scholarly journals Improved double Fourier series on a sphere and its application to a semi-implicit semi-Lagrangian shallow water model

2021 ◽  
Author(s):  
Hiromasa Yoshimura
Keyword(s):  
Fourier Series ◽  
Shallow Water ◽  
Least Squares Method ◽  
Computational Cost ◽  
Expansion Method ◽  
Double Fourier Series ◽  
Water Model ◽  
Test Case ◽  
Shallow Water Model ◽  
Transform Method

Abstract. The computational cost of a spectral model using spherical harmonics (SH) increases significantly at high resolution because the transform method with SH requires O(N3) operations, where N is the truncation wavenumber. One way to solve this problem is to use double Fourier series (DFS) instead of SH, which requires O(N2 log N) operations. This paper proposes a new DFS method that improves the numerical stability of the model compared with the conventional DFS methods by adopting the following two improvements: a new expansion method that employs the least-squares method (or the Galerkin method) to calculate the expansion coefficients in order to minimize the error caused by wavenumber truncation, and new basis functions that satisfy the continuity of both scalar and vector variables at the poles. In the semi-implicit semi-Lagrangian shallow water model using the new DFS method, the Williamson test cases 2 and 5 and the Galewsky test case give stable results without the appearance of high-wavenumber noise near the poles, even without using horizontal diffusion. The new DFS model is faster than the SH model, especially at high resolutions, and gives almost the same results.

scholarly journals A Discontinuous Galerkin Global Shallow Water Model

2005 ◽  
Vol 133 (4) ◽  
pp. 876-888 ◽  
Author(s):  
Ramachandran D. Nair ◽  
Stephen J. Thomas ◽  
Richard D. Loft
Keyword(s):  
Shallow Water ◽  
Discontinuous Galerkin ◽  
Numerical Solutions ◽  
Time Integration ◽  
Curvilinear Coordinates ◽  
Basis Set ◽  
Water Model ◽  
Test Case ◽  
Shallow Water Model ◽  
Cubed Sphere

A discontinuous Galerkin shallow water model on the cubed sphere is developed, thereby extending the transport scheme developed by Nair et al. The continuous flux form nonlinear shallow water equations in curvilinear coordinates are employed. The spatial discretization employs a modal basis set consisting of Legendre polynomials. Fluxes along the element boundaries (internal interfaces) are approximated by a Lax–Friedrichs scheme. A third-order total variation diminishing Runge–Kutta scheme is applied for time integration, without any filter or limiter. Numerical results are reported for the standard shallow water test suite. The numerical solutions are very accurate, there are no spurious oscillations in test case 5, and the model conserves mass to machine precision. Although the scheme does not formally conserve global invariants such as total energy and potential enstrophy, conservation of these quantities is better preserved than in existing finite-volume models.

scholarly journals Numerical study of building drag dissipation for- mulations in the integral porosity shallow water model

2018 ◽  
Vol 40 ◽  
pp. 06017
Author(s):  
Özgen Ilhan ◽  
Martin Bruwier ◽  
Jiaheng Zhao ◽  
Dongfang Liang ◽  
Pierre Archambeau ◽  
...  
Keyword(s):  
Shallow Water ◽  
Source Term ◽  
Numerical Study ◽  
Research Question ◽  
Computational Cost ◽  
Macroscopic Model ◽  
Water Model ◽  
Shallow Water Model ◽  
Urban Flood ◽  
Existing Building

The integral porosity shallow water model is a type of porous shallow water model for urban flood modeling, that defines two types of porosity, namely a volumetric porosity inside the computational cell and a conveyance porosity at each edge. Porosity terms are determined directly from the underlying building geometry, hence buildings do not need to be discretized exactly. This enables simulations with significantly reduced CPU time on meshes with cell sizes larger than the building size. Here, the macroscopic model view leads to an additional source term at the unresolved building-fluid interface, yielding a building drag dissipation source term. In literature, several formulations for this term can be found. The integral porosity shallow water model is sensitive to the building drag dissipation, and using the drag parameters as a calibration parameter enhances the accuracy of model results. However, the ideal way to achieve this is still an open research question. In this contribution, we present a simple technique to estimate building drag dissipation that uses the conveyance porosity configuration to estimate the projected area inside the cell, which is then used in a drag force equation. The advantage of this approach is that it is computationally inexpensive, no additional parameters need to be stored, and only a single parameter has to be calibrated. The proposed approach is compared with drag dissipation formulations from existing literature in a laboratory experiment that features a dam-break against an isolated obstacle. The aim of the comparison is to evaluate present existing building drag dissipation models with regard to accuracy and computational cost.

scholarly journals Towards district scale flood simulations using conventional and anisotropic porosity shallow water models with high-resolution topographic information

2018 ◽  
pp. 90-98
Author(s):  
Ilhan Özgen ◽  
Morgan Abily ◽  
Jiaheng Zhao ◽  
Dongfang Liang ◽  
Philippe Gourbesville ◽  
...  
Keyword(s):  
High Resolution ◽  
Shallow Water ◽  
Large Deviation ◽  
Computational Cost ◽  
Water Model ◽  
Shallow Water Model ◽  
Data Set ◽  
Shallow Water Models ◽  
Urban Catchments ◽  
Water Models

Current topographic survey technology provides high-resolution (HR) datasets for urban environments. Incorporating this HR information in models aiming to provide flood risk assessment is desirable because the flood wave propagation is depending on the urban topographic features, i.e. buildings, bridges and street networks. Conceptual, numerical and practical challenges arise from the application of shallow water models to HR urban flood modeling. For instance, numerical challenges are occurrence of wet-dry fronts, geometric discontinuities in the urban environment and discontinuous solutions, i.e. shock waves. These challenges can be overcome by using a Godunov-type scheme. However, the computational cost of this type of schemes is high, such that HR two-dimensional shallow water simulations with practical relevance have to be run on supercomputers. The porous shallow water model is an alternative approach that aims to reduce computational cost by using a coarse resolution and accounting for unresolved processes by means of the porosity terms. Usually, a speedup between two and three orders of magnitude in comparison to HR simulations can be obtained. This study reports preliminary results of a practical test case concerning pluvial flooding in a district of the city of Nice, France, caused by the intense rainfall event on October 3rd, 2015. HR topography data set on a 1 m resolution is available for the district, whereby street features of infra-metric dimensions have been included. A reference solution is calculated by a HR shallow water model on a 1 m by 1 m structured computational grid. The porous shallow water model is run on a 10 m by 10 m grid and the influence of the drag source term is studied. The model results show a large deviation, which is caused by the poor meshing strategy of the porous shallow water (AP) model. The study also summarizes practical challenges that arise during the application of the AP and HR models to a large urban catchment. The main difficulty is to obtain a good mesh. In smaller scale investigations, the mesh is currently constructed by hand such that the cell edges align with buildings. This approach is not feasible for large scale urban catchments with a large number of buildings. Future steps that have to be taken, such as a strategy for automatic mesh generation, are reported on.

scholarly journals Data assimilation of two-dimensional geophysical flows with a Variational Ensemble Kalman Filter

2014 ◽  
Vol 1 (1) ◽  
pp. 403-446 ◽  
Author(s):  
Z. Mussa ◽  
I. Amour ◽  
A. Bibov ◽  
T. Kauranne
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Shallow Water ◽  
Ensemble Kalman Filter ◽  
Geophysical Flows ◽  
Water Model ◽  
Test Case ◽  
Two Dimensional ◽  
Shallow Water Model ◽  
Model Bias

Abstract. The Variational Ensemble Kalman Filter (VEnKF), a recent data assimilation method that combines a variational assimilation of the Bayesian estimation problem with an ensemble of forecasts, is demonstrated in two-dimensional geophysical flows using a Quasi-Geostrophic (QG) model and a shallow water model. Using a synthetic experiment, a two layer QG model with model bias is solved on a cylindrical 40 x 20 domain. The performance of VEnKF on the QG model with increasing ensemble size is compared with the classical Extended Kalman Filter (EKF). It is shown that although convergence can be achieved with just 20 ensemble members, increasing the number of members results in a better estimate that approaches the one produced by EKF. In the second test case, a 2-D shallow water model is described using a real dam-break experiment. The VEnKF algorithm was used to assimilate observations obtained from a modified laboratory dam-break experiment with a two-dimensional setup of sensors at the downstream end. The wave meters are placed parallel to the direction of the flow alongside the flume walls to capture both cross flow and stream flow. In both test cases, VEnKF was able to predict genuinely two-dimensional flow patterns when the sensors had a two-dimensional geometry and was stable against model bias in the first test case. In the second test case, the experiments are complemented with an empirical study of the impact of observation interpolation on the stability of the VEnKF filter. In this study, a novel Courant–Friedrichs–Lewy type filter stability condition is observed that relates ensemble variance to the time interpolation distance between observations. The results of the two experiments shows that VEnKF is a good candidate for data assimilation problems and can be implemented in higher dimensional nonlinear models.

scholarly journals Porous Shallow Water Modeling for Urban Floods in the Zhoushan City, China

2021 ◽  
Vol 9 ◽  
Author(s):  
Wei Li ◽  
Bingrun Liu ◽  
Peng Hu ◽  
Zhiguo He ◽  
Jiyu Zou
Keyword(s):  
Shallow Water ◽  
Computational Cost ◽  
Water Model ◽  
Shallow Water Model ◽  
Complex Flow ◽  
Local Complex ◽  
Building Effects ◽  
Refined Meshes ◽  
Complex Building ◽  
The City

Typhoon-induced intense rainfall and urban flooding have endangered the city of Zhoushan every year, urging efficient and accurate flooding prediction. Here, two models (the classical shallow water model that approximates complex buildings by locally refined meshes, and the porous shallow water model that adopts the concept of porosity) are developed and compared for the city of Zhoushan. Specifically, in the porous shallow water model, the building effects on flow storage and conveyance are modeled by the volumetric and edge porosities for each grid, and those on flow resistance are considered by adding extra drag in the flow momentum. Both models are developed under the framework of finite volume method using unstructured triangular grids, along with the Harten-Lax-van Leer-Contact (HLLC) approximate Riemann solver for flux computation and a flexible dry-wet treatment that guarantee model accuracy in dealing with complex flow regimes and topography. The pluvial flooding is simulated during the Super Typhoon Lekima in a 46 km2 mountain-bounded urban area, where efficient and accurate flooding prediction is challenged by local complex building geometry and mountainous topography. It is shown that the computed water depth and flow velocity of the two models agree with each other quite well. For a 2.8-day prediction, the computational cost is 120 min for the porous model using 12 cores of the Intel(R) Xeon(R) Platinum 8173M CPU @ 2.00 GHz processor, whereas it is as high as 17,154 min for the classical shallow water model. It indicates a speed-up of 143 times and sufficient pre-warning time by using the porous shallow water model, without appreciable loss in the quantitative accuracy.

The instability of vertically curved fronts in a two-layer shallow water model

2020 ◽  
Vol 32 (12) ◽  
pp. 124117
Author(s):  
M. W. Harris ◽  
F. J. Poulin ◽  
K. G. Lamb
Keyword(s):  
Shallow Water ◽  
Water Model ◽  
Shallow Water Model

scholarly journals Modelling Weirs in Two-Dimensional Shallow Water Models

Water ◽  
2021 ◽  
Vol 13 (16) ◽  
pp. 2152
Author(s):  
Gonzalo García-Alén ◽  
Olalla García-Fonte ◽  
Luis Cea ◽  
Luís Pena ◽  
Jerónimo Puertas
Keyword(s):  
Experimental Data ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Model ◽  
Two Dimensional ◽  
Shallow Water Model ◽  
Experimental Dataset ◽  
River Hydraulics ◽  
Shallow Water Models ◽  
Water Models

2D models based on the shallow water equations are widely used in river hydraulics. However, these models can present deficiencies in those cases in which their intrinsic hypotheses are not fulfilled. One of these cases is in the presence of weirs. In this work we present an experimental dataset including 194 experiments in nine different weirs. The experimental data are compared to the numerical results obtained with a 2D shallow water model in order to quantify the discrepancies that exist due to the non-fulfillment of the hydrostatic pressure hypotheses. The experimental dataset presented can be used for the validation of other modelling approaches.

scholarly journals Development of a Practical Model for Predicting Soil Salinity in a Salt Marsh in the Arakawa River Estuary

Water ◽  
2021 ◽  
Vol 13 (15) ◽  
pp. 2054
Author(s):  
Naoki Kuroda ◽  
Katsuhide Yokoyama ◽  
Tadaharu Ishikawa
Keyword(s):  
Salt Marsh ◽  
Hydraulic Conductivity ◽  
Shallow Water ◽  
Soil Salinity ◽  
River Estuary ◽  
Flow Simulation ◽  
Design Tool ◽  
Water Model ◽  
Shallow Water Model ◽  
Practical Model

Our group has studied the spatiotemporal variation of soil and water salinity in an artificial salt marsh along the Arakawa River estuary and developed a practical model for predicting soil salinity. The salinity of the salt marsh and the water level of a nearby channel were measured once a month for 13 consecutive months. The vertical profile of the soil salinity in the salt marsh was measured once monthly over the same period. A numerical flow simulation adopting the shallow water model faithfully reproduced the salinity variation in the salt marsh. Further, we developed a soil salinity model to estimate the soil salinity in a salt marsh in Arakawa River. The vertical distribution of the soil salinity in the salt marsh was uniform and changed at almost the same time. The hydraulic conductivity of the soil, moreover, was high. The uniform distribution of salinity and high hydraulic conductivity could be explained by the vertical and horizontal transport of salinity through channels burrowed in the soil by organisms. By combining the shallow water model and the soil salinity model, the soil salinity of the salt marsh was well reproduced. The above results suggest that a stable brackish ecotone can be created in an artificial salt marsh using our numerical model as a design tool.

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