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 at each time step. Such a fully-implicit strategy is computationally demanding due to the need of Newton-Raphson iterations, each having 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 lower numerical stability and accuracy. If we count the total number of floating-point operations needed to achieve stable numerical solutions with a prescribed level of accuracy, the fully-implicit approach probably wins over its fully-explicit counterpart. However, the latter may nevertheless win in the overall computation time, because computers achieve higher hardware efficiency for simpler numerical computations. Adding to this competition, there are semi-implicit numerical schemes that lie between the two extremes. This paper has two novel contributions. First, we device a new semi-implicit scheme that has secondorder accuracy in the temporal direction. Second, and more importantly, we propose a simple prediction model for the overall computation time on multicore architectures, applicable to many numerical implementations. Based on performance prediction, appropriate numerical schemes can be chosen by considering accuracy, stability, and computing speed at the same time. Our methodology is tested by numerical experiments modeling the sediment transport in Monterey Bay.