Title
Exponential Integrators for the Solution of the Tracer Equations appearing in Primitive Equation Ocean Models
Authors
Sara Calandrini (Florida State University), Konstantin Pieper (Oak Ridge National Laboratory), Max Gunzburger (Florida State University)
Abstract
Exponential time differencing (ETD) methods, also known as exponential integrators, constitute a class of numerical methods for the time integration of stiff systems of differential equations. The main idea behind exponential integrators is a splitting of the right-hand side term of an equation into a linear part and a remainder, with an appropriate choice of the linear operator A. Exponential integrators have recently gained attention in the ocean modeling community due to their stability properties that allow time steps considerably larger than those dictated by the CFL condition. We present is an ETD scheme for the tracer equations appearing in the primitive equation ocean models, where the vertical terms (transport and diffusion) are treated with a matrix exponential, whereas the horizontal terms are dealt with in an explicit way. By treating exponentially terms related to fast time-scales, bigger time steps can be taken, and so computational speed-ups can be obtained over explicit methods. Compared to semi-implicit methods, higher accuracy is expected due to an exact treatment of the fast scales. We investigate numerically the computational speed-ups that can be obtained over other semi-implicit methods, and analyze the advantages of the method in the case of multiple tracers.