Efficient Time-Integration Solvers for Shallow Water Equations on GPUs
A Case Study in Tidal Modeling
M.E.F. Daemen (TU Delft - Electrical Engineering, Mathematics and Computer Science)
M Verlaan – Mentor (TU Delft - Mathematical Physics)
J. Zhao – Mentor (TU Delft - Numerical Analysis)
M.B. van Gijzen – Graduation committee member (TU Delft - Numerical Analysis)
Firmijn Zijl – Graduation committee member (Deltares)
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Abstract
The Shallow Water Equations (SWEs) for ocean applications can be discretized using finite differences, resulting in a system of time-dependent ordinary differential equations (ODEs). These ODEs can then be solved on a GPU using various time-integration schemes, which can be categorized as explicit and implicit methods. The primary aim of this thesis is to evaluate the performance of various time-integration solvers implemented on a GPU for a simplified tidal model of the North Sea. The investigation includes a comparison of explicit second-, third-, and fourth-order Runge-Kutta (RK) and multistep methods as well as several second-order implicit schemes. Moreover, a novel approach is proposed for solving the tidal model and addressing the nonlinear systems within the implicit time iterations. This approach is a combination of an implicit SDIRK2-scheme with a pseudo-time-stepping approach and a multi-level technique. All numerical schemes are implemented on the GPU using the Julia programming language. The most efficient explicit time-integration scheme was RK4. However, on a high resolution grid , the newly developed implicit solver outperformed RK4, in terms of speed.