Recent advances on the discontinuous Galerkin method for shallow water equations with topography source terms

A Duran, F Marche - Computers & Fluids, 2014 - Elsevier
We consider in this work the discontinuous Galerkin discretization of the nonlinear shallow
water equations on unstructured triangulations. In the recent years, several improvements …

Numerical simulation of water resources problems: Models, methods, and trends

CT Miller, CN Dawson, MW Farthing, TY Hou… - Advances in Water …, 2013 - Elsevier
Mechanistic modeling of water resources systems is a broad field with abundant challenges.
We consider classes of model formulations that are considered routine, the focus of current …

Analysis of adaptive mesh refinement for IMEX discontinuous Galerkin solutions of the compressible Euler equations with application to atmospheric simulations

MA Kopera, FX Giraldo - Journal of Computational Physics, 2014 - Elsevier
The resolutions of interests in atmospheric simulations require prohibitively large
computational resources. Adaptive mesh refinement (AMR) tries to mitigate this problem by …

A high-performance integrated hydrodynamic modelling system for urban flood simulations

Q Liang, LS Smith - Journal of Hydroinformatics, 2015 - iwaponline.com
A new High-Performance Integrated hydrodynamic Modelling System (Hi-PIMS) is tested for
urban flood simulation. The software solves the two-dimensional shallow water equations …

Discontinuous Galerkin methods for modeling hurricane storm surge

C Dawson, EJ Kubatko, JJ Westerink, C Trahan… - Advances in Water …, 2011 - Elsevier
Storm surge due to hurricanes and tropical storms can result in significant loss of life,
property damage, and long-term damage to coastal ecosystems and landscapes. Computer …

Scalability of an unstructured grid continuous Galerkin based hurricane storm surge model

S Tanaka, S Bunya, JJ Westerink, C Dawson… - Journal of Scientific …, 2011 - Springer
This paper evaluates the parallel performance and scalability of an unstructured grid
Shallow Water Equation (SWE) hurricane storm surge model. We use the ADCIRC model …

Optimal strong-stability-preserving Runge–Kutta time discretizations for discontinuous Galerkin methods

EJ Kubatko, BA Yeager, DI Ketcheson - Journal of Scientific Computing, 2014 - Springer
Discontinuous Galerkin (DG) spatial discretizations are often used in a method-of-lines
approach with explicit strong-stability-preserving (SSP) Runge–Kutta (RK) time steppers for …

[HTML][HTML] A dynamic hp-adaptive discontinuous Galerkin method for shallow-water flows on the sphere with application to a global tsunami simulation

S Blaise, A St-Cyr - Monthly Weather Review, 2012 - journals.ametsoc.org
A Dynamic hp-Adaptive Discontinuous Galerkin Method for Shallow-Water Flows on the Sphere
with Application to a Global Tsunami Simulation in: Monthly Weather Review Volume 140 Issue 3 …

Locally limited and fully conserved RKDG2 shallow water solutions with wetting and drying

G Kesserwani, Q Liang - Journal of scientific computing, 2012 - Springer
This work extends a well-balanced second-order Runge-Kutta discontinuous Galerkin
(RKDG2) scheme to provide conservative simulations for shallow flows involving wetting …

p-adaptive discontinuous Galerkin method for the shallow water equations with a parameter-free error indicator

S Faghih-Naini, V Aizinger - GEM-International Journal on …, 2022 - Springer
We propose a p-adaptive quadrature-free discontinuous Galerkin method for the shallow
water equations based on a computationally efficient adaptivity indicator which works …