Abstract
We investigate in this paper the behaviors of the Riemann solvers (Roe and Harten-Lax-van Leer-Contact (HLLC) schemes) and the Riemann-solver-free method (central-upwind scheme) regarding their accuracy and efficiency for solving the 2D shallow water equations. Our model was devised to be spatially second-order accurate with the Monotonic Upwind Scheme for Conservation Laws (MUSCL) reconstruction for a cell-centered finite volume scheme—and be temporally fourth-order accurate using the Runge–Kutta fourth-order method. Four benchmark cases of dam-break and tsunami events dealing with highly-discontinuous flows and wet–dry problems were simulated. To this end, we applied a reordering strategy for the data structures in our code supporting efficient vectorization and memory access alignment for boosting the performance. Two main features are pointed out here. Firstly, the reordering strategy employed has enabled highly-efficient vectorization for the three solvers investigated on three modern hardware (AVX, AVX2, and AVX-512), where speed-ups of 4.5–6.5× were obtained on the AVX/AVX2 machines for eight data per vector while on the AVX-512 machine we achieved a speed-up of up to 16.7× for 16 data per vector, all with singe-core computation; with parallel simulations, speed-ups of up to 75.7–121.8× and 928.9× were obtained on AVX/AVX2 and AVX-512 machines, respectively. Secondly, we observed that the central-upwind scheme was able to outperform the HLLC and Roe schemes 1.4× and 1.25×, respectively, by exhibiting similar accuracies. This study would be useful for modelers who are interested in developing shallow water codes.
Highlights
Dam-break or tsunami flows cause potential dangers to human life, and great losses of property
We note that the Roe scheme may in some cases produce negative depths, see [29]; in all implementations tested here, we did not find any negative depth with the Roe scheme
We have shown in the previous sections that the HLLC, Roe, and CU schemes are quite accurate for simulating the test cases, where only non-significant differences are shown between them
Summary
Dam-break or tsunami flows cause potential dangers to human life, and great losses of property. To solve the time-dependent SWEs, all the aforementioned schemes must be temporally discretized either by using an implicit or an explicit time stepping method Despite its simplicity, the latter may, suffer from a stability computational issue when simulating a very low water on a very rough bed [16,17]. We observe that the CU scheme is capable of outperforming the performance of the HLLC and Roe schemes by exhibiting similar accuracies These findings would be useful for modelers as a reference to select the numerical solvers to be included in their models as well as to optimize their codes for vectorization.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
