Author(s): Haegyun Lee; Namjoo Lee

Linked Author(s): haegyun Lee, Namjoo Lee

Keywords: Discontinuous Galerkin; Implicit scheme; Primal formulation; Shallow water equations; Turbulent stress

Abstract: Though the discontinuous Galerkin (DG) method has been widely applied as an effective numerical tool for hyperbolic conservation equations (such as shallow water equations, compressible Navier-Stokes equations, etc.), one of the well-known drawbacks is its inconvenience in the treatment of second or higher derivative terms. For this reason, since the beginning of DG in 1970s, many researchers have made efforts in devising consistent schemes to incorporate the possible jumps in solutions. The turbulent stress terms of the shallow water equations are expressed as second order derivatives and, of course, can not be neglected due to its practical importance. So far, as a traditional approach, a flux formulation has been applied in DG shallow water equations modeling. However, it is criticized for not being efficient in terms of memory and computation time. In this study, the BR2 scheme, a well known primal formulation in the DG community, was employed and combined with the implicit Euler backward difference scheme for shallow water equations. The developed model was applied to several benchmark problems (including channel contraction and widening, curved channels, etc.) and good agreements were observed.

DOI: https://doi.org/10.3850/IAHR-39WC25217119202252

Year: 2022