Efficient GPU implementation of a two waves TVD-WAF method for the two-dimensional one layer shallow water system on structured meshes

Abstract

The numerical solutions of Shallow Water Equations are useful for applications related to geophysical flows that usually take place in large computational domains and could require real time calculation. Therefore, parallel versions of accurate and efficient numerical solvers for high performance platforms are needed to be able to deal with these simulation scenarios in reasonable times. In this paper we present an efficient CUDA implementation of a first and second order HLL methods and a two-waves TVD-WAF one. We propose to write all these methods under a common framework, the WAF method is slightly slower that the first order HLL method and two times faster than the second order HLL method, but it provides numerical results almost as accurate as the second order HLL scheme.

Accelerating an Adaptive Mesh Refinement Code for Depth‐Averaged Flows Using GPUs

“…GPU acceleration has been applied to tsunami models in the past, although primarily on grids with fixed spatial resolution, including those of Acuña and Aoki (), Lastra et al (), De La Asunción et al (), Brodtkorb et al (), de la Asunción et al (), Smith and Liang (), Amouzgar et al (), and De La Asunción et al (). A recent application to an AMR code is presented by de la Asunción and Castro () for a landslide‐generated tsunami, and GPU acceleration of other AMR algorithms have been pursued in other communities, particularly in astrophysics (e.g., Schive et al, ; Wang et al, ).…”

Third‐ and fourth‐order well‐balanced schemes for the shallow water equations based on the CWENO reconstruction

“…Here, only structured grids on ( x , y ) or ( θ , φ ) plane are considered. We use the HLLC scheme written as a PVM method . We use the three stages TVD RK method that is also third‐order accurate in time.…”

GPU-enhanced Finite Volume Shallow Water solver for fast flood simulations

“…Subsequently a Roe scheme was presented by de la Asunción et al (2011), a first order accurate, finite difference model is adopted by Kalyanapu et al (2011) andLamb et al (2009) developed a diffusion wave model, based on CUDA programming language. More recently, several attempts to develop numerical schemes with high order of accuracy have been proposed de la Asunción et al, 2013) also adopting unstructured mesh de la Asunción et al, 2013). Simulations of practical test cases have been reported by de la Asunción et al (2013); Brodtkorb et al (2012) which showed relevant speed-ups (in comparison with nonparallel codes) for dam-break waves.…”

“…More recently, several attempts to develop numerical schemes with high order of accuracy have been proposed de la Asunción et al, 2013) also adopting unstructured mesh de la Asunción et al, 2013). Simulations of practical test cases have been reported by de la Asunción et al (2013); Brodtkorb et al (2012) which showed relevant speed-ups (in comparison with nonparallel codes) for dam-break waves. Moreover, attempts to use multiple GPUs to tackle larger simulations have been presented .…”