High Accuracy Mantle Convection Simulation through Modern Numerical Methods. II: Realistic Models and Problems (1702.05075v2)

Abstract: Computations have helped elucidate the dynamics of Earth's mantle for several decades already. The numerical methods that underlie these simulations have greatly evolved within this time span, and today include dynamically changing and adaptively refined meshes, sophisticated and efficient solvers, and parallelization to large clusters of computers. At the same time, many of these methods -- discussed in detail in a previous paper in this series -- were developed and tested primarily using model problems that lack many of the complexities that are common to the realistic models our community wants to solve today. With several years of experience solving complex and realistic models, we here revisit some of the algorithm designs of the earlier paper and discuss the incorporation of more complex physics. In particular, we re-consider time stepping and mesh refinement algorithms, evaluate approaches to incorporate compressibility, and discuss dealing with strongly varying material coefficients, latent heat, and how to track chemical compositions and heterogeneities. Taken together and implemented in a high-performance, massively parallel code, the techniques discussed in this paper then allow for high resolution, 3d, compressible, global mantle convection simulations with phase transitions, strongly temperature dependent viscosity and realistic material properties based on mineral physics data.

• The paper explores advanced numerical methods to enhance the accuracy and realism of simulating Earth's mantle convection.
• Key improvements include dynamic mesh refinement, effective handling of compressibility, and methods for incorporating latent heat effects.
• These methods enable high-resolution models that provide more nuanced insights into mantle dynamics and geodynamic processes.

Enhancements in Simulating Realistic Mantle Convection

The computational modeling of Earth's mantle convection, a complex geological process driven by temperature gradients and material properties, has benefited significantly from advances in numerical methods. The paper "High Accuracy Mantle Convection Simulation through Modern Numerical Methods. II: Realistic Models and Problems" revisits conventional numerical methods for mantle convection, emphasizing the shift from simple to more realistic, complex models. The authors Timo Heister, Juliane Dannberg, Rene Gassmöller, and Wolfgang Bangerth explore methodologies incorporating dynamic mesh refinements, compressibility, and latent heat effects within a high-performance computational framework.

Key Contributions

This paper builds on earlier works in mantle convection modeling, focusing on overcoming limitations associated with traditional models. The authors perform an analytical reassessment of several crucial aspects of mantle convection simulations:

1. Time Stepping and Mesh Refinement: The paper explores the implications of using various time-stepping methods in complex simulations. The authors advocate for fully implicit time discretization techniques that can handle large time steps efficiently, mitigating the computational burden in three-dimensional models. Moreover, dynamic mesh refinement strategies are discussed, highlighting their necessity in resolving narrow regions with high accuracy, such as phase boundaries.
2. Handling Compressibility: A significant portion of this paper is dedicated to addressing the challenges posed by compressible flow formulations. Specifically, it investigates the trade-offs between implicit and explicit methods for managing the compressibility in simulation models. The authors emphasize the importance of these approaches in improving solver performance and achieving accurate, stable convergence—critical in maintaining the fidelity of global mantle simulations.
3. Averaging and Latent Heat Incorporation: Given the immense variability in material properties across mantle phases, the paper discusses the impact of employing different averaging techniques on numerical accuracy and solver efficiency. These techniques are crucial in moderating the effects of discontinuous coefficients in simulations. Moreover, the incorporation of latent heat is tackled by adopting appropriate reformulations to handle abrupt energy changes due to phase transitions.
4. Tracking Compositional Fields: To simulate the transport of chemical and isotopic compositions alongside thermal dynamics, the paper considers field-based approaches as alternatives to conventional tracer particles. This methodological shift enhances computational efficiency and maintains high-resolution tracking of compositional variations.
5. Application of High-Resolution Models: The authors demonstrate the efficacy of their methods through large-scale simulations of mantle convection with contemporary complexity, showcasing their framework's scalability and precision. These applications reveal the potential for more nuanced insights into mantle dynamics and geodynamically consistent models of Earth's interior.

Implications and Future Directions

The paper's advancements in numerical methods have practical implications for geophysical research, particularly in enhancing model resolutions and predictive capabilities. The authors' methodologies facilitate the exploration of geodynamic phenomena with greater realism, offering improved alignment with empirical observations. Future developments may involve integrating additional physical complexities, such as grain size evolution and plasticity effects, to further bridge the gap between computational models and natural processes.

Furthermore, the findings underscore the ongoing need for interdisciplinary research and collaboration within the computational geodynamics community to optimize simulation techniques for increasingly detailed and multifaceted geological models. The potential expansion of these methods to model mantle convection in exoplanets initiates exciting avenues for addressing universal geological processes.

By providing robust computational tools to untangle the intricate dynamics of mantle convection, this research contributes meaningfully to the growing body of knowledge at the intersection of computational science and geophysics.