Modelling chemical advection during magma ascent

Abstract

Modelling magma transport requires robust numerical schemes for chemical advection. Current numerical schemes vary in their ability to be mass conservative, computationally efficient, and accurate. This study compares four of the most commonly used numerical schemes for advection: an upwind scheme, a weighted essentially non-oscillatory (WENO-5) scheme, a semi-Lagrangian (SL) scheme, and a marker-in-cell (MIC) method. The behaviour of these schemes is assessed using the passive advection of two different magmatic compositions. This is coupled in 2D with the temporal evolution of a melt anomaly that generates porosity waves. All algorithms, except the upwind scheme, are able to predict the melt composition with reasonable accuracy, but none of them is fully mass conservative. However, the WENO-5 scheme shows the best mass conservation. In terms of total running time and when multithreaded, the upwind, SL, and WENO-5 schemes show similar performance, while the MIC scheme is the slowest due to reseeding and removal of markers. The WENO-5 scheme has a reasonable total run time, has the best mass conservation, is easily parallelisable, and is therefore best suited for this problem.