WELL-BALANCED SECOND-ORDER FINITE ELEMENT APPROXIMATION OF THE SHALLOW WATER EQUATIONS WITH FRICTION

abstract

• 2018 Society for Industrial and Applied Mathematics. This paper investigates the approximation of the shallow water equations with topography and friction, using continuous fnite elements. A new, second-order, parameter-free, wellbalanced and positivity preserving explicit approximation technique is introduced. The novelties of the method are the explicit treatment of the friction term, the robust approximation of dry states, a commutator-based, high-order, entropy viscosity, and a local limiting procedure. The computational method is illustrated on various benchmark tests.

authors

• Guermond, Jean-Luc
• Popov, Bojan

published proceedings

• SIAM JOURNAL ON SCIENTIFIC COMPUTING

author list (cited authors)

• Guermond, J., de Luna, M. Q., Popov, B., Kees, C. E., & Farthing, M. W.

citation count

• 18

complete list of authors

• Guermond, Jean-Luc||de Luna, Manuel Quezada||Popov, Bojan||Kees, Christopher E||Farthing, Matthew W

publication date

• January 2018

publisher

• Society for Industrial & Applied Mathematics (SIAM)  Publisher

published in

• SIAM Journal on Scientific Computing  Journal

keywords

• Finite Element Method
• Friction Term
• Invariant Domain
• Positivity Preserving
• Second-order Accuracy
• Shallow Water
• Well-balanced Approximation

Digital Object Identifier (DOI)

• 10.1137/17M1156162

start page

• A3873

end page

• A3901

volume

• 40

issue

• 6

URL

• http://dx.doi.org/10.1137/17m1156162