The tracer nudging method for correcting and preventing uneven tracer distributions in geodynamical models

Abstract

Tracers/markers/particles are commonly used in geodynamical models to track composition and sometimes other quantities throughout the domain. A common problem is that over time, gaps in the tracer distribution can develop, often resulting in cells with no tracers as well as bunching of tracers. These arise when tracer advection does not perfectly respect the mass conservation equation, so here this equation is used to derive a correction method that perturbs or "nudges"the positions of tracers in such a way as to close gaps and eliminate bunching. Test results show that this tracer nudging method is highly effective. Starting from an extremely heterogeneous tracer distribution with large regions of the domain devoid of tracers, it can produce an even distribution in only a few nudge iterations. In a time-stepping situation with a nudge every time-step, the amplitudes of the nudges are small yet sufficient to prevent gaps and bunches, allowing a low-order tracer advection method to be used while maintaining a tracer distribution that is more even than that obtained using higher-order advection methods alone. The computational cost is small-slightly larger than that of a first-order tracer advection step alone-because the method simply requires solving a Poisson equation. If an accuracy threshold is applied, a nudge correction may be necessary in only a fraction of time steps, with tests indicating that it is fastest to use low order advection with more frequent nudges than high order advection with less frequent nudges.