scholarly journals Non-negative depth reconstruction for a two-dimensional partial inertial inundation model

2014 ◽  
Vol 16 (5) ◽  
pp. 1158-1177 ◽  
Author(s):  
Hongbin Zhang ◽  
Yueling Wang ◽  
Qiuhua Liang ◽  
Luke S. Smith ◽  
Chris G. Kilsby
Keyword(s):  
Momentum Equation ◽  
Steep Slope ◽  
Test Cases ◽  
Reconstruction Method ◽  
Two Dimensional ◽  
Low Friction ◽  
Depth Reconstruction ◽  
Practical Challenge ◽  
Numerical Performance ◽  
Flood Simulations

This paper proposes a non-negative depth reconstruction method for improving the numerical performance of a partial inertial model (PIM) for applications involving steep-slope and low-friction conditions. The PIM solves the continuity equation of two-dimensional (2D) shallow water equations (SWEs) with the interface fluxes evaluated by a simplified momentum equation that partially restores the inertial terms. In applying the PIM to flood simulations, a practical challenge is to represent complex topography and to track the moving wet–dry interface without resulting in negative water depths. Another challenge is to avoid the numerical issue caused by the lack of physical diffusive terms when it is applied to low-friction cases. To cope with these difficulties, the PIM is improved by introducing a non-negative depth reconstruction method, featuring two different ways for calculating the interface fluxes. The performance of the improved PIMs is investigated through applications to several theoretical and practical benchmark test cases. The comparison of the numerical results against analytical solutions or predictions from the original PIM and a full 2D finite-volume hydrodynamic model shows that the proposed reconstruction method can avoid non-negative water depth predictions, and improve the numerical performance of the original PIM when applied to steep-slope and low-friction conditions.

A Stable and Efficient Flood Routing Model Based on Unstructured Grid

2020 ◽  
Author(s):  
Shan Zhou ◽  
Hongchang Hu
Keyword(s):  
Shallow Water ◽  
Computational Cost ◽  
Flood Routing ◽  
Test Cases ◽  
Reconstruction Method ◽  
Two Dimensional ◽  
Time Stepping ◽  
Shallow Water Flows ◽  
Local Time Stepping ◽  
Muscl Reconstruction

<p>Godunov-type schemes are widely applied to solve shallow water equations. In this study, a novel non-negative water depth Multislope MUSCL reconstruction method is incorporated into a two-dimensional unstructured cell-centered Godunov-type finite volume model to simulate shallow water flows, It is verified that the method performs well in avoiding non-physical oscillation and also has well-balanced performance by simulate three test cases. Due to the limitation of CFL conditions, mesh refinement will greatly increase the computational cost. In this study, A Local Time Stepping(LTS) strategy is specifically designed to greatly improve the computational efficiency. In addition, in order to make the model suitable for more application scenarios, we have realized the coupling of one-dimensional and two-dimensional models. Based on the above three improvements, we have developed a stable and efficient flood routing model.</p>

Boundary Layer Closure and Heat Transfer in Constant Base Pressure and Simple Wave Guns

1978 ◽  
Vol 100 (4) ◽  
pp. 690-696 ◽  
Author(s):  
A. D. Anderson ◽  
T. J. Dahm
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Method Of Characteristics ◽  
Simple Wave ◽  
Momentum Equation ◽  
Base Pressure ◽  
Two Dimensional ◽  
The Method Of Characteristics

Solutions of the two-dimensional, unsteady integral momentum equation are obtained via the method of characteristics for two limiting modes of light gas launcher operation, the “constant base pressure gun” and the “simple wave gun”. Example predictions of boundary layer thickness and heat transfer are presented for a particular 1 in. hydrogen gun operated in each of these modes. Results for the constant base pressure gun are also presented in an approximate, more general form.

Effects of Curvature on Laminar Boundary Layers in Sink-Type Flows

1969 ◽  
Vol 91 (3) ◽  
pp. 353-358 ◽  
Author(s):  
W. A. Gustafson ◽  
I. Pelech
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Momentum Equation ◽  
Similarity Solutions ◽  
Momentum Thickness ◽  
Two Dimensional ◽  
Thickness Increase ◽  
Laminar Boundary Layers ◽  
Converging Channel ◽  
Special Case

The two-dimensional, incompressible laminar boundary layer on a strongly curved wall in a converging channel is investigated for the special case of potential velocity inversely proportional to the distance along the wall. Similarity solutions of the momentum equation are obtained by two different methods and the differences between the methods are discussed. The numerical results show that displacement and momentum thickness increase linearly with curvature while skin friction decreases linearly.

Some Measurements of Boundary-Layer Growth in a Two-Dimensional Diffuser

1959 ◽  
Vol 81 (3) ◽  
pp. 285-294 ◽  
Author(s):  
J. F. Norbury
Keyword(s):  
Boundary Layer ◽  
Static Pressure ◽  
Momentum Equation ◽  
Layer Growth ◽  
Area Ratio ◽  
Momentum Thickness ◽  
Two Dimensional ◽  
Static Pressure Distribution ◽  
Boundary Layer Growth ◽  
Flow Experiments

Low-speed experiments were carried out in a two-dimensional diffuser having a square throat and an area ratio of two to one. Measurements were made of static pressure distribution, velocity contours at throat and outlet, and boundary-layer growth along the four wall center lines. Visual flow experiments were performed using tufts and smoke filaments. Similar experiments were carried out with the throat boundary layers artificially thickened by means of round rods placed on the walls upstream. Disparities between the measured growth of momentum thickness and that predicted by the simple momentum equation are discussed, as well as the effect of the artificial thickening on diffuser efficiency.

scholarly journals Two-Dimensional Evaluation of ATHAM-Fluidity, a Nonhydrostatic Atmospheric Model Using Mixed Continuous/Discontinuous Finite Elements and Anisotropic Grid Optimization

2016 ◽  
Vol 144 (11) ◽  
pp. 4349-4372 ◽  
Author(s):  
Julien Savre ◽  
James Percival ◽  
Michael Herzog ◽  
Chris Pain
Keyword(s):  
Optimization Algorithm ◽  
Large Scale ◽  
Atmospheric Model ◽  
Computational Time ◽  
Limited Area ◽  
Test Cases ◽  
Two Dimensional ◽  
Element Discretization ◽  
Wide Range ◽  
Grid Optimization

Abstract This paper presents the first attempt to apply the compressible nonhydrostatic Active Tracer High-Resolution Atmospheric Model–Fluidity (ATHAM-Fluidity) solver to a series of idealized atmospheric test cases. ATHAM-Fluidity uses a hybrid finite-element discretization where pressure is solved on a continuous second-order grid while momentum and scalars are computed on a first-order discontinuous grid (also known as ). ATHAM-Fluidity operates on two- and three-dimensional unstructured meshes, using triangular or tetrahedral elements, respectively, with the possibility to employ an anisotropic mesh optimization algorithm for automatic grid refinement and coarsening during run time. The solver is evaluated using two-dimensional-only dry idealized test cases covering a wide range of atmospheric applications. The first three cases, representative of atmospheric convection, reveal the ability of ATHAM-Fluidity to accurately simulate the evolution of large-scale flow features in neutral atmospheres at rest. Grid convergence without adaptivity as well as the performances of the Hermite–Weighted Essentially Nonoscillatory (Hermite-WENO) slope limiter are discussed. These cases are also used to test the grid optimization algorithm implemented in ATHAM-Fluidity. Adaptivity can result in up to a sixfold decrease in computational time and a fivefold decrease in total element number for the same finest resolution. However, substantial discrepancies are found between the uniform and adapted grid results, thus suggesting the necessity to improve the reliability of the approach. In the last three cases, corresponding to atmospheric gravity waves with and without orography, the model ability to capture the amplitude and propagation of weak stationary waves is demonstrated. This work constitutes the first step toward the development of a new comprehensive limited area atmospheric model.

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