Implementation of OpenMP for Solving Linear Shallow Water Equations using Staggered Grid and MacCormack Scheme

This study outlines the implementation of OpenMP parallelization techniques to solve the Linear Shallow Water Equations (LSWE) using the MacCormack scheme and a staggered grid. These simulations are essential in various scientific disciplines, including but not limited to environmental modeling and fluid dynamics. The distribution of computational resources over several threads is the key to this attempt, resulting in significant improvements in computational performance. This highlights the possibility of developing scalable and highly efficient approaches for simulating the complicated dynamics of shallow water, addressing a significant demand in various research and applications. We discover insights within our experimental grid size trial. In general, the staggered grid outperforms the MacCormack scheme regarding computational speed and root mean square error. However, compared to the MacCormack scheme, the staggered grid technique achieves an error cap of 2 × +10
⁻⁴
, still higher than the MacCormack schemes for the Cauchy or initial value problem in early time of simulation. Our research also delves into the actual application of parallel processing, which is a significant tool for increasing the computing efficacy of LSWE simulations. Compared to typical serial computation, our approach achieves a significant speed-up score improvement of up to 3.721 times via the distribution of computational work among four threads. This practical advancement highlights the viability of scalable and robust systems when confronted with the complicated simulation of shallow water dynamics, highlighting a promising trajectory for future developments in this subject area.