Mingchao Cai
Morgan State University, MD·Mathematics & Statistics
Many porous materials are under constant change, from rock deep underground to soft body tissue. When such a material is squeezed, heated, or has fluid pushed through it, all three effects influence one another.
- Fields
Mathematics & Statistics
Engineering
Computer Science
- Topics
thermo-poroelasticity
multiphysics modeling
numerical analysis
- Grants
- 1 known grant, through Jul 2029
What they work on
- Develop monolithic parameter-robust preconditioners, which speed up solvers for the whole coupled system, for quasi-static and fully dynamic thermo-poroelastic models, with mathematical proofs of stability and convergence.
- Design iterative decoupling and semi-decoupled algorithms that solve the deformation, fluid flow and heat equations separately while avoiding elastic locking and pressure oscillations.
- Build stabilization techniques for linear and nonlinear multiphysics systems that remain accurate when physical parameters vary widely, and make them work with parallel computing and heterogeneous time stepping.
- Explore AI-assisted strategies, including data-driven acceleration and reduced-order models, to further cut the cost of large thermo-poroelastic simulations, and release the methods as open-source software.
More about the research
Thermo-poroelastic models are equations that capture this three-way coupling of solid deformation, fluid flow and heat transport. They are used in geothermal energy, nuclear waste disposal, shale gas recovery, cleanup of contaminated ground by heating, and modeling of soft tissues and tumors. These simulations, however, are very expensive to compute. They also become unstable when physical properties vary over huge ranges, which limits their use at large scale or in real time.
Why it matters
Faster and more reliable simulations of coupled heat, fluid flow and deformation could improve predictions for geothermal energy production, nuclear waste storage, shale gas recovery and subsurface cleanup. They could also improve biomechanical models of soft tissue and tumors. The open-source software would give engineers and geoscientists tools for larger simulations that may run close to real time.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Qingguo Hong
Missouri University of Science and Technology, MO·Mathematics & Statistics
Develop discretizations of multiple-network poroelastic (MPET) models that remain robust across parameter ranges, strongly conserve mass, and keep the stress tensor exactly symmetric.
Lin Mu
University of Georgia, GA·Mathematics & Statistics
Design a finite element scheme for incompressible flow that achieves pressure robustness and exact mass conservation at once, using a divergence-preserving discretization rather than the trade-off made by traditional solvers.
Matthias Maier
Texas A&M University-College Station, TX·Mathematics & Statistics·Early-career
Develop and analyze numerical methods for time-harmonic (single-frequency) simulations of non-local conductivity, where a material's electrical response depends on nearby conditions, in nanoscale optical geometries.
The school
Morgan State University: 3 labs on PI Pages, $56M a year on research, 62 research doctorates a year.
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