Extension of an explicit finite volume method to large time steps (CFL>1): application to shallow water flows

2005 ◽  
Vol 50 (1) ◽  
pp. 63-102 ◽  
Author(s):  
J. Murillo ◽  
P. García-Navarro ◽  
P. Brufau ◽  
J. Burguete
Keyword(s):  
Shallow Water ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Large Time ◽  
Water Flows ◽  
Shallow Water Flows ◽  
Volume Method

scholarly journals Projection finite volume method for shallow water flows

2015 ◽  
Vol 118 ◽  
pp. 87-101 ◽  
Author(s):  
Fayssal Benkhaldoun ◽  
Saida Sari ◽  
Mohammed Seaid
Keyword(s):  
Shallow Water ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Water Flows ◽  
Shallow Water Flows ◽  
Volume Method

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.

scholarly journals Adaptive Finite Volume Method for the Shallow Water Equations on Triangular Grids

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Sudi Mungkasi
Keyword(s):  
Shallow Water ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Shallow Water Equations ◽  
Adaptive Mesh Refinement ◽  
Adaptive Mesh ◽  
Error Indicator ◽  
Triangular Grids ◽  
Volume Method ◽  
Numerical Entropy

This paper presents a numerical entropy production (NEP) scheme for two-dimensional shallow water equations on unstructured triangular grids. We implement NEP as the error indicator for adaptive mesh refinement or coarsening in solving the shallow water equations using a finite volume method. Numerical simulations show that NEP is successful to be a refinement/coarsening indicator in the adaptive mesh finite volume method, as the method refines the mesh or grids around nonsmooth regions and coarsens them around smooth regions.

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