article published yes Stefan Jeschke author 44D6411A-F248-11E8-B48F-1D18A9856A87 Christopher J Wojtan author 3C61F1D2-F248-11E8-B48F-1D18A9856A870000-0001-6646-5546 ChWo department Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena project This paper introduces a novel method for simulating large bodies of water as a height field. At the start of each time step, we partition the waves into a bulk flow (which approximately satisfies the assumptions of the shallow water equations) and surface waves (which approximately satisfy the assumptions of Airy wave theory). We then solve the two wave regimes separately using appropriate state-of-the-art techniques, and re-combine the resulting wave velocities at the end of each step. This strategy leads to the first heightfield wave model capable of simulating complex interactions between both deep and shallow water effects, like the waves from a boat wake sloshing up onto a beach, or a dam break producing wave interference patterns and eddies. We also analyze the numerical dispersion created by our method and derive an exact correction factor for waves at a constant water depth, giving us a numerically perfect re-creation of theoretical water wave dispersion patterns. https://research-explorer.ista.ac.at/download/14240/14704/PaperVideo_final.mp4 video/mp4no https://research-explorer.ista.ac.at/download/14240/14725/2023_ACMToG_Jeschke.pdf application/pdfno https://creativecommons.org/licenses/by/4.0/ Association for Computing Machinery2023 eng 0730-0301 1557-7368 00104467130004910.1145/3592098 424 S. Jeschke, C. Wojtan, ACM Transactions on Graphics 42 (2023). Jeschke, Stefan, and Chris Wojtan. “Generalizing Shallow Water Simulations with Dispersive Surface Waves.” <i>ACM Transactions on Graphics</i>, vol. 42, no. 4, 83, Association for Computing Machinery, 2023, doi:<a href="https://doi.org/10.1145/3592098">10.1145/3592098</a>. Jeschke S, Wojtan C. 2023. Generalizing shallow water simulations with dispersive surface waves. ACM Transactions on Graphics. 42(4), 83. Jeschke, S., &#38; Wojtan, C. (2023). Generalizing shallow water simulations with dispersive surface waves. <i>ACM Transactions on Graphics</i>. Association for Computing Machinery. <a href="https://doi.org/10.1145/3592098">https://doi.org/10.1145/3592098</a> S. Jeschke and C. Wojtan, “Generalizing shallow water simulations with dispersive surface waves,” <i>ACM Transactions on Graphics</i>, vol. 42, no. 4. Association for Computing Machinery, 2023. Jeschke, Stefan, and Chris Wojtan. “Generalizing Shallow Water Simulations with Dispersive Surface Waves.” <i>ACM Transactions on Graphics</i>. Association for Computing Machinery, 2023. <a href="https://doi.org/10.1145/3592098">https://doi.org/10.1145/3592098</a>. Jeschke S, Wojtan C. Generalizing shallow water simulations with dispersive surface waves. <i>ACM Transactions on Graphics</i>. 2023;42(4). doi:<a href="https://doi.org/10.1145/3592098">10.1145/3592098</a> 142402023-08-27T22:01:17Z2025-04-14T08:01:13Z