Topography discretization techniques for Godunov-type shallow water numerical models: a comparative study

Abstract

This paper compares various topography discretization approaches for Godunov-type shallow water numerical models. Many different approaches have emerged popular with Godunov-type water wave models. To date, literature lacks an investigative study distinguishing their pros and the cons, and assessing their reliability relating to issues of practical interest. To address this gap, this work reviews and assesses five standard topography discretization methods that consist of the Upwind, the surface gradient method (SGM), the mathematically balanced set of the SWE (Etta-SWE), the hydrostatic reconstruction technique (Hydr-Rec) and the RKDG2 model. The study further considers mix-mode approaches that incorporate wetting and drying together with the topography discretization. Steady and transient hydraulic tests are employed to measure the performance of the approaches relating to the issues of mesh size, topography's differentiability, accuracy-order of the numerical scheme, and impact of wetting and drying.

A robust and well-balanced numerical model for solving the two-layer shallow water equations over uneven topography

“…(35) is a central difference approximation, and the second term acts as a diffusion term to stabilize the scheme [14], and in viewing that the standard HLL flux defined by Eq. (35) actually predicts promising results in unsteady flow conditions under all flow regimes [27,36,37], it is reasonable to assume that Eq. (35) may be inaccurate solely for flow with weak motions, in which case the diffusion term can be omitted to maintain the stationary flow at rest.…”

Performance study of the multiwavelet discontinuous Galerkin approach for solving the Green‐Naghdi equations

“…2 The nonlinearity parameter is another related identifier, which is defined as the ratio of the wave amplitude scale to the water depth scale, = a/h 0 . [9][10][11] DG methods are becoming increasingly popular in solving BT equations. Removing this assumption (ie, let = O(1)) while keeping all the O( ) terms gives the so-called Green-Naghdi (GN) equations.…”

A mass conservative well‐balanced reconstruction at wet/dry interfaces for the Godunov‐type shallow water model

“…The interface between a wet and a dry cell is usually referred to as the wet/dry front or wet/dry interface [12,13]. Especially wet/dry interfaces over complex topography are known to cause numerical errors such as spurious oscillations in the flow velocity and negative water depths [13][14][15][16][17][18][19][20][21].…”