A multi-resolution sparse hash table strategy for efficient numerical integration of stiff combustion systems using the G-Scheme

The G-Scheme is an explicit integration method designed to address the multi-scale stiffness challenges inherent in systems of ordinary and partial differential equations, particularly those encountered in combustion modelling. Its efficiency hinges on min- imising the computational cost of evaluating the eigensystem of the Jacobian matrix of the vector field that defines the system dynamics. This work introduces a novel multi- resolution hash table strategy to accelerate the G-Scheme by reusing precomputed eigensystems. The hash table enables efficient storage and retrieval of the eigen- system, either from a predefined training dataset or dynamically during integration. This approach demonstrates a ten- to twenty-fold speedup for systems with varying dimensionalities and maintains robustness by ensuring accuracy even when retriev- ing approximate eigensystems. The methodology is validated through simulations of autoignition processes using skeletal mechanisms of varying complexity, showcas- ing its potential for large-scale turbulent reacting flow simulations. By combining the G-Scheme with the proposed hash table and skeletal mechanism simplification, com- putational efficiency is enhanced, promising a paradigm shift in handling stiff reactive systems.