scholarly journals A Particle-Mesh Method for the Shallow Water Equations Near Geostrophic Balance

2002 ◽  
Vol 180 (2) ◽  
pp. 407-426 ◽  
Author(s):  
Jason Frank ◽  
Sebastian Reich
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Geostrophic Balance ◽  
Mesh Method

scholarly journals Numerical approximation of the shallow water equations with coriolis source term

2021 ◽  
Vol 70 ◽  
pp. 31-44
Author(s):  
E. Audusse ◽  
V. Dubos ◽  
A. Duran ◽  
N. Gaveau ◽  
Y. Nasseri ◽  
...  
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Coriolis Force ◽  
Shallow Water Equations ◽  
Numerical Approximation ◽  
Energy Estimates ◽  
Discrete Energy ◽  
Geostrophic Balance ◽  
Low Froude Number ◽  
Numerical Fluxes

We investigate in this work a class of numerical schemes dedicated to the non-linear Shallow Water equations with topography and Coriolis force. The proposed algorithms rely on Finite Volume approximations formulated on collocated and staggered meshes, involving appropriate diffusion terms in the numerical fluxes, expressed as discrete versions of the linear geostrophic balance. It follows that, contrary to standard Finite-Volume approaches, the linear versions of the proposed schemes provide a relevant approximation of the geostrophic equilibrium. We also show that the resulting methods ensure semi-discrete energy estimates. Numerical experiments exhibit the efficiency of the approach in the presence of Coriolis force close to the geostrophic balance, especially at low Froude number regimes.

On a Moving Mesh Method Applied to the Shallow Water Equations

2010 ◽  
Author(s):  
J. Felcman ◽  
L. Kadrnka ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Moving Mesh ◽  
Moving Mesh Method ◽  
Mesh Method

MAPPING TIDAL CURRENTS AND RESIDUAL CURRENTS BY USE OF COASTAL ACOUSTIC TOMOGRAPHY

2017 ◽  
Author(s):  
Xiao-Hua Zhu ◽  
Xiao-Hua Zhu ◽  
Ze-Nan Zhu ◽  
Ze-Nan Zhu ◽  
Xinyu Guo ◽  
...  
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Mean Amplitude ◽  
Momentum Equation ◽  
Tidal Currents ◽  
Acoustic Tomography ◽  
Mean Values ◽  
Residual Currents ◽  
Water Depths ◽  
Deep Area

A coastal acoustic tomography (CAT) experiment for mapping the tidal currents in the Zhitouyang Bay was successfully carried out with seven acoustic stations during July 12 to 13, 2009. The horizontal distributions of tidal current in the tomography domain are calculated by the inverse analysis in which the travel time differences for sound traveling reciprocally are used as data. Spatial mean amplitude ratios M2 : M4 : M6 are 1.00 : 0.15 : 0.11. The shallow-water equations are used to analyze the generation mechanisms of M4 and M6. In the deep area, velocity amplitudes of M4 measured by CAT agree well with those of M4 predicted by the advection terms in the shallow water equations, indicating that M4 in the deep area where water depths are larger than 60 m is predominantly generated by the advection terms. M6 measured by CAT and M6 predicted by the nonlinear quadratic bottom friction terms agree well in the area where water depths are less than 20 m, indicating that friction mechanisms are predominant for generating M6 in the shallow area. Dynamic analysis of the residual currents using the tidally averaged momentum equation shows that spatial mean values of the horizontal pressure gradient due to residual sea level and of the advection of residual currents together contribute about 75% of the spatial mean values of the advection by the tidal currents, indicating that residual currents in this bay are induced mainly by the nonlinear effects of tidal currents.

Sign in / Sign up

Export Citation Format

Share Document