Zirui Mao

Multiscale problems with evolving interfaces are ubiquitous in science and engineering. Phase-field models are a powerful tool for simulating interface-dominated phenomena in computational mechanics and materials modeling, but their application to large-scale problems is often constrained by the high computational cost of resolving thin diffuse interfaces over the entire domain. This paper presents an efficient strong-form phase-field solver that couples the Gradient Smoothing Method (GSM) with a hierarchical adaptive and moving structured mesh, enabling automatic localization of resolution within a narrow interfacial region while retaining coarse discretization in bulk domains. A layered refinement design is introduced to preserve locally uniform resolution across the interface, allowing the GSM discretization to maintain overall second-order accuracy despite strong mesh non-uniformity away from the interface. The adaptive framework substantially reduces the total number of degrees of freedom, resulting in near-linear computational scaling superior to the uniform-grid approaches. Numerical examples based on the Allen-Cahn and Cahn-Hilliard equations demonstrate that the proposed adaptive GSM solver delivers desired accuracy for interface evolution while attaining more favorable computational complexity, O(N) , than existing weak-form and strong-form solvers, becoming significantly more efficient for large-scale problems with thin interfaces or a small interfacial area fraction relative to the whole domain.

Multiscale problems with evolving interfaces are ubiquitous in science and engineering. Phase-field models are a powerful tool for simulating interface-dominated phenomena in computational mechanics and materials modeling, but their application to large-scale problems is often constrained by the high computational cost of resolving thin diffuse interfaces over the entire domain. This paper presents an efficient strong-form phase-field solver that couples the Gradient Smoothing Method (GSM) with a hierarchical adaptive and moving structured mesh, enabling automatic localization of resolution within a narrow interfacial region while retaining coarse discretization in bulk domains. A layered refinement design is introduced to preserve locally uniform resolution across the interface, allowing the GSM discretization to maintain overall second-order accuracy despite strong mesh non-uniformity away from the interface. Although GSM incurs a higher per-degree-of-freedom cost than standard finite-difference schemes, the adaptive framework substantially reduces the total number of degrees of freedom, resulting in near-linear computational scaling compared with the quadratic scaling of uniform-grid approaches. Numerical examples based on the Allen–Cahn and Cahn–Hilliard equations demonstrate that the proposed adaptive GSM solver delivers desired accuracy for interface evolution while attaining more favorable computational complexity, [[EQUATION]], than existing weak-form and strong-form solvers, becoming significantly more efficient for large-scale problems with thin interfaces or a small interfacial area fraction relative to the whole domain.

Electrode drying is an energy-intensive and performance-critical step in lithium-ion battery manufacturing, strongly influencing electrode microstructure, mechanical integrity, and electrochemical behavior. Drying involves tightly coupled processes, including heat and mass transfer, solvent evaporation, multiphase flow, and binder migration, which collectively govern porous structure evolution and often lead to binder inhomogeneity. In this work, we develop a unified continuum framework to simulate binder transport and microstructure formation during electrode drying. The governing mass, momentum, and energy equations, coupled with a newly proposed phase-transition model and spatially varying material properties, are solved using a Lagrangian meshfree method: Smoothed Particle Hydrodynamics (SPH). A fraction-based continuum representation within each SPH particle captures interactions among solvent, carbon binder, and vapor phases with composition- and temperature-dependent material properties. Surface detection and particle initialization algorithms are implemented to ensure accurate treatment of interfacial physics and consistent initial states. A multi-level time-stepping strategy is employed to efficiently resolves disparate thermal, evaporation, and binder transport time scales. The SPH solver is verified against benchmark problems and reproduces experimentally observed binder redistribution trends. Parametric studies further quantify the effects of operating conditions on the final electrode microstructure, demonstrating the framework’s utility for process optimization.

The extraction of critical metals, such as rare earth elements (REEs), from dilute feedstocks like geothermal brine, mine tailings, and produced water is crucial for advancing clean energy technologies and sustainable manufacturing. However, the efficient separation of REE ions from these sources remains challenging due to their similar chemical properties and the complex interactions within dilute mixtures. This study explores an electrohydrodynamic-based approach for separating REE ions from a dilute feedstock containing competing cations using a Computational Fluid Dynamics (CFD) continuum model that incorporates ion transport via diffusion, advection, and electromigration. Numerical simulations highlight the competition between flow velocity, microfluidic channel dimensions, and electrohydrodynamic effects in determining separation selectivity. We showed that the e-field-based separation process is governed by three distinct regimes: (i) a diffusion-advection balance regime, where diffusion counteracts flow-induced advection, resulting in limited ion separation and reducing separation selectivity by promoting a more uniform ion concentration distribution; (ii) an electromigration-dominant regime, where the applied electric field overcomes advection effects, enabling selective ion migration and enhanced separation selectivity; and (iii) an advection-dominant regime, where high flow velocities dominate electromigration, leading to poor separation performance. Our results reveal that optimal separation is achieved when electromigration dominates over both diffusion and advection, which occurs under conditions of slow flow and strong electric fields. Additionally, narrower channel geometries intensify local electric field gradients, further enhancing electromigration and improving ion selectivity but also increasing sensitivity to flow velocity variations. This work emphasizes the need to address charge neutrality issues in CFD modeling and, more importantly, a fundamental understanding of the interplay between flow dynamics, channel design, and electrohydrodynamic forces to develop efficient methods for extracting critical metals from dilute feedstocks. These advancements are essential for enabling sustainable resource recovery and supporting emerging technologies.

In nature, many complex multi‐physics coupling problems exhibit significant diffusivity inhomogeneity, where one process occurs several orders of magnitude faster than others temporally. Simulating rapid diffusion alongside slower processes demands intensive computational resources due to the necessity for small time steps. To address these computational challenges, we have developed an efficient numerical solver named Finite Difference informed Random Walker (FDiRW). In this study, we propose a GPU‐accelerated, mixed‐precision configuration for the FDiRW solver to maximize efficiency through GPU multi‐threaded parallel computation and lower precision computation. Numerical evaluation results reveal that the proposed GPU‐accelerated mixed‐precision FDiRW solver can achieve a 117× speedup over the CPU baseline, while an additional 1.75× speedup is achieved by employing lower precision GPU computation. Notably, for large model sizes, the GPU‐accelerated mixed‐precision FDiRW solver demonstrates strong scaling with the number of nodes used in simulation. When simulating radionuclide absorption processes by porous wasteform particles with a medium‐sized model of 192 × 192 × 192, this approach reduces the total computational time to 10 min, enabling the simulation of larger systems with strongly inhomogeneous diffusivity.

In nature, many complex multi-physics coupling problems exhibit significant diffusivity inhomogeneity, where one process occurs several orders of magnitude faster than others in temporal. Simulating rapid diffusion alongside slower processes demands intensive computational resources due to the necessity for small time steps. To address these computational challenges, we have developed an efficient numerical solver named Finite Difference informed Random Walker (FDiRW). In this study, we propose a GPU-accelerated, mixed-precision configuration for the FDiRW solver to maximize efficiency through GPU multi-threaded parallel computation and lower precision computation. Numerical evaluation results reveal that the proposed GPU-accelerated mixed-precision FDiRW solver can achieve a 117X speedup over the CPU baseline, while an additional 1.75X speedup by employing lower precision GPU computation. Notably, for large model sizes, the GPU-accelerated mixed-precision FDiRW solver demonstrates strong scaling with the number of nodes used in simulation. When simulating radionuclide absorption processes by porous wasteform particles with a medium-sized model of 192x192x192, this approach reduces the total computational time to 10 minutes, enabling the simulation of larger systems with strongly inhomogeneous diffusivity.