My PhD research involves the development of advanced numerical methods to simulate biogeochemical processes mediated by microorganisms. Microbial processes play an important role in energy and environmental applications, such as geothermal energy development, underground hydrogen storage, and mitigation/remediation of water. Microorganisms, like sulfate-reducing bacteria, can dramatically change the geochemical environment and could lead to loss of efficiency (through H₂S production) and even safety concerns.
The fundamental challenge is the mathematical modeling of microbial activity. Most of these models take the form of empirical kinetics and result in highly stiff systems of differential equations which can be computationally intensive, and typically lead to sensitivity stability issues. Specifying stability, accuracy, positivity of solutions and computational cost can be challenging and may require specific numerical methods.
My work seeks to use dynamical systems theory, stability analysis, and scientific computing to better understand the dynamics of these models and propose robust, efficient, and stable numerical integration schemes. By appropriately addressing mathematical and numerical computability challenges, my goal is to demonstrate a major advancement in the development of trustworthy simulation tools that can be applied to complex environmental and energy systems.
