Numerical algorithms for water waves with background flow over obstacles and topography

• Published in: Advances in computational mathematics Vol. 48; no. 4
• Main Authors: Ambrose, David M., Camassa, Roberto, Marzuola, Jeremy L., McLaughlin, Richard M., Robinson, Quentin, Wilkening, Jon
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.08.2022; Springer Nature B.V; Springer Science + Business Media
• Subjects: Advances in Computational Integral Equations; Algorithms; Barriers; Boundaries; Capillary flow; Capillary waves; Computational mathematics; Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Euler-Lagrange equation; Fluid flow; Fredholm equations; Free surfaces; Graphics processing units; Incompressible flow; Integral equations; Linear systems; Mathematical analysis; Mathematical and Computational Biology; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Singularity (mathematics); Stream functions (fluids); Topography; Two dimensional flow; Velocity; Visualization; Vortex sheets; Water waves; Water waves; Multiply connected domain; Splash singularity; Overturning waves; 76B15; Layer potentials; 65E05; 35Q31; 65M22; 35R37; Cauchy integrals; GPU acceleration

We present two accurate and efficient algorithms for solving the incompressible, irrotational Euler equations with a free surface in two dimensions with background flow over a periodic, multiply connected fluid domain that includes stationary obstacles and variable bottom topography. One approach is...