Applied Mathematics
NLR's research in applied mathematics develops computational methods for high-fidelity simulations and uses high-performance computing and data-driven models to enable the optimization and scale-up of energy systems.
NLR applied mathematics research focuses on developing and optimizing modeling methods and paradigms to tackle energy challenges, advancing real‑world applications, and releasing our software as open source tools.
NLR researchers combine their knowledge with advanced computing resources, utilizing analytical and numerical methods and regularly collaborating with domain experts and researchers—as well as conducting their own computational research—to apply our tools and techniques as real-world solutions to energy questions.
Applied mathematicians improve NLR's ability to address research challenges by bringing new and advanced mathematical techniques to scientific, technical, and analysis problems. Mathematics are required to describe, model, simulate, solve, explore, and optimize complex systems, whether those systems are interacting atoms, systems of chemical reactions, or engineered systems describing the electrical power grid. Capabilities in this area include:
- Computational fluid dynamics (CFD)
Simulation of gas and liquid flows to analyze velocities, pressures, and forces without physical testing, informing the design of energy technologies. - Non-continuum methods
Mathematics for describing, modeling, simulating, solving, optimizing, and exploring complex systems of discrete components, where continuum assumptions fail, such as molecular dynamics. - Surrogate modeling
Formulation and implementation of simplified models trained on data from complex systems to replicate expensive simulations and experiments, enabling rapid design exploration and advanced optimization and control while balancing model fidelity and computational cost. - Uncertainty quantification
Mathematics for quantifying how incomplete information and inherent variability affect predictions, and for conveying that uncertainty with ranges or confidence levels to support decision-making—for example, evaluating and managing uncertainty in AI model performance and deployment. - Optimization
Mathematical solutions to choose the best option from many—like minimizing cost or maximizing benefit—while meeting all the required limits and rules.
Computational Fluid Dynamics
NLR's CFD research focuses on energy efficiency opportunities and improving energy technologies. Often, we leverage adaptive mesh refinement via techniques such as the AMReX framework, an open-source software library for solving equations with local grid refinement to enhance resolution (accuracy) at affordable computational cost. AMReX is designed to be efficient on high-performance computing systems composed of diverse architectures, which enables its use on cutting-edge and upcoming supercomputers.
Incompressible and low-Mach-number flows are solved using low-speed solvers.
Adaptive Mesh and Algorithm Refinement
AMAR: adaptive mesh and algorithm refinement
BioReactorDesign (BiRD)
Gas-liquid flows for biofuel production
ExaWind Software Suite
AmrWind - AMReX-based solver for atmospheric flows
Mesoflow
AMReX-based code for catalytic upgrading and pyrolysis
Pele Software Suite
PeleLMeX—low Mach solver for turbulent reacting flows
Energy Research and Forecasting
AMReX-based mesoscale atmospheric wind code
Pele Software Suite
PeleC – compressible turbulent reacting flows
Non-Continuum Methods
NLR's research in discrete simulation advances techniques for the transport of dispersed phases, solid mechanics, and particle-based models for fluid dynamics.
MARBLES: Multi-Scale Adaptively Refined Boltzmann LatticE Solver
An open-source CFD package that efficiently simulates fluid flow around intricate geometries—including moving or porous surfaces—without the need for a body-conforming mesh
NLR's research in Monte Carlo simulations includes techniques for crystal growth and fluid dynamics.
Adaptive Mesh and Algorithm Refinement
SPPARKS – KMC code for material growth
BDEM: Discrete-Element Simulator for High-Solids Granular Flows (GitHub)
A discrete element method-based simulation tool for modeling high-solids granular
flows that include polydispersity, heat transfer, moving boundaries, and chemistry.
The solver provides facilities for simulating spherical/nonspherical particles with
modified contact and friction models in complex dynamic geometries defined using level-sets
or triangulated files.
SPADES: Scalable Parallel Discrete Events Solvers
Event-driven simulations of complex systems
Biomass Feedstock Conversion Interface Handling Computational Models
Simulating the handling and flowability of organic biomass feedstock in coupled feed
systems
Exagoop (GitHub)
An open-source material point method solver that efficiently simulates the dynamics
of highly deformable continuum phases.
Biomass Feedstock Conversion Interface Handling Computational Models
Simulating the handling and flowability of organic biomass feedstock in coupled feed
systems
Surrogate Modeling, Statistics, and Uncertainty Quantification
NLR researchers leverage high- and multi-fidelity data from simulations and experiments to develop computationally efficient methods for control and optimization of complex systems. Mathematics to quantify uncertainty are used to enable decision-making and numerics that take the uncertainty of variable energy sources into account.
Pipeline of simulation capabilities—including simulation of pretreatment, enzymatic hydrolysis, and fermentation processes—for the conversion of biomass into second-generation biofuels
PVade: Photovoltaic Aerodynamic Design Engineering Software Wind Loading and Aerodynamic
Stability for PV Systems
Simulates wind loading and stability in solar-tracking PV systems
Aerodynamic Shape Parametrization Using Separable Shape Tensors
For design optimization
Framework for performing multi-fidelity modeling
High-fidelity simulations of biofuels used in aircraft engines to affect performance, fuel economy, and reliability
Optimization and Control
Adaptive Computing
Framework for performing multifidelity modeling
NLR supports large-scale stochastic optimization for multistage, multiscenario decision problems arising in energy systems and infrastructure planning. These models are formulated with mathematical structure that enables parallel-scalable solution via decomposition-based algorithms, including progressive hedging and related scenario-based methods.
The capability leverages flexible algebraic modeling environments, sparsity-aware data structures, and distributed orchestration of commercial and open-source solvers, including large-scale deployments of FICO® Xpress Solvers across thousands of parallel workers. Problem instances may involve hundreds of millions of variables and constraints, enabling tightly coupled, integrated stochastic simulations as well as high-throughput evaluation of scenario ensembles. This capability provides a production-ready platform for research in large-scale optimization under uncertainty.
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Last Updated April 16, 2026