American Institute of Mathematical Sciences

Advanced
2005, 2005(Special): 355-364. doi: 10.3934/proc.2005.2005.355

A global semi-Lagrangian spectral model of shallow water equations with time-dependent variable resolution

Daniel Guo 1, and  John Drake 2,

1. 

Department of Mathematics and Statistics, University of North Carolina at Wilmington, Wilmington, NC 28403-3297, United States
2. 

Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States

Received  October 2004 Revised  March 2005 Published  September 2005

A time-dependent focusing grid works together with the formulation of a semi-implicit, semi-Lagrangian spectral method for the shallow-water equations in a rotated and stretched spherical geometry. The conformal mapping of the underlying discrete grid based on the Schmidt transformation, focuses grid on a particular region or path with variable resolution. A new advective form of the vorticity-divergence equations allows for the conformal map to be incorporated while maintaining an efficient spectral transform algorithm. A shallow water model on the sphere is used to test the spectral model with variable resolution. We are able to focus on a specified location resolving local details of the flow. More importantly, we could follow the features of the flow at all time.
Keywords: Semi-Lagrangian Method; Spectral Transformation; Shallow-Water Equations; Time-Dependent; Variable Resolution; Standard Test Cases..
Mathematics Subject Classification: Primary: 30C30, 35Q35, 65M70, 65T50, 86A1.
Citation: Daniel Guo, John Drake. A global semi-Lagrangian spectral model of shallow water equations with time-dependent variable resolution. Conference Publications, 2005, 2005 (Special) : 355-364. doi: 10.3934/proc.2005.2005.355
[1]

Daniel Guo, John Drake. A global semi-Lagrangian spectral model for the reformulated shallow water equations. Conference Publications, 2003, 2003 (Special) : 375-385. doi: 10.3934/proc.2003.2003.375
[2]

Leonardo J. Colombo, María Emma Eyrea Irazú, Eduardo García-Toraño Andrés. A note on Hybrid Routh reduction for time-dependent Lagrangian systems. Journal of Geometric Mechanics, 2020, 12 (2) : 309-321. doi: 10.3934/jgm.2020014
[3]

Bashar Khorbatly. Long, intermediate and short-term well-posedness of high precision shallow-water models with topography variations. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022068
[4]

Holger Heumann, Ralf Hiptmair. Eulerian and semi-Lagrangian methods for convection-diffusion for differential forms. Discrete and Continuous Dynamical Systems, 2011, 29 (4) : 1471-1495. doi: 10.3934/dcds.2011.29.1471
[5]

Guoliang Zhang, Shaoqin Zheng, Tao Xiong. A conservative semi-Lagrangian finite difference WENO scheme based on exponential integrator for one-dimensional scalar nonlinear hyperbolic equations. Electronic Research Archive, 2021, 29 (1) : 1819-1839. doi: 10.3934/era.2020093
[6]

Yueqiang Shang, Qihui Zhang. A subgrid stabilizing postprocessed mixed finite element method for the time-dependent Navier-Stokes equations. Discrete and Continuous Dynamical Systems - B, 2021, 26 (6) : 3119-3142. doi: 10.3934/dcdsb.2020222
[7]

P. Cerejeiras, U. Kähler, M. M. Rodrigues, N. Vieira. Hodge type decomposition in variable exponent spaces for the time-dependent operators: the Schrödinger case. Communications on Pure and Applied Analysis, 2014, 13 (6) : 2253-2272. doi: 10.3934/cpaa.2014.13.2253
[8]

Andrey Itkin, Dmitry Muravey. Semi-analytic pricing of double barrier options with time-dependent barriers and rebates at hit. Frontiers of Mathematical Finance, 2022, 1 (1) : 53-79. doi: 10.3934/fmf.2021002
[9]

Masahiro Ikeda, Ziheng Tu, Kyouhei Wakasa. Small data blow-up of semi-linear wave equation with scattering dissipation and time-dependent mass. Evolution Equations and Control Theory, 2022, 11 (2) : 515-536. doi: 10.3934/eect.2021011
[10]

Olivier Delestre, Arthur R. Ghigo, José-Maria Fullana, Pierre-Yves Lagrée. A shallow water with variable pressure model for blood flow simulation. Networks and Heterogeneous Media, 2016, 11 (1) : 69-87. doi: 10.3934/nhm.2016.11.69
[11]

Elisabetta Carlini, Francisco J. Silva. A semi-Lagrangian scheme for a degenerate second order mean field game system. Discrete and Continuous Dynamical Systems, 2015, 35 (9) : 4269-4292. doi: 10.3934/dcds.2015.35.4269
[12]

Alexandre Mouton. Two-scale semi-Lagrangian simulation of a charged particle beam in a periodic focusing channel. Kinetic and Related Models, 2009, 2 (2) : 251-274. doi: 10.3934/krm.2009.2.251
[13]

Mourad Choulli, Yavar Kian. Stability of the determination of a time-dependent coefficient in parabolic equations. Mathematical Control and Related Fields, 2013, 3 (2) : 143-160. doi: 10.3934/mcrf.2013.3.143
[14]

Feng Zhou, Chunyou Sun, Xin Li. Dynamics for the damped wave equations on time-dependent domains. Discrete and Continuous Dynamical Systems - B, 2018, 23 (4) : 1645-1674. doi: 10.3934/dcdsb.2018068
[15]

Stephen Anco, Maria Rosa, Maria Luz Gandarias. Conservation laws and symmetries of time-dependent generalized KdV equations. Discrete and Continuous Dynamical Systems - S, 2018, 11 (4) : 607-615. doi: 10.3934/dcdss.2018035
[16]

Fengjuan Meng, Meihua Yang, Chengkui Zhong. Attractors for wave equations with nonlinear damping on time-dependent space. Discrete and Continuous Dynamical Systems - B, 2016, 21 (1) : 205-225. doi: 10.3934/dcdsb.2016.21.205
[17]

Tingting Liu, Qiaozhen Ma. Time-dependent asymptotic behavior of the solution for plate equations with linear memory. Discrete and Continuous Dynamical Systems - B, 2018, 23 (10) : 4595-4616. doi: 10.3934/dcdsb.2018178
[18]

Ying Sui, Huimin Yu. Singularity formation for compressible Euler equations with time-dependent damping. Discrete and Continuous Dynamical Systems, 2021, 41 (10) : 4921-4941. doi: 10.3934/dcds.2021062
[19]

Andreas Hiltebrand, Siddhartha Mishra. Entropy stability and well-balancedness of space-time DG for the shallow water equations with bottom topography. Networks and Heterogeneous Media, 2016, 11 (1) : 145-162. doi: 10.3934/nhm.2016.11.145
[20]

Alexander Zlotnik, Ilya Zlotnik. Finite element method with discrete transparent boundary conditions for the time-dependent 1D Schrödinger equation. Kinetic and Related Models, 2012, 5 (3) : 639-667. doi: 10.3934/krm.2012.5.639

 Impact Factor: 

Tools

Metrics

  • PDF downloads (48)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy