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

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.

Towards the application of Stokes flow equations to structural restoration simulations

“…In a second part, we introduce the numerical code we developed for this application. Finally, we show the results that were obtained on an upscaled version of the model presented by van Keken et al (1997), on a model with no prior knowledge on the material properties and boundary conditions to apply and on a model with faults and a non-flat free top surface.…”

“…It relies almost entirely on the deal.II library (Bangerth et al, 2007;Arndt et al, 2019Arndt et al, , 2020 for all finite-element-related algorithms. The material tracking is based on the PIC method (e.g., Asgari and Moresi, 2012;Thielmann et al, 2014;Gassmöller et al, 2018Gassmöller et al, , 2019Trim et al, 2019). The general workflow of the code is shown in Fig.…”

“…The free surface stabilization algorithm (referred to as FSSA in the rest of the paper) developed by Kaus et al (2010) and showcased in Quinquis et al (2011) Figure 4. Setup of the model scaled up from van Keken et al (1997).…”

“…The first model is scaled up from van Keken et al (1997). The setup consists of a simple two-layered system driven by gravity, as shown in Fig.…”

“…A sinusoidal instability initiates the movement at the beginning of the simulation. The model is limited to a 10 km × 9.142 km domain (the width value is given by van Keken et al (1997) to yield the largest growth rate for the diapir) with free-slip boundary conditions on the sides and no-slip boundary conditions on the top and bottom sides. The grid has 32 2 initial elements and two levels of additional adaptive refinement.…”