Exshall: A Turkel-Zwas explicit large time-step FORTRAN program for solving the shallow-water equations in spherical coordinates

1991 ◽  
Vol 17 (9) ◽  
pp. 1311-1343 ◽  
Author(s):  
I.M. Navon ◽  
Jian Yu
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Large Time ◽  
Fortran Program ◽  
Spherical Coordinates ◽  
Time Step ◽  
Large Time Step

scholarly journals A large time-step and well-balanced Lagrange-projection type scheme for the shallow water equations

2017 ◽  
Vol 15 (3) ◽  
pp. 765-788 ◽  
Author(s):  
Christophe Chalons ◽  
Pierre Kestener ◽  
Samuel Kokh ◽  
Maxime Stauffert
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Large Time ◽  
Time Step ◽  
Large Time Step

A large time step 1D upwind explicit scheme (CFL>1): Application to shallow water equations

2012 ◽  
Vol 231 (19) ◽  
pp. 6532-6557 ◽  
Author(s):  
M. Morales-Hernandez ◽  
P. García-Navarro ◽  
J. Murillo
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Large Time ◽  
Explicit Scheme ◽  
Time Step ◽  
Large Time Step

A large time step Godunov scheme for free-surface shallow water equations

2014 ◽  
Vol 59 (21) ◽  
pp. 2534-2540 ◽  
Author(s):  
Renyi Xu ◽  
Deyu Zhong ◽  
Baosheng Wu ◽  
Xudong Fu ◽  
Runze Miao
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Large Time ◽  
Godunov Scheme ◽  
Time Step ◽  
Large Time Step

IMEX Large Time Step Finite Volume Methods for Low Froude Number Shallow Water Flows

2014 ◽  
Vol 16 (2) ◽  
pp. 307-347 ◽  
Author(s):  
Georgij Bispen ◽  
K. R. Arun ◽  
Mária Lukáčová-Medvid’ová ◽  
Sebastian Noelle
Keyword(s):  
Shallow Water ◽  
Froude Number ◽  
Finite Volume ◽  
Large Time ◽  
Time Step ◽  
Water Flows ◽  
Shallow Water Flows ◽  
Nonlinear Advection ◽  
Low Froude Number ◽  
Large Time Step

AbstractWe present new large time step methods for the shallow water flows in the low Froude number limit. In order to take into account multiscale phenomena that typically appear in geophysical flows nonlinear fluxes are split into a linear part governing the gravitational waves and the nonlinear advection. We propose to approximate fast linear waves implicitly in time and in space by means of a genuinely multidimensional evolution operator. On the other hand, we approximate nonlinear advection part explicitly in time and in space by means of the method of characteristics or some standard numerical flux function. Time integration is realized by the implicit-explicit (IMEX) method. We apply the IMEX Euler scheme, two step Runge Kutta Cranck Nicolson scheme, as well as the semi-implicit BDF scheme and prove their asymptotic preserving property in the low Froude number limit. Numerical experiments demonstrate stability, accuracy and robustness of these new large time step finite volume schemes with respect to small Froude number.

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