Argiris Delis

We present a high-order well-balanced unstructured finite volume (FV) scheme on triangular meshes for modeling weakly nonlinear and weakly dispersive water waves over slowly varying bathymetries, as described by the 2D depth-integrated extended Boussinesq equations of Nwogu, rewritten here in conservation law form. The FV scheme numerically solves the conservative form of the equations following the median dual node-centered approach, for both the advective and dispersive part of the equations. For the advective fluxes, the scheme utilizes an approximate Riemann solver along with a well-balanced topography source term upwinding. Higher order accuracy in space and time is achieved through a MUSCL-type reconstruction technique and through a strong stability preserving explicit Runge–Kutta time stepping. Special attention is given to the accurate numerical treatment of moving wet/dry fronts and boundary conditions. The model is applied to several examples of non-breaking wave propagation over variable topographies and the computed solutions are compared to experimental data. The presented results indicate that the presented FV model is robust and capable of simulating wave transformations from relatively deep to shallow water, providing accurate predictions of the wave's propagation, shoaling and runup.► A novel approach for numerically integrating Nwogu's 2D Boussinsesq equations on unstructured meshes. ► Equations recast in conservation law form, having an identical flux term as the nonlinear shallow water equations. ► A higher-order well-balanced finite volume scheme is developed with accurate treatment for shoreline motion. ► The approach combines state of the art discretizations and accurately simulates wave shoaling and runup.

We construct a parallel algorithm, suitable for distributed memory architectures, of an explicit shock-capturing finite volume method for solving the two-dimensional shallow water equations. The finite volume method is based on the very popular approximate Riemann solver of Roe and is extended to second order spatial accuracy by an appropriate TVD technique. The parallel code is applied to distributed memory architectures using domain decomposition techniques and we investigate its performance on a grid computer and on a Distributed Shared Memory supercomputer. The effectiveness of the parallel algorithm is considered for specific benchmark test cases. The performance of the realization measured in terms of execution time and speedup factors reveals the efficiency of the implementation.

We numerically study a relatively simple two-dimensional (2D) model for landslide-generated nonlinear surface water waves. The landslides are modeled as rigid and impervious bodies translating on a flat or an inclined bottom. The water motion is assumed to be properly modeled by the 2D nonlinear system of shallow water equations. The resulting 2D system is numerically solved by means of a conservative well-balanced high-resolution finite volume upwind scheme esspecially adapted to treat advancing wet/dry fronts over irregular topography. Numerical results for 1D and 2D benchmark cases include comparisons with analytical or asymptotic solutions as well as comparisons with experimental data. The numerical investigation reveals that although the presented model has certain limitations, it appears to be able to model important aspects and the most significant characteristics of wave formation and propagation in their initial generation stage, namely, the waves moving toward the shore, the subsequent run-up and run-down, the waves propagating toward deep water, as well as the shape and arrival time of these waves. Copyright © 2009 John Wiley & Sons, Ltd.

A formally fourth-order well-balanced hybrid finite volume/difference (FV/FD) numerical scheme for approximating the conservative form of two 1D extended Boussinesq systems is presented. The FV scheme is of the Godunov type and utilizes Roeʼs approximate Riemann solver for the advective fluxes along with well-balanced topography source term upwinding, while FD discretizations are applied to the dispersive terms in the systems. Special attention is given to the accurate numerical treatment of moving wet/dry fronts. To access the performance and applicability, by exposing the merits and differences of the two formulations, the numerical models have been applied to idealized and challenging experimental test cases. Special attention is paid in comparing both Boussinesq models to the nonlinear shallow water equations (NSWE) in the simulation of the experimental results. The outcomes from this work confirm that, although the NSWE can be sufficient in some cases to predict the general characteristics of propagating waves, the two Boussinesq models provided considerable more accurate results for highly dispersive waves over increasing water depths.

Several explicit high resolution TVD methods and their detailed application to steady and unsteady one-dimensional free surface channel flow problems are presented. Some of these methods are widely presented in the literature. Their evaluation is based on computations ...

... 9 in order to validate the accuracy and per-formance of each scheme. ... The well-known system of the 2D NSWE models the behav-ior of shallow free surface flows under the action ... Performance and Comparison of Cell-Centered and Node-Centered Unstructured Finite Volume ...

The Saint Venant equations for modelling flow in open channels are solved in this paper, using a variety of total variation diminishing (TVD) schemes. The performance of second-and third-order-accurate TVD schemes is investigated for the computation of free-surface ...

Page 1. Evaluation of some approximate Riemann solvers for transient open channel flows ... These solvers are usually the building blocks towards the construction of higher order accurate shock-capturing schemes. Details of the governing equations are presented. ...

The present work addresses the numerical prediction of shallow water ows with the application of the HLLE approximate Riemann solver. This Riemann solver has several desirable properties, such as, ease of implementation, satisfaction of entropy conditions, high shock ...