# High Accuracy Mantle Convection Simulation through Modern Numerical Methods. II: Realistic Models and Problems

## TL;DR

This paper reviews advanced numerical methods for realistic 3D mantle convection simulations, emphasizing algorithm improvements and physics incorporation, enabling high-resolution, massively parallel modeling of Earth's mantle dynamics.

## Contribution

It revisits and enhances numerical algorithms for complex mantle models, integrating physics like compressibility, phase transitions, and heterogeneities in a high-performance computing framework.

## Key findings

- Successful implementation of high-resolution 3D simulations
- Effective incorporation of complex physics into models
- Demonstrated scalability on large parallel computing systems

## 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.