Evaluation of Selected Finite-Difference and Finite-Volume Approaches to Rotational Shallow-Water Flow (Communications in Computational Physics, 2020)
The shallow-water equations in a rotating frame of reference are importantfor capturing geophysical flows in the ocean. In this paper, we examine and comparetwo traditional finite-difference schemes and two modern finite-volume schemes forsimulating these equations. We evaluate how well they capture the relevant physicsfor problems such as storm surge and drift trajectory modelling, and the schemes areput through a set of six test cases. The results are presented in a systematic mannerthrough several tables, and we compare the qualitative and quantitative performancefrom a cost-benefit perspective. Of the four schemes, one of the traditional finite-difference schemes performs best in cases dominated by geostrophic balance, and oneof the modern finite-volume schemes is superior for capturing gravity-driven motion.The traditional finite-difference schemes are significantly faster computationally thanthe modern finite-volume schemes.