OpenMP Performance for 1D Shallow Water Equations with High Order of Time Discretization

OpenMP is pivotal in simulating shallow water equations (SWE), a foundational model with applications in diverse fields like hydrodynamics and environmental engineering. These equations describe fluid motion in scenarios where the depth is significantly smaller than the horizontal length scale. Efficient numerical simulations of SWE require parallel processing to handle computational complexity and achieve prompt results. OpenMP facilitates this parallelization by enabling developers to identify regions in the code for concurrent execution by multiple threads. This approach is particularly advantageous in solving discretized SWE, where the computational domain is partitioned, with each thread managing a portion of the workload. By employing OpenMP directives, programmers can harness modern multicore processors’ parallel capabilities, significantly accelerating shallow water dynamics simulations. This acceleration contributes to flood modeling, coastal engineering, and environmental risk assessment advancements. The research uses the Runge-Kutta method to analyze OpenMP performance for high-order time discretization of SWE. Results indicate that the 4th-order Runge-Kutta method outperforms Euler and the 2nd-order Runge-Kutta method in RMSE evaluation. Moreover, employing four threads in OpenMP reduces computational time by 3.5 times compared to serial execution, with an efficiency rate exceeding 80%.