Speaker: Shuyu Sun
Time: June 10, 2025, 10 a.m.
Location: R1610, SIMIS
Abstract:
Simulation of fluid flow in geological formation is crucial in geo-energy applications and environmental protection. Petroleum reservoir engineers spend great efforts in the development and production of oil and gas reservoirs by conducting and interpreting the simulation of multiphase flows in porous geological formation. Meanwhile, environmental scientists use subsurface flow and transport models to investigate and compare for example various schemes to inject and store carbon dioxide in subsurface geological formations, such as depleted reservoirs and deep saline aquifers. Most of these numerical problems are challenging majorly due to the nonlinear coupling among various physics, where tiny time steps are needed due to stability concern instead of maintaining accuracy in temporal discretization. In these cases, it is crucial to design unconditional energy stable schemes for improving its computational efficiency and enhancing its robustness. To address these challenges, we formulate a gradient flow framework at both the continuous PDE level (as a physical model) and a discrete level (as a numerical approximation scheme), where the dynamics is modeled using thermodynamic driving forces (the negative energy gradient) and a kinetic rate tensor (the inverse of the resistance tensor). Many geo-energy applications, in particular most multi-phase flow and transport problems, can be formulated using this framework. In this talk, we review our work on unconditionally energy stable schemes for geo-energy problems at various scales by highlighting four stories below:
1) Navier-Stokes-Cahn-Hilliard (NSCH) simulation for two-phase flow at the pore scale (micrometers’ scale): We present a pioneering study on the design of an unconditionally energy stable SPH (Smoothed Particle Hydrodynamics) discretization of the NSCH model for incompressible two-phase flows based on a number of novel techniques: subtle treatment of capillary forces at the discrete level, particles’ divergence-free projection, energy factorization, and discretization with physical consistency.
2) Darcy-scale simulation for two-phase flow (meters to kilometers’ scale): Conventional two-phase modeling consists of conservation laws and extended Darcy’s laws do not have a background dissipated energy. With a single primary pressure variable, it fails to work in the degenerated single-phase regions, and it also difficult to be coupled with geomechanics due to capillarity. We derive a general and thermodynamically consistent formulation of two-phase flow using our gradient flow framework, so the total Helmholtz energy is rigorously dissipating and it also yields a well-defined effective pressure. This new framework allows us to propose an energy stable numerical method, preserving energy dissipation, conservation for both fluids and pore volumes, and positivity of porosity and saturations.
3) Phase behavior calculation (scale independent): Conventional flash calculation methods based on fixed point iterations or Newton’s method is known to lack robustness. To design a fully robust scheme for flash, we first derived a gradient flow model for VT flash that preserves both Onsager’s reciprocal principle and the energy dissipation. We then design unconditional stable yet linear semi-implicit scheme to update the moles and volume. Then, with the convex splitting approach and the component-wise iteration, our scheme becomes fully explicit, but still maintaining unconditional stability.
4) Density functional theory (DFT) calculations of the structural, physical and chemical properties of reservoir fluid mixture (Angstroms’ scale): This is a very recent and still on-going work. From algorithms’ perspective, we design an unconditionally energy stable, but orthonormality-preserving scheme for the Kohn-Sham gradient flow-based model in the electronic structure calculation. The scheme is fully robust and it does not contain any tuned parameters. Unconditional stability of the scheme allows us to use large time step sizes and thus achieves great computational efficiency. The scheme is also fully robust; it converges for any initial guesses; it completely removes the non-convergence issued faced by SCF methods for open shell problems. Our initial numerical test on the electronic structure calculation of the Lithium hydride (LiH) and the methane (CH4) molecules indicates that the new algorithm can speed up 100 times as compared to other orthonormality-preserving schemes for the Kohn-Sham gradient flow-based model in the literature.
About Speaker:
Shuyu Sun is a professor and the Dean of the School of Mathematical Sciences at Tongji University. He graduated from Tianjin University with a Bachelor’s degree in Industrial Chemistry in 1991, a Master’s degree in Chemical Engineering in 1994, and a Ph.D. in Chemical Engineering in 1997. His PhD in Tianjin was under the supervision of Prof. Yu Guocong, an Academician of the Chinese Academy of Sciences. He then pursued a Ph.D. in in Computational and Applied Mathematics at The University of Texas at Austin, USA, and obtained this Ph.D. in 2003, under the guidance of Mary F. Wheeler, a world-renowned expert in computational science. From 2003 to 2006, he served first as a postdoctoral fellow and then as an associate researcher at The University of Texas at Austin. Since 2006, he worked as an assistant professor at Clemson University, USA. In August 2009, as one of the hundred founding professors, he joined King Abdullah University of Science and Technology (KAUST, ranked among the top 100 globally and first in the Middle East by U.S. News & World Report), where he served as the Director of the Computational Transport Phenomena Laboratory (CTPL), Professor in Earth Science, Professor in Petroleum Engineering, and Professor in Mathematics. In December 2024, he joined Tongji University. He has published more than 400 SCI journal papers, with a total of over 13,000 citations and an H-index of 59 (according to Google Scholar). He has supervised more than 50 master’s and doctoral students (20 doctoral students have graduated) and more than 20 postdoctoral researchers. Currently, he serves as an editorial board member for internationally renowned journals such as the Journal of Computational Physics and Computational Geoscience, and as a guest editor for internationally renowned journals including Applied Energy, Applied Thermal Engineering, Fuel, and Computer Methods in Applied Mechanics and Engineering. Currently he is the president of InterPore (International Society for Porous Media) Saudi Chapter.
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