Non-Hydrostatic Discontinuous/Continuous Galerkin Model for Wave Propagation, Breaking and Runup

Abstract

This paper presents a new depth-integrated non-hydrostatic finite element model for simulating wave propagation, breaking and runup using a combination of discontinuous and continuous Galerkin methods. The formulation decomposes the depth-integrated non-hydrostatic equations into hydrostatic and non-hydrostatic parts. The hydrostatic part is solved with a discontinuous Galerkin finite element method to allow the simulation of discontinuous flows, wave breaking and runup. The non-hydrostatic part led to a Poisson type equation, where the non-hydrostatic pressure is solved using a continuous Galerkin method to allow the modeling of wave propagation and transformation. The model uses linear quadrilateral finite elements for horizontal velocities, water surface elevations and non-hydrostatic pressures approximations. A new slope limiter for quadrilateral elements is developed. The model is verified and validated by a series of analytical solutions and laboratory experiments.

Three-Dimensional Hole Size (3DHS) Approach for Water Flow Turbulence Analysis over Emerging Sand Bars: Flume-Scale Experiments

“…As shown in Figure 1 In the present experimental study, the 3D velocity components over x, y, and z directions in the proximity of the examined emerging sand bar [38][39][40][41][42][43], respectively indicated as streamwise (u), spanwise (v), and vertical (w) velocity components, were measured by using a 4-beam down-looking acoustic Doppler velocimeter (ADV) device [44][45][46][47][48] with an acquisition frequency of 20 Hz. The time-series data having a signal average Correlation coefficient-the average correlation between acoustic wave signals recorded by each couple of ADV beams-of less than 0.70 were excluded from the further data processing [49][50][51][52].…”

Comparison between the Lagrangian and Eulerian Approach for Simulating Regular and Solitary Waves Propagation, Breaking and Run-Up

“…The Eulerian grid-based method used in this paper is the non-hydrostatic D/C Galerkin, presented in Calvo et. al [7]. The model is a two-dimensional depth-integrated non-hydrostatic model with the capacity of simulating wave propagation, breaking and run-up in a finite element framework.…”

“…Details of the entire solution process can be found in Calvo et. al [7]. After each of the three solution steps, a special slope limiter for quadrilateral elements is applied.…”

“…Eulerian approaches or grid-based methods such as the finite element method (FEM), finite difference method (FDM) and finite volume method (FVM) have been applied to a wide range of engineering applications such as breaking waves [5][6][7], eddies [8], hydraulic jumps [9][10][11][12], sediment transport [13] and current and oil drift modeling [14][15][16][17].…”