The Mathematical Institute, University of Oxford, Eprints Archive

Well-balanced $r$-adaptive and moving mesh space-time discontinuous Galerkin method for the shallow water equations

Rhebergen, Sander (2013) Well-balanced $r$-adaptive and moving mesh space-time discontinuous Galerkin method for the shallow water equations. Technical Report. Unspecified. (Submitted)

[img]
Preview
PDF
3MB

Abstract

In this article we introduce a well-balanced discontinuous Galerkin method for the shallow water equations on moving meshes. Particular emphasis will be given on $r$-adaptation in which mesh points of an initially uniform mesh move to concentrate in regions where interesting behaviour of the solution is observed. Obtaining well-balanced numerical schemes for the shallow water equations on fixed meshes is nontrivial and has been a topic of much research. In [S. Rhebergen, O. Bokhove, J.J.W. van der Vegt, Discontinuous Galerkin finite element methods for hyperbolic nonconservative partial differential equations, J. Comput. Phys. 227 (2008) 1887–1922] we introduced a well-balanced discontinuous Galerkin method using the theory of weak solutions for nonconservative products introduced in [G. Dal Maso, P.G. LeFloch, F. Murat, Definition and weak stability of nonconservative products, J. Math. Pures Appl. 74 (1995) 483–548]. In this article we continue this approach and prove well-balancedness of a discontinuous Galerkin method for the shallow water equations on moving meshes. Numerical simulations are then performed to verify the $r$-adaptive method in combination with the space-time discontinuous Galerkin method against analytical solutions and showing its robustness on more complex problems.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1757
Deposited By: Lotti Ekert
Deposited On:09 Nov 2013 12:02
Last Modified:29 May 2015 19:27

Repository Staff Only: item control page