Dynamically consistent shallow-water equation sets in non-spherical geometry with latitudinal variation of gravity

2015 ◽  
Vol 141 (691) ◽  
pp. 2429-2443 ◽  
Author(s):  
Andrew Staniforth
Keyword(s):  
Shallow Water ◽  
Shallow Water Equation ◽  
Spherical Geometry ◽  
Latitudinal Variation

scholarly journals Data‐Driven Learning of Reduced‐Order Dynamics for a Parametrized Shallow Water Equation

PAMM ◽  
2021 ◽  
Vol 20 (S1) ◽  
Author(s):  
Süleyman Yıldız ◽  
Pawan Goyal ◽  
Peter Benner ◽  
Bülent Karasözen
Keyword(s):  
Shallow Water ◽  
Shallow Water Equation ◽  
Data Driven ◽  
Reduced Order

Stream Computation of Shallow Water Equation Solver for FPGA-based 1D Tsunami Simulation

2016 ◽  
Vol 43 (4) ◽  
pp. 82-87 ◽  
Author(s):  
Kentaro Sano ◽  
Fumiya Kono ◽  
Naohito Nakasato ◽  
Alexander Vazhenin ◽  
Stanislav Sedukhin
Keyword(s):  
Shallow Water ◽  
Shallow Water Equation ◽  
Tsunami Simulation

scholarly journals A Weighted-Least-Squares Meshless Model for Non-Hydrostatic Shallow Water Waves

Water ◽  
2021 ◽  
Vol 13 (22) ◽  
pp. 3195
Author(s):  
Nan-Jing Wu ◽  
Yin-Ming Su ◽  
Shih-Chun Hsiao ◽  
Shin-Jye Liang ◽  
Tai-Wen Hsu
Keyword(s):  
Least Squares ◽  
Shallow Water ◽  
Water Waves ◽  
Dynamic Pressure ◽  
Weighted Least Squares ◽  
Shallow Water Equation ◽  
Analytic Solutions ◽  
Numerical Results ◽  
Benchmark Problems ◽  
Time Marching

In this paper, an explicit time marching procedure for solving the non-hydrostatic shallow water equation (SWE) problems is developed. The procedure includes a process of prediction and several iterations of correction. In these processes, it is essential to accurately calculate the spatial derives of the physical quantities such as the temporal water depth, the average velocities in the horizontal and vertical directions, and the dynamic pressure at the bottom. The weighted-least-squares (WLS) meshless method is employed to calculate these spatial derivatives. Though the non-hydrostatic shallow water equations are two dimensional, on the focus of presenting this new time marching approach, we just use one dimensional benchmark problems to validate and demonstrate the stability and accuracy of the present model. Good agreements are found in the comparing the present numerical results with analytic solutions, experiment data, or other numerical results.

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