Τίτλος:
Galerkin finite element methods for the Shallow Water equations over variable bottom
Γλώσσες Τεκμηρίου:
Αγγλικά
Περίληψη:
We consider the one-dimensional shallow water equations (SW) in a finite channel with variable bottom topography. We pose several initial–boundary-value problems for the SW system, including problems with transparent (characteristic) boundary conditions in the supercritical and the subcritical case. We discretize these problems in the spatial variable by standard Galerkin-finite element methods and prove L2-error estimates for the resulting semidiscrete approximations. We couple the schemes with the 4th order-accurate, explicit, classical Runge–Kutta time stepping procedure and use the resulting fully discrete methods in numerical experiments of shallow water wave propagation over variable bottom topographies with several kinds of boundary conditions. We discuss issues related to the attainment of a steady state of the simulated flows, including the good balance of the schemes. © 2019 Elsevier B.V.
Συγγραφείς:
Kounadis, G.
Dougalis, V.A.
Περιοδικό:
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Λέξεις-κλειδιά:
Boundary conditions; Boundary value problems; Equations of motion; Galerkin methods; Numerical methods; Runge Kutta methods; Topography; Water waves; Wave propagation, Characteristic boundary conditions; Error estimates; Galerkin finite element methods; Shallow water equations; Variable bottom topographies, Finite element method
DOI:
10.1016/j.cam.2019.06.031
