Balancing efficiency and accuracy for sediment transport simulations

Simulating multi-lithology sediment transport requires numerically solving a fully coupled system of nonlinear partial differential equations. The most standard approach is to simultaneously update all the unknown fields. Such a fully implicit strategy can be computationally demanding due to the need for Newton–Raphson iterations to set up and solve a large system of linearized algebraic equations. Fully explicit numerical schemes that do not solve linear systems are possible to devise, but suffer from considerably lower numerical stability and accuracy. Adding to this competition, there are semi-implicit numerical schemes that lie between the two extremes. This paper presents two contributions. First, we devise a new semi-implicit scheme that has second-order accuracy in the temporal direction. Second, and more importantly, we propose a novel methodology for comparing numerical schemes by considering accuracy, stability and computing speed at the same time. This methodology is general and easy to use, based on simple prediction models for the overall computation time on multicore architectures. Our findings are accompanied by numerical experiments modeling the sediment transport in Monterey Bay.