Abstract In this paper, we describe some existing slope limiters (Cockburn and Shu's limiter Hoteit's limiter) for the two‐dimensional Runge–Kutta discontinuous Galerkin (RKDG) method on arbitrary unstructured triangular grids. We strategies detecting discontinuities limiting spurious oscillations near such discontinuities, when solving hyperbolic systems of conservation laws by high‐order methods. The disadvantage these is that they depend a positive constant, which is, specific hydraulic...

The Cauchy problem for the Laplace equation in an annular bounded region consists of finding a harmonic function from Dirichlet and Neumann data known on exterior boundary. This work considers fractional boundary condition instead circular region. We found solution to using harmonics. Then, Tikhonov regularization is used handle numerical instability problem. parameter was chosen L-curve method. From tests, we that series expansion can be truncated N=20, N=25, or N=30. Thus, stable method...

<p>Additional details on methods, Figures S1–S6, and Tables S1–S2.</p>

Sinuous channels occur across the Solar System, forming by many distinct processes. Qualitative similarities between these have led to hypotheses that some, or all, aspects of channel sinuosity are universal. One aspect shape sinuous is skewness their bends, with alluvial meandering rivers thought dominantly upstream skewed bends. We present new observations test universality bend skewness, comparing 294 bends from lunar volcanic (sinuous rilles), 466 natural and experimental ice melt...

Abstract Discontinuous Galerkin (DG) finite element methods have salient features that are mainly highlighted by their locality, easiness in balancing the flux and source term gradients component‐wise structure. In light of this, this paper aims to provide insights into well‐balancing property a second‐order Runge–Kutta (RKDG2) method. For purpose, Godunov‐type RKDG2 method is presented for solving shallow water equations. The scheme based on local DG linear approximations does not entail...

In this paper, a comparison between the 1D and 2D approaches for simulating combining flows at open-channel junctions is presented. The two are described allowing full comprehension of flow modelling. For in an network, mutual effects exist among channel branches junction. Therefore, Saint-Venant equations branch supplemented by various junction models. existing models empirical nature depend on regime thus not practical all cases. numerical approximation performed Runge–Kutta discontinuous...

Abstract The present work addresses the numerical prediction of discontinuous shallow water flows by application a second‐order Runge–Kutta Galerkin scheme (RKDG2). unsteady flow in one‐dimensional approach is described Saint Venant's model which incorporates source terms practical applications. Therefore, RKDG2 reformulated with simple way to integrate terms. Further, an adequate boundary conditions handling, theory characteristics, was overviewed be adapted external points mesh, as well...

Finding new, safe and renewable energy is becoming more of a priority with global warming. One solution that gaining popularity the Archimedean Screw Generator (ASG). This kind hydroelectric plant allows transforming potential fluid into mechanical convenient for low-head hydraulic sites. As it new growing technology, there are few references dealing their design performance optimization. The present contribution proposes to investigate experimentally numerically ASG performances....

An unsteady mathematical model for predicting flow divisions at a right-angled open-channel junction is presented. Existing dividing models depend on prior knowledge of constant regime. In addition, their strong nonlinearity does not guarantee compatibility with the St. Venant solutions in context an internal boundary condition treatment. Assuming zero crest height region, side weir explicitly introduced within one-dimensional equations used to cope two-dimensional pattern flow. upwind...

In open channel networks, flow is usually approximated by the one-dimensional (1D) Saint-Venant equations coupled with an empirical junction model. this work, a comparison in terms of accuracy and computational cost between 1D-2D shallow water model fully two-dimensional (2D) presented. The paper explores ability to simulate processes during supercritical flows crossroads. This combination leads significant reduction time, as 1D approach used branches 2D employed selected areas only where...

Modeling floods in urban areas remains a challenge. To understand flow patterns geometries better and constrain models, an experimental rig representing 1/200 scale geometry with various street widths angles is presented. Measurements of hydraulic variables for conditions ranging from moderate to extreme flooding were performed. Over this range, accurate inflow outflow boundary condition measurements allow the effect on inlet–outlet discharge conservation be studied each street. Froude...