually provides a numerical instability. Usually, dam break problem is solved by Saint Venant equation using a finite difference method with artificial dissipation or Total Variation Diminishing (TVD) filter. But in this research, finite element method and the finite difference method are used. To verify the accuracy of the model, a comparison against the Stoker analytical method for dam break case was performed. Numerical modeling of dam break is required to find out the collapse area, thus it is used for determining mitigation that can be done in the area, related to dam safety. In numerical modeling, oscillation or numerical instability often occurs, for which special treatment is required to reduce or eliminate the oscillations. In this research, the treatment for that case is a Hansen filter for both methods. From the simulation result, it is found that Hansen filter is sensitive in reducing oscillation depending on the correction factor value and Δt that used. For dam break case, after filter applied, the value of Pearson Correlation Coefficient of Taylor Galerkin and Mac-Cormack methods are 0.999. The error rate for a Taylor Galerkin method are 0.118% at t = 3s and 0.123% at t = 10s. The error rate for Mac-Cormack method are 0.043% at t = 3s and 5.048% at t = 10s. From the comparison of the model, it can be concluded that Taylor Galerkin finite element method proved to be capable and more accurate in simulating dam break compared to Mac-Cormack finite difference method.