Artificial Viscosity Technique: A Riemann-Solver-Free Method for 2D Urban Flood Modelling on Complex Topography

Comparison of Shallow Water Solvers: Applications for Dam-Break and Tsunami Cases with Reordering Strategy for Efficient Vectorization on Modern Hardware

“…where A is the cell area, ∆t is the time step, α p is the coefficient being 1/4, 1/3 , 1/2, and 1 for p = 1-4, respectively. The numerical procedures for Equations (4) and (6) are given in detail in [17,25,26], thus are not presented here.…”

“…Based on these results, one can see although the Roe scheme experiences the largest speed-up on the AVX machine or the HLLC scheme achieves the largest improvement factor on the AVX-512 machine, both of these schemes are still significantly outperformed by the CU scheme with average multiplication factors of 1.4× and 1.25×, respectively. This is not so surprising since the computational procedures of both the HLLC and Roe solvers include complex branch statements (if-then-else), thus should theoretically be much more expensive than the CU scheme, see [17]. The HLLC scheme requires the nested branch statements; the first one is to compute the wave speeds, which are later required in the second branch statement for calculating the final convective fluxes.…”

“…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, however, suffer from a stability computational issue particularly when simulating a very low water on a very rough bed [16,17]. The former is unconditionally stable and even is very flexible to use a large time step.…”

“…We use here an in-house code of the first-author-numerical simulation of free surface shallow water 2D (NUFSAW2D). Some successful applications were shown using NUFSAW2D for varying shallow water-type simulations, e.g., dam-break cases, overland flows, and turbulent flows, see [17,21,24,25]. This paper is organized as follows.…”

“…The first loop corresponds to the edges 1-16 and the second one to the edges 17-31. In the first loop (lines 1-7), each flux computation accesses the array with the farthest alignment of seg_y, whereas the arrays are designed in the second loop (lines [8][9][10][11][12][13][14][15][16][17] to have contiguous patterns. Every edge has a certain pattern for its two corresponding cells, where no data-dependency exists, thus enabling an efficient vectorization.…”