Lorenzo Campoli — Computational Scientist

Research

Projects & Focus Areas

From kinetic theory and shock-fitting to turbulence modelling and open-source scientific software.

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Data-Driven Turbulence Modelling

Applying unsupervised ML and Gene Expression Programming (GEP) to improve the generalisability and interpretability of RANS closure models across diverse flow regimes.

UniMelb

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Hypersonic Non-Equilibrium Flows

Development of numerical methods for high-speed viscous reactive flows in state-to-state (STS) and multi-temperature formulations, with a focus on shock-heated air.

SPbU

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UnDiFi-2D: Shock-Fitting

Co-developer of an open-source unstructured discontinuity fitting code for 2D grids, enabling sharp shock representation on unstructured meshes without numerical diffusion.

Open Source

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KAPPA Library

C++ library implementing kinetic approaches to physical processes in planetary and re-entry atmospheres — transport coefficients, relaxation rates, thermodynamic properties.

Published · CPC 2019

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Viscous Fingering

Numerical investigation of the viscous finger instability in porous media using real field data, in collaboration with Gazprom Neft, for enhanced hydrocarbon recovery modelling.

Applied

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ML for State-to-State Kinetics

Systematic benchmarking of machine learning regression methods — neural networks, GPR, random forests — as surrogates for expensive STS thermochemical relaxation databases.

Published · Mathematics 2022

Teaching

Courses

Hypersonics

Sep 2020 – Sep 2022 · SPbU

Machine Learning for Fluid Mechanics

Mar 2021 – Sep 2022 · SPbU

Modern Scientific Visualisation

Mar 2021 – Jun 2021 · SPbU

Scientific Paper Writing

Mar 2021 – Jun 2021 · SPbU

Concepts of Modern Natural Science

Mar 2021 – Jun 2021 · SPbU

Service & Outreach

Peer Review

Reviewer for journals in computational fluid dynamics, aeronautics, and applied mathematics.

Conference Activity

Regular presentations at RGD, ISSW, ECFD, and other major international symposia.

Open Source

Actively maintaining scientific software repositories on GitHub across multiple research domains.

Publications

Selected Works

Full list on Google Scholar · ORCID 0000-0002-0510-9422

2022

Assessment of Machine Learning Methods for State-to-State Approach in Nonequilibrium Flow Simulations

L. Campoli, E. Kustova, P. Maltseva

Mathematics 10(6), 928 (2022)DOI →

2021

UnDiFi-2D: An Unstructured Discontinuity Fitting Code for 2D Grids

L. Campoli, A. Assonitis, M. Ciallella, R. Paciorri, A. Bonfiglioli, M. Ricchiuto

Computer Physics Communications 271, 108202 (2021)DOI →

2020

Models Validation and Code Profiling in State-to-State Simulations of Shock Heated Air Flows

L. Campoli, O. Kunova, E. Kustova, M. Melnik

Acta Astronautica 175, 493–509 (2020)DOI →

Numerical Investigation of Viscous Fingering Phenomenon for Raw Field Data

F. Bakharev, L. Campoli, A. Enin, S. Matveenko, Y. Petrova, S. Tikhomirov, A. Yakovlev

Transport in Porous Media 132(2), 443–464 (2020)DOI →

2019

KAPPA: Kinetic Approach to Physical Processes in Atmospheres Library in C++

L. Campoli, G.P. Oblapenko, E.V. Kustova

Computer Physics Communications 236, 244–267 (2019)DOI →

2016–2017

Unsteady Shock-Fitting for Unstructured Grids

A. Bonfiglioli, R. Paciorri, L. Campoli

Int. J. Numer. Methods Fluids 81(4), 245–261 (2016)DOI →

Shock-Fitting and Predictor-Corrector Explicit ALE Residual Distribution (Book Chapter)

L. Campoli, P. Quemar, A. Bonfiglioli, M. Ricchiuto

Shock Fitting, pp. 113–129, Springer, Cham (2017)

Resources

Software & Tools

A curated collection of packages and tools I use or recommend across CFD, hypersonics, discontinuity fitting, scientific ML, HPC, meshing, and data formats.

Thermodynamics & Transport CFD — General CFD — Compressible & Hypersonic Spectral, FEM & PDE Discontinuity Fitting ML & Physics-Informed Scientific Computing HPC & Parallel Meshing Visualization Data Formats Optimisation & UQ

Thermodynamics & Transport

KAPPAC++
Kinetic Approach to Physical Processes in Atmospheres — multi-temperature transport coefficients for partially-ionised gas mixtures.
CanteraC++/Python
Chemical kinetics, thermodynamics, and transport processes. Widely used for combustion and reacting-flow simulations.
Mutation++C++
Multicomponent Thermodynamic And Transport in C++. Rigorous Chapman-Enskog transport for high-temperature and plasma flows.
CEA / STANJANmulti
NASA's Chemical Equilibrium with Applications — standard reference for equilibrium composition and thermodynamic properties at high temperatures.
REFPROPNIST
NIST Reference Fluid Thermodynamic and Transport Properties. The authoritative source for real-gas equations of state.
CoolPropPython/C++
Open-source thermodynamic property library for 120+ fluids. Excellent Python interface and REFPROP-compatible calls.

CFD Solvers — General

OpenFOAMC++MPI
The reference open-source CFD toolbox. Finite-volume, unstructured, covers incompressible to reacting multi-phase flows. Vast community and solver library.
SU2C++MPI
Multiphysics simulation and design software with discrete adjoint for aerodynamic optimisation and shape design.
COOLFluiDC++MPI
HPC platform for multi-physics simulations developed at VKI. Supports aerodynamics, MHD, radiation, and atmospheric re-entry.
Code_SaturneC/FortranMPI
EDF's open-source solver for incompressible, weakly-compressible, and thermal flows. Robust RANS and LES turbulence models.
PalabosC++
Lattice Boltzmann solver from the University of Geneva. Modular and suited for complex geometry and porous-media flows.
MFCFortranGPU
Exascale compressible multiphase flow solver with NVIDIA and AMD GPU acceleration. 2025 Gordon Bell Prize finalist.
T-FlowsFortranMPI
Turbulent Flows CFD code originally from TU Delft. LES/DNS capability on unstructured meshes.

CFD Solvers — Compressible & Hypersonic

UCNS3DFortranMPI
High-order unstructured compressible Navier-Stokes 3D solver. WENO/TENO schemes for shock-dominated flows.
EilmerD/Python
Transient, compressible flow solver from the University of Queensland. Designed for hypersonic and high-enthalpy flows; supports thermally-perfect and equilibrium gas models.
MPI-AMRVACFortranMPI
Parallel adaptive mesh refinement framework for hyperbolic PDEs. Hydrodynamics and MHD modules with AMR shock-capturing.
hy2FoamC++
Two-temperature open-source CFD model for hypersonic reacting flows built on OpenFOAM. Validated for non-equilibrium aerothermodynamics.
AMReXC++GPUMPI
Block-structured adaptive mesh refinement framework from LBNL. GPU-ready, exascale-capable, widely used in combustion and reacting flow codes.
WaterLily.jlJuliaGPU
Fast and simple fluid simulator in Julia. Immersed-boundary approach; runs on CPU and GPU with identical code.

Spectral, FEM & PDE Frameworks

DedalusPython
Flexible framework for solving PDEs with spectral methods. Supports Chebyshev, Fourier, and Jacobi bases; ideal for stratified/rotating flows.
Nek5000 / NekRSFortran/C++GPU
Spectral-element DNS/LES code from Argonne National Laboratory. NekRS is the GPU-accelerated rewrite targeting exascale machines.
FEniCSx / DolfinPython/C++
Automated finite element framework. Expressive variational formulation via UFL; supports complex multiphysics and adjoint problems.
deal.IIC++MPI
High-performance finite element library with AMR, hp-adaptivity, and large-scale parallel linear algebra via Trilinos/PETSc.
FourierFlows.jlJulia
Pseudospectral PDE solver on periodic domains. GPU-ready; excellent for 2D turbulence and geophysical fluid dynamics.

Discontinuity Fitting

UnDiFi-2DFortran
Unstructured Discontinuity Fitting code in 2D. Reference implementation for fitting-based shock-boundary treatment on unstructured meshes.
OF_DBFC++
OpenFOAM-based discontinuity boundary fitting library for general reacting compressible flows.
Fortran DF FrameworkFortranMPI/OpenMP
Modern Fortran discontinuity fitting framework supporting structured/unstructured meshes, Euler, Navier-Stokes and MHD physics, and hybrid parallelism.

ML & Physics-Informed Methods

DeepXDEPython
Scientific machine learning library for PINNs and operator learning. Supports TensorFlow, PyTorch, JAX, and PaddlePaddle backends.
NVIDIA ModulusPythonGPU
AI-driven multi-physics simulation framework from NVIDIA. PINNs, neural operators, FNO, and physics-constrained surrogate models.
JAXPythonGPU/TPU
Composable function transformations (grad, jit, vmap, pmap) for high-performance numerical computing. Foundation for a growing ML-physics ecosystem.
DiffraxPython
Differentiable ODE/SDE/CDE solvers in JAX. Ideal for neural ODEs and adjoint-based training of dynamical models.
neuraloperatorPython
Fourier Neural Operator (FNO) and related operator-learning architectures. Surrogate models for PDE solutions mapping function spaces.
GraphCast / GNNs for CFDPython
Graph neural network architectures for mesh-based physics simulation. Increasingly applied for data-driven turbulence closure and flow prediction.
PyTorchPythonGPU
Leading deep learning framework. Strong ecosystem for custom physics loss functions, adjoint training, and surrogate CFD workflows.
scikit-learnPython
Comprehensive classical ML toolkit. Useful for regression/classification in CFD data analysis, PCA of flow fields, and clustering of shock topologies.

Scientific Computing Libraries

PETScC/C++/FortranMPI
Portable, extensible toolkit for parallel scientific computation. The workhorse for large-scale linear and non-linear solvers in CFD.
TrilinosC++MPI
Collection of reusable scientific software libraries from Sandia. Linear algebra, solvers (Belos), preconditioners (MueLu/ML), and more.
hypreCMPI
High-performance preconditioners and solvers including algebraic multigrid (BoomerAMG). Used inside PETSc and standalone for elliptic CFD sub-problems.
NumPy / SciPyPython
Foundation of scientific Python. SciPy adds ODE integrators, sparse linear algebra, special functions, and optimisation essential for CFD post-processing.
CuPyPythonGPU
GPU-accelerated NumPy-compatible array library (CUDA/ROCm). Drop-in replacement for NumPy in performance-critical post-processing pipelines.
OpenBLAS / LAPACKFortran/C
Optimised basic linear algebra subroutines and eigensolvers. The numerical backbone of virtually every CFD solver.
FFTWCMPI
Fastest Fourier Transform in the West. MPI-parallel version used in spectral flow solvers and turbulence spectrum analysis.
pyCGNS / cgnslibPython/C
Python and C interfaces to the CFD General Notation System. For reading, writing, and converting CFD mesh and solution data.

HPC & Parallel Computing

Open MPIMPI
High-performance MPI implementation. Standard choice for inter-node communication in distributed-memory CFD simulations.
OpenMPmulti
Shared-memory parallel programming API. Routinely combined with MPI in hybrid parallelisation of CFD codes.
CUDA ToolkitGPU
NVIDIA's parallel computing platform and API. Essential for GPU-accelerated CFD solvers, ML training, and large-scale linear algebra.
Spackmulti
HPC package manager from LLNL. Indispensable for reproducible environment management on clusters and supercomputers.
Zoltan / PT-ScotchC/C++MPI
Graph and mesh partitioning tools for load-balanced parallel CFD. PT-Scotch and ParMETIS are the standard partitioners used by most CFD frameworks.
HDF5 / NetCDFStandard
Parallel I/O libraries for large scientific datasets. HDF5 is the storage backend for many CFD post-processing and restart workflows.

Meshing

GmshC++/Python
Full-featured 3D finite element mesh generator with CAD kernel, scripting API, and post-processing. The open-source standard for research meshes.
SALOMEPython/C++
Open-source platform integrating CAD (GEOM), meshing (SMESH), and physics solver coupling. Strong GUI and Python scripting interface.
cfMeshC++
Robust automatic volume meshing library integrated with OpenFOAM. Delivers quality hex-dominant and polyhedral meshes on complex geometries.
enGridC++
Qt-based mesh generation tool with automatic prismatic boundary layer insertion for Navier-Stokes simulations. Outputs OpenFOAM and SU2 format.
TetGenC++
Quality tetrahedral mesh generator and Delaunay mesh refinement. Widely used for unstructured 3D volume meshes in CFD and FEM.
TriangleC
Constrained Delaunay triangulation and quality 2D mesh generation by J. R. Shewchuk. Reference tool for 2D unstructured mesh research.
PyMeshPython/C++
Geometry processing library for Python. Wraps Triangle, TetGen, and CGAL; useful for mesh pre-processing and repair pipelines.
CGALC++
Computational Geometry Algorithms Library. Rigorous implementations of Delaunay triangulation, mesh generation, and surface remeshing.
meshioPython
Reads and writes mesh data in 40+ formats (Gmsh, VTK, CGNS, Abaqus, etc.). Essential for cross-code mesh conversion in CFD workflows.

Visualization & Post-processing

ParaViewPython/C++MPI
The open-source standard for large-scale scientific visualisation. Server-client architecture enables in-situ and remote post-processing of HPC data.
VisItPython/C++MPI
LLNL's interactive parallel visualisation and graphical analysis tool. Strong support for AMR data and large-scale turbulence datasets.
Tecplot 360
CFD-focused visualisation with automated PyTecplot scripting, precise contour control, and high-quality publication graphics.
MatplotlibPython
2D plotting library for Python. Combined with NumPy and SciPy, the standard tool for CFD data analysis, spectral plots, and convergence histories.
Plotly / DashPython
Interactive visualisation library. Dash enables browser-based dashboards for CFD parameter sweeps and surrogate model exploration.
PyVistaPython
3D visualisation for Python built on VTK. Scriptable mesh inspection, streamline tracing, and interactive Jupyter rendering of CFD fields.
VTKC++/Python
Visualisation Toolkit — the algorithmic backbone of ParaView and PyVista. Direct access to volume rendering, iso-surfacing, and streamline algorithms.

Data Formats & Standards

CGNSStandard
CFD General Notation System — the community standard for storing and exchanging CFD mesh and solution data. Supported by most major solvers.
HDF5Standard
Hierarchical Data Format for large, complex, heterogeneous data. Underpins CGNS and many restart/checkpoint formats for HPC simulations.
VTK XML FormatsStandard
VTK's XML-based unstructured and rectilinear grid formats (.vtu, .vts). The native output of OpenFOAM post-processing and most modern solvers.
NetCDFStandard
Self-describing array data format common in geophysical and atmospheric CFD. Supports parallel I/O via PnetCDF and HDF5 backends.
meshioPython
Universal mesh format converter. Bridges CGNS, Gmsh, VTK, Abaqus, MEDIT, and 35+ other formats in a single Python package.

Optimisation & Uncertainty Quantification

DAFoamPython/C++
Discrete Adjoint with OpenFOAM for high-fidelity MDO. Gradient-based aerodynamic shape optimisation with parallel adjoint sensitivity computation.
OpenTURNSPython/C++
Industrial framework for uncertainty treatment, reliability analysis, and sensitivity analysis (Sobol indices) for complex simulation codes.
SMTPython
Surrogate Modeling Toolbox. Kriging/GP, RBF, and polynomial chaos surrogates for CFD design-space exploration and aerodynamic optimisation.
BoTorch / AxPythonML
Bayesian optimisation framework built on PyTorch. Used for sample-efficient parameter tuning of computationally expensive CFD simulations.
scikit-optimizePython
Sequential model-based optimisation in Python. Gaussian Process and Random Forest surrogate methods for blackbox CFD objective minimisation.

Lorenzo
Campoli

Modelling Flow,
from Shocks to Turbulence

Projects & Focus Areas

Data-Driven Turbulence Modelling

Hypersonic Non-Equilibrium Flows

UnDiFi-2D: Shock-Fitting

KAPPA Library

Viscous Fingering

ML for State-to-State Kinetics

Courses

Hypersonics

Machine Learning for Fluid Mechanics

Modern Scientific Visualisation

Scientific Paper Writing

Concepts of Modern Natural Science

Selected Works

Career Timeline

Software & Tools

Get in Touch

LorenzoCampoli

Modelling Flow,from Shocks to Turbulence

Projects & Focus Areas

Data-Driven Turbulence Modelling

Hypersonic Non-Equilibrium Flows

UnDiFi-2D: Shock-Fitting

KAPPA Library

Viscous Fingering

ML for State-to-State Kinetics

Courses

Hypersonics

Machine Learning for Fluid Mechanics

Modern Scientific Visualisation

Scientific Paper Writing

Concepts of Modern Natural Science

Selected Works

Career Timeline

Software & Tools

Get in Touch

Lorenzo
Campoli

Modelling Flow,
from Shocks to Turbulence