| Abstract: |
Earth’s mantle convection is a fundamental phenomenon that transports material and heat within the Earth’s interior. However, its numerical simulation is challenging, especially in regions where oceanic plates subduct, which involves large deformation and breakup of continua, and migration of phase boundaries. The Smoothed Particle Hydrodynamics (SPH) method, a mesh-free particle method, is effective for such problems. On the other hand, since conventional SPH methods are formulated under the ideal assumption that the particle distribution is regular and symmetric, their discretization accuracy is significantly reduced when the particle distribution becomes disordered due to flow. In addition, since the SPH method is based on explicit methods, the maximum time step is restricted by the speed of sound and viscosity. The restriction becomes so severe for mantle convection simulations with low Mach numbers and high Prandtl numbers that enormous computational time should be required without acceleration techniques. The purpose of this study is to improve the accuracy of the SPH method and to accelerate explicit mantle convection simulations. First, we have developed a high-accuracy SPH scheme based on the least squares method, namely the Least Squares SPH (LS-SPH) method, which does not assume a symmetric particle distribution. Second, we have combined the Reduced Speed of Sound Technique (RSST) with the Variable Inertia Method (VIM). Furthermore, we have theoretically constrained the upper limits of the parameters introduced by these techniques through linear stability analysis. Finally, we have implemented the high-accuracy particle method and the acceleration schemes in explicit mantle convection simulations.
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