Lin Mu
University of Georgia, GA·Mathematics & Statistics
Simulating how liquids move through soil, rock or an engineered device sounds routine, but standard computer methods often cheat on physics in small ways: they let a tiny amount of fluid appear or vanish, or they lose accuracy when the pressure is large relative to the flow. Those errors compound in hard cases, such as fluid squeezing through the twisting pore channels of porous media.
- Fields
Mathematics & Statistics
Engineering
Computer Science
- Topics
finite element method
incompressible flow
porous media
- Grants
- 1 known grant, through Aug 2027
What they work on
- 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.
- Develop a parameter-uniform scheme of minimal computational cost that stays accurate as physical parameters vary across the mixed regime where different flow behaviors coexist.
- Construct a flexible discretization able to handle porous media with complex geometries and high grid flexibility, and validate it with numerical experiments.
- Investigate linear solvers for the resulting discrete systems that remain efficient and robust with respect to both physical and discretization parameters, with proofs of stability and convergence.
More about the research
This project develops numerical schemes for incompressible fluid flow that conserve mass exactly and stay accurate as physical parameters change.
Why it matters
Flow simulations in porous media underpin groundwater and petroleum engineering and many engineered systems, where small violations of mass conservation can mislead predictions. Methods that guarantee mass conservation, hold up across parameter ranges and handle complicated pore geometries, released as open-source code, could make such simulations cheaper and more trustworthy for the scientists and engineers who rely on them.
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.
Mingchao Cai
Morgan State University, MD·Mathematics & Statistics
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.
Benjamin Seibold
Temple University, PA·Mathematics & Statistics
Construct explicit and implicit-explicit Runge-Kutta time-stepping methods that satisfy weak stage order, an algebraic condition on the method's coefficients that prevents the loss of accuracy known as order reduction, and build the supporting algebraic theory.
The school
University of Georgia: 27 labs on PI Pages, $628M a year on research, 598 research doctorates a year.
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