Dr. Amirmehran Mahdavi’s research lies at the intersection of rarefied gas dynamics, molecular simulation, and micro/nanoscale heat transfer. His work focuses on developing advanced kinetic-based numerical algorithms and applying them to study non-equilibrium flow phenomena in microscale geometries, MEMS/NEMS, and miniaturized thermal systems. By bridging molecular modeling and continuum mechanics, he aims to enhance the physical understanding and computational efficiency of rarefied and transitional gas flow simulations.
1. Micro/Nano Flow Simulation Using DSMC and CFD Hybrid Analysis
In his early research, Dr. Mahdavi conducted a detailed numerical investigation of gas flow through micro/nano backward-facing step geometries using the Direct Simulation Monte Carlo (DSMC) technique.
This study systematically compared DSMC results with Computational Fluid Dynamics (CFD) predictions employing hybrid slip/jump boundary conditions based on the Langmuir adsorption model.
The results demonstrated that these hybrid boundary conditions offer superior accuracy for modeling velocity slip, temperature jump, and pressure distribution, especially within flow separation and reattachment regions.
2. Thermal Separation and Cold-to-Hot Transfer in Nano Step Geometries
In a subsequent work published in Physics of Fluids (2015), Dr. Mahdavi explored thermal behavior in nanostep geometries using DSMC simulations.
He was among the first to report the existence of a thermal separation zone and the counterintuitive phenomenon of “cold-to-hot” heat transfer, where local energy transport occurs from cooler to hotter regions — a clear deviation from classical Fourier behavior.
The study revealed how this effect depends on parameters such as Knudsen number, wall temperature ratio, and pressure gradient, leading to a deeper understanding of non-Fourier heat conduction in the transition regime.
This research opened new perspectives for the design of nano heat exchangers, micropumps, and thermal actuators.
These findings provided valuable insights into non-equilibrium transport phenomena and guided the development of improved boundary formulations for microfluidic and thermal management applications.
3. Hybrid DSMC–Fokker Planck Algorithm for Efficient Rarefied Flow Simulation
To overcome the computational cost of DSMC while maintaining its accuracy, Dr. Mahdavi developed a novel hybrid DSMC–Fokker Planck (FP) algorithm, published in Vacuum (2020).
The hybrid method dynamically switches between DSMC and FP solvers based on a local Knudsen ratio criterion, enabling the simulation of whole Knudsen regime flows with up to 50% reduction in computational cost.
The approach was validated for cavity flow and micro-nozzle configurations, showing excellent agreement with DSMC results in both flow and temperature fields.
This algorithm provides a powerful framework for modeling non-equilibrium gas dynamics, micro-propulsion, and aerospace micro-thruster design.
Dr. Mahdavi continues to extend this methodology to include nanofluid-based cooling and multi-scale coupling in combustion and energy systems.
4. Physics-Informed Deep Learning for Rarefied Flow Simulation
In his most recent work, Dr. Mahdavi introduced a Deep Operator Network (DeepONet)-based surrogate model that reproduces DSMC solutions at a fraction of the computational cost.
This framework integrates a novel physics-guided zonal loss function, which explicitly prioritizes accuracy in critical flow regions—particularly recirculation zones (U < 0)—where conventional global metrics fail to capture physical fidelity.
The model successfully learns mappings such as:
from Knudsen number → velocity field, and
from step-height ratio → flow solution,
demonstrating excellent agreement with DSMC data.
By focusing on localized accuracy rather than purely global errors, the method captures subtle vortex dynamics and separated flow structures that are essential in engineering design.
The surrogate achieves several orders of magnitude speedup compared to DSMC, enabling uncertainty quantification, parametric optimization, and real-time design-space exploration — previously intractable for kinetic solvers.
This research represents a new direction in physics-informed machine learning (PIML), merging first-principles modeling with deep neural operators to accelerate rarefied flow simulations without compromising physical accuracy.