Abstract
This paper presents a new meshless numerical scheme to overcome the problem of shock waves and to apply boundary conditions in cases of dam-break flows in channels with constant and variable widths. The numerical program solves shallow water equations based on the discrete mixed subdomain least squares (DMSLS) meshless method with collocation points. The DMSLS meshless method is based on the minimization of a least squares functional defined as the weighted summation of the squared residuals of the governing equations over the entire domain and requiring the summation of residual function to be zero at collocation points in boundary subdomains. The collocated discrete subdomain meshless method is applied on the boundary, whereas the collocated discrete least squares meshless technique is applied to the interior domain. The meshless scheme extends for dam-break formulation of shallow water equations. The model is verified by comparing computed results with analytical and experimental data for constant and varying width channels. The developed model is also used to study one-dimensional dam-break problems involving different flow situations by considering changes to the channel width, a bumpy channel with various downstream boundary conditions, and the effects of bed friction and bed slope as source terms on wave propagation. The accuracy of the results is acceptable.
Highlights
Dam-break flows propagate along rivers and can lead to devastating floods, damage to property, and loss of human life
This study investigated the discrete mixed subdomain least squares (DMSLS) meshless method using collocation points
A key feature of the model is the use of collocated points to minimize the sum of the squared residual functional
Summary
Dam-break flows propagate along rivers and can lead to devastating floods, damage to property, and loss of human life. Darbani et al ( ) used the natural element method to simulate 2-D shallow water equations in the presence of strong gradients Despite their advantages, meshless methods have the difficulties of imposing boundary and treatment of boundary values, whereas the unreliable selection of weight functions and the complexity of algorithms for computing interpolation functions are all serious technical problems in such methods. This study investigated the discrete mixed subdomain least squares (DMSLS) meshless method using collocation points To generalize this method, an attempt was made to check the balance of this approach for some dam-break flow simulations (where the definition and location of the boundary surface is not easy) for different bed and geometry conditions with maximum variables in boundary conditions (where applying boundary conditions are not straightforward). The results of this study illustrate the potential ability of the DMSLS method to reproduce the detailed features of flow structure for highly transient flow with the large geometrical changes of the computational domain
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