Assessment of numerical integration schemes and boundary conditions for Lagrangian tracking of marine debris

University essay from Lunds universitet/Matematik LTH

Abstract: A growing environmental issue today is the amount plastic pollution in the ocean. To investigate how it might affect marine life, an important aspect is to study how plastics are transported by ocean currents and where it ends up. This can be done by use of Lagrangian simulation of plastic particles in computer ocean models. To improve the quality of the output from such simulations the number of simulated particles is continuously increased, and grid resolutions are refined. This puts increasing pressure on the simulation programs to perform the computations as efficiently as possible. In the main part of this project the numerical time stepping schemes used in a Lagrangian ocean simulator, and their influence on the efficiency and accuracy of the simulations, were studied. The currently used 4th order Runge-Kutta method (RK4) was compared to the Runge-Kutta-Fehlberg method (RKF45) to assess the potential performance gain by switching to a more advanced scheme. The Explicit Euler method was included in initial tests to illustrate the benefit of using a higher order method. Error testing was performed on an idealized test case based on the Stommel equations, and time testing was performed on model data from the Agulhas region off the coast of South Africa. RKF45 was found to produce less accurate results than RK4 in very similar computation time. However, it used less function evaluations, which means it might still be useful in the future if more advanced interpolation schemes are introduced. Another numerical aspect was targeted in the secondary part of the project, namely the effect of the boundary conditions between land and sea on the particle trajectories. Simple conditions, such as the currently used no-normal flow partial slip condition, include slowing particles as they approach land to prevent them from accidentally beaching. To allow them to flow freely even along shorelines, a free-slip condition was introduced and evaluated. The two different methods were compared using the Agulhas data. With partial slip, many particles beached along the shorelines, but with free-slip not a single one of the 300 particles used got stuck.

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