Improving Mass Conservation With the Tracer Ratio Method: Application to Thermochemical Mantle Flows

Abstract

Abstract Modeling the evolution of composition in a convecting mantle is difficult since the associated chemical diffusivity is very small. Consequently, compositional evolution is often modeled using the advection equation which is prone to overdiffusion and spurious oscillations unless special numerical schemes are employed. Similar errors can also occur while modeling the evolution of temperature, since mantle convection is advection dominated. One numerical scheme designed to minimize such errors is the tracer ratio method, in which Lagrangian tracers are used to track each composition in the system in addition to carrying local temperature values that are time dependent. However, tracer spacing may become very uneven during evolution, which can contribute to errors in mass and energy conservation. In this study, a tracer repositioning algorithm designed to promote even tracer coverage is presented and tested using over 400 calculations in a large thermal Rayleigh number/buoyancy ratio parameter space. In particular, the effect of tracer repositioning on mass and energy conservation errors is examined. In most cases, we find that energy errors are roughly an order of magnitude less than mass errors, regardless of tracer repositioning. However, in situations with substantial entrainment of compositionally distinct material, mass errors can be reduced by up to an order of magnitude if tracers are repositioned during model evolution. We also find that for a fixed buoyancy ratio, entrainment of basal material decreases as the thermal Rayleigh number increases.

Keywords

• mantle convection
• tracer
• compositional variations
• numerical modeling
• entrainment
• Rayleigh number