the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
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)
Grant Thomas Euen
Shangxin Liu
Rene Gassmöller
Timo Heister
Scott David King
Abstract. Due to the increasing availability of high-performance computing over the past 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. We here 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: 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 convective vigor expected for Earth, Venus, and Mars.
Grant Thomas Euen et al.
Status: final response (author comments only)
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RC1: 'Comment on gmd-2022-252', Christian Hüttig, 06 Feb 2023
The paper demonstrates the ability of ASPECT v2.2.0 to reproduce the benchmark by Zhong et al 2008 and therefore its ability to handle varying viscosity in a natural convection scenario within a 3D spherical shell. The authors prove that by comparing vital benchmarking parameters like Nusselt number, v_rms and temperatures, along with profile plots of steady-state solutions.
A few remarks:
- Although equation 5 states this, it is usually important to point out that the Rayleigh number is defined with the viscosity at T=0.5
- Please cite http://dx.doi.org/10.1016/j.pepi.2013.04.002 as we did a similar study with the CITCOM benchmark.
A comment: The usability of ASPECT for 3D spherical shells seems questionable as you write in 3.1 that the case A8/9 (viscosity contrasts of 10^6 and 10^7) would have required excessive computing resources. Given that this is a benchmark from 2008 and computers got a bit faster nowadays, it seems there is an issue. If this is not the main use-case of the code this is fine, but people need to be aware of that in order to not waste computing resources and help the environment.
Citation: https://doi.org/10.5194/gmd-2022-252-RC1 -
AC1: 'Reply on RC1', Grant Euen, 06 Feb 2023
Thank you so much for all of your points. Your remarks will be added to the manuscript. In regards to your comment, there are several ways to improve performance for larger 3-D problems. ASPECT can use adaptive refinement to resolve features dynamically or statically which can reduce computing resources. ASPECT also has a newer geometric multigrid solver (see https://doi.org/10.1002/nla.2375 ) that can speed up computation by a factor of 3. These points will also be added to the manuscript as a short discussion.
Citation: https://doi.org/10.5194/gmd-2022-252-AC1
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AC1: 'Reply on RC1', Grant Euen, 06 Feb 2023
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RC2: 'Comment on gmd-2022-252', Anonymous Referee #2, 17 Feb 2023
This manuscript is a solid contribution, demonstrating the validity of ASPECT at low to moderate Rayleigh number when compared against the CitcomS model. I only have a few questions/comments to add to the previous review.
Some time is spent comparing and discussing different stabilization techniques but did the authors find that stabilization was actually necessary at these low Rayleigh numbers?
Since one of the response to a previous review mentioned that it might be, would it be possible to include a demonstration of ASPECT at more extreme viscosity contrasts/Rayleigh number even if a comparison to CitcomS isn't possible? This could prove useful for future code comparisons using this paper as a benchmark.
Rather than just comparing the '%diff' in top and bottom Nusselt numbers in the results tables could some quantitative comparisons be made between the codes to clearly demonstrate their similarity.
A few minor comments:
- line 27: presumably the length-scale is D not D^3
- line 9: the Rayleigh number alone doesn't describe the problem as it also depends on the choice of boundary conditions, which are given later but perhaps this sentence could be rephrased to "The Rayleigh number (plus apropriate boundary conditions) can describe this problem..."?
- line 21: only equations (1-3) are solved, not (1-4), which includes the definition of Ra
- equation 5/table 2: it would be a convenience to those trying to reproduce this to provide the values of E used in table 2 rather than just the viscosity differences
- equation 10: assuming Omega is the volume of the domain (is this defined somewhere?) it seems unusual that the definition of RMS velocity uses the square root of Omega, is this a typo?
- line 23: "This allowed isolate" -> "This allowed us to isolate"? This paragraph feels a bit repetetive of the previous paragraph, which also discusses the use of uniformly-spaced meshes in the radial direction.
- line 27: the doi given for Bangerth et al. (2020b) only appears to go up to Figure 123, could you please check this reference to Figure 130?
- line 23: please clarify the phrase "ASPECT is very likely converging with higher mesh resolution for this parameter as well"
- table 1: units for gravitational acceleration are incorrect
- tables 5-10: incorrect quotation mark used around '% diff' in all captions
Citation: https://doi.org/10.5194/gmd-2022-252-RC2 -
AC2: 'Reply on RC2', Grant Euen, 24 Feb 2023
Thank you so much for your points. Changes have been made to the manuscript. For your question on stabilization, no tests were performed without stabilization. These cases were run with as many default parameters as possible, so default stabilization was used for both codes. For higher viscosity cases, these would need significant computational resources, which is not feasible at this time. This could be performed as a future work. For further comparison between the codes, the reported parameters were chosen to best match the Zhong et al., 2008 benchmark paper. Radial plots, isotherms and Degrees of Freedom for the various mesh refinements used are all provided as comparisons. Your minor points have also been added, thank you so much for the variety of typos pointed out. For the question on equation 10, this is not a typo, and the volume is defined in equation 8.
Citation: https://doi.org/10.5194/gmd-2022-252-AC2
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AC2: 'Reply on RC2', Grant Euen, 24 Feb 2023
Grant Thomas Euen et al.
Grant Thomas Euen et al.
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