A comparison of 3-D spherical shell thermal convection results at low to moderate Rayleigh number using ASPECT (version 2.2.0) and CitcomS (version 3.3.1)

Abstract

Due to the increasing availability of high-performance computing over the past few decades, numerical models have become an important tool for research in geodynamics. Several generations of mantle convection software have been developed, but due to their differing methods and increasing complexity it is important to evaluate the accuracy of each new model generation to ensure published geodynamic research is reliable and reproducible. Here we explore the accuracy of the open-source, finite-element codes ASPECT and CitcomS as a function of mesh spacing using low to moderate-Rayleigh-number models in steady-state thermal convection. ASPECT (Advanced Solver for Problems in Earth's ConvecTion) is a new-generation mantle convection code that enables modeling global mantle convection with realistic parameters and complicated physical processes using adaptive mesh refinement (Kronbichler et al., 2012; Heister et al., 2017). We compare the ASPECT results with calculations from the finite-element code CitcomS (Zhong et al., 2000; Tan et al., 2006; Zhong et al., 2008), which has a long history of use in the geodynamics community. We find that the globally averaged quantities, i.e., root-mean-square (rms) velocity, mean temperature, and Nusselt number at the top and bottom of the shell, agree to within 1 % (and often much better) for calculations with sufficient mesh resolution. We also show that there is excellent agreement of the time evolution of both the rms velocity and the Nusselt numbers between the two codes for otherwise identical parameters. Based on our results, we are optimistic that similar agreement would be achieved for calculations performed at the convective vigor expected for Earth, Venus, and Mars.