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Posts
Fast spectral Boltzmann solvers: where they shine, where they stop, and what industry actually needs
Published:
The Boltzmann collision operator is one of the most expensive pieces of kinetic theory. In three velocity dimensions, a naive quadrature costs on the order of (N^6) operations per evaluation, where (N) is the resolution in each direction. For decades, that cost made full deterministic kinetic simulations impractical outside academic benchmarks. Fast spectral methods changed the picture—not by simplifying the physics, but by exploiting the convolution structure hidden inside the collision integral.
cluster-smi: CLI tool for monitoring Raspberry Pi clusters
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When you run a rack full of Raspberry Pis, the question that comes up constantly is not “which process is on which CPU,” but something simpler:
How is my cluster’s hardware doing right now?
Building a Raspberry Pi Compute Cluster in the era of AI
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This is not another tutorial on how to build a Raspberry Pi SLURM Cluster
Originally published on Medium.
From Kinetic Theory to Quantum Fluids: A Guided Journey Through the Emergence of Hydrodynamics – Chapter 15
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This is the right place to bring the journey to a deeper level.
From Kinetic Theory to Quantum Fluids: A Guided Journey Through the Emergence of Hydrodynamics – Chapter 14
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We have reached the point where the formal machinery meets real quantum matter. Up to now we have built a hierarchy: \(\text{Boltzmann} \rightarrow \text{BGK} \rightarrow \text{Chapman–Enskog} \rightarrow \text{quantum transport} \rightarrow \text{quantum hydrodynamics}.\)
From Kinetic Theory to Quantum Fluids: A Guided Journey Through the Emergence of Hydrodynamics – Chapter 13
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This is the point where the two threads we have developed—quantum kinetic theory and wave-mechanical quantum hydrodynamics—are brought together.
From Kinetic Theory to Quantum Fluids: A Guided Journey Through the Emergence of Hydrodynamics – Chapter 12
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This chapter takes us into a subtle but very important distinction in quantum fluid theory.
From Kinetic Theory to Quantum Fluids: A Guided Journey Through the Emergence of Hydrodynamics – Chapter 11
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This is where the kinetic derivation connects with modern quantum fluids. Up to now we have treated quantum statistics as a modification of the equilibrium distribution. In this chapter we will explore what happens in the strongly quantum regimes, where the gas is no longer a small correction to the classical picture.
From Kinetic Theory to Quantum Fluids: A Guided Journey Through the Emergence of Hydrodynamics – Chapter 10
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This is a very good point in the derivation to stop and compare the three theories side by side, because the underlying architecture is now visible.
From Kinetic Theory to Quantum Fluids: A Guided Journey Through the Emergence of Hydrodynamics – Chapter 9
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We now arrive at the final closure step: extracting the quantum viscous stress tensor and quantum heat flux from \(f_q^{(1)}\).
From Kinetic Theory to Quantum Fluids: A Guided Journey Through the Emergence of Hydrodynamics – Chapter 8
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We now proceed to repeat the Chapter 5 calculation for \(f_q^{eq}\) and derive the explicit quantum \(f_q^{(1)}\).
From Kinetic Theory to Quantum Fluids: A Guided Journey Through the Emergence of Hydrodynamics – Chapter 7
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We have now completed the classical derivation up to the Navier–Stokes closure. This gives us a very useful reference point, because the quantum derivation will not be a completely new calculation—it will be a deformation of the classical calculation.
From Kinetic Theory to Quantum Fluids: A Guided Journey Through the Emergence of Hydrodynamics – Chapter 6
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Most books state identities like \(\int c_i c_j c_k c_l e^{-\beta c^2}\,d^3c = A(\delta_{ij}\delta_{kl}+\delta_{ik}\delta_{jl}+\delta_{il}\delta_{jk})\) without proving them. That is unfortunate, because these tensor identities are the entire mathematical engine behind the Navier–Stokes constitutive laws.
From Kinetic Theory to Quantum Fluids: A Guided Journey Through the Emergence of Hydrodynamics – Chapter 5
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We have now arrived at what I consider the centerpiece of the entire Chapman–Enskog derivation. From this point onward, every line of algebra has a direct physical interpretation.
From Kinetic Theory to Quantum Fluids: A Guided Journey Through the Emergence of Hydrodynamics – Chapter 4
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To derive the Navier–Stokes equations from the Boltzmann equation, we need to introduce the Chapman–Enskog expansion. Let’s begin.
From Kinetic Theory to Quantum Fluids: A Guided Journey Through the Emergence of Hydrodynamics – Chapter 3
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Having derived the classical Maxwell–Boltzmann equilibrium distribution and its moments, let us now derive the macroscopic conservation laws from the Boltzmann equation.
From Kinetic Theory to Quantum Fluids: A Guided Journey Through the Emergence of Hydrodynamics – Chapter 2
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Let us now derive the classical Maxwell–Boltzmann equilibrium distribution from first principles (rather than simply stating it), prove why it is isotropic in the peculiar velocity, evaluate all of its velocity moments explicitly using Gaussian integrals, and show how the ideal-gas equation of state emerges directly from kinetic theory.
From Kinetic Theory to Quantum Fluids: A Guided Journey Through the Emergence of Hydrodynamics – Chapter 1
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Since I was a PhD student in kinetic theory, one question that got stuck in my mind was:
How does a microscopic description forget information and become a macroscopic fluid?
portfolio
Numerical Simulation of Mechanical Systems
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Solving ODEs to describe the dynamics of mechanical systems
Design of a Banki Waterwheel Prototype
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Bachelor thesis: design of a Banki waterwheel for a micro-hydro power plant
Exact Riemann Solver for Ideal Quantum Gases of Arbitrary Statistics
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Solve Shock Tube Problems for ideal quantum Bose and Fermi gases
publications
Asymptotic-Preserving Weno Schemes for Boltzmann Model Equations and Rarefied Gas Flow Simulation
Published in In the proceedings of Proceedings of the Korea Society of Computational Fluids Engineering, 2014
Use Google Scholar for full citation
Recommended citation: Jaw-Yen Yang, Manuel Diaz, WY Kang, JC Huang, "Asymptotic-Preserving Weno Schemes for Boltzmann Model Equations and Rarefied Gas Flow Simulation." In the proceedings of Proceedings of the Korea Society of Computational Fluids Engineering, 2014.
Numerical Solutions of Ideal Quantum Gas Dynamical Flows Governed by Semiclassical Ellipsoidal-Statistical Distribution
Published in In the proceedings of Proc. R. Soc. A, 2014
Recommended citation: Jaw-Yen Yang, Chih-Yuan Yan, Manuel Diaz, Juan-Chen Huang, Zhihui Li, Hanxin Zhang, "Numerical Solutions of Ideal Quantum Gas Dynamical Flows Governed by Semiclassical Ellipsoidal-Statistical Distribution." In the proceedings of Proc. R. Soc. A, 2014.
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High-Order Conservative Asymptotic-Preserving Schemes for Modeling Rarefied Gas Dynamical Flows with Boltzmann-BGK Equation
Published in Communications in Computational Physics, 2015
Recommended citation: Manuel Diaz, Min-Hung Chen, Jaw-Yen Yang, "High-Order Conservative Asymptotic-Preserving Schemes for Modeling Rarefied Gas Dynamical Flows with Boltzmann-BGK Equation." Communications in Computational Physics, 2015.
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Modeling Rarefied Gas Flows of Arbitrary Statistics with the Semiclassical Boltzmann-BGK Equation
Published in Institute of Applied Mechanics, Taiwan University, 2015
Recommended citation: Manuel Diaz, "Modeling Rarefied Gas Flows of Arbitrary Statistics with the Semiclassical Boltzmann-BGK Equation." Institute of Applied Mechanics, Taiwan University, 2015.
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An Efficient Direct Solver for Rarefied Gas Flows with Arbitrary Statistics
Published in Journal of Computational Physics, 2016
Recommended citation: Manuel Diaz, Jaw-Yen Yang, "An Efficient Direct Solver for Rarefied Gas Flows with Arbitrary Statistics." Journal of Computational Physics, 2016.
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A Conservative Numerical Scheme for Modeling Nonlinear Acoustic Propagation in Thermoviscous Homogeneous Media
Published in Journal of Computational Physics, 2018
Recommended citation: Manuel Diaz, Maxim Solovchuk, Tony Sheu, "A Conservative Numerical Scheme for Modeling Nonlinear Acoustic Propagation in Thermoviscous Homogeneous Media." Journal of Computational Physics, 2018.
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High-performance multi-GPU solver for describing nonlinear acoustic waves in homogeneous thermoviscous media
Published in Computers & Fluids, 2018
Recommended citation: Manuel Diaz, Maxim Solovchuk, Tony Sheu, "High-performance multi-GPU solver for describing nonlinear acoustic waves in homogeneous thermoviscous media." Computers & Fluids, 2018.
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Aeroacoustic Source Identification with Effects of Solid Boundaries Using a Numerical Time-reversal Technique
Published in In the proceedings of Forum Acusticum, 2020
Recommended citation: Yinshi Zhou, Manuel Escobar, Régis Marchiano, David Marx, Christian Prax, Vincent Valeau, "Aeroacoustic Source Identification with Effects of Solid Boundaries Using a Numerical Time-reversal Technique." In the proceedings of Forum Acusticum, 2020.
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Identification of Aeroacoustics Sources with Data Assimilation
Published in In the proceedings of Forum Acusticum, 2020
Use Google Scholar for full citation
Recommended citation: Manuel Escobar, Régis Marchiano, Jean-Camille Chassaing, "Identification of Aeroacoustics Sources with Data Assimilation." In the proceedings of Forum Acusticum, 2020.
A High-Order Immersed Boundary Technique for Computational Aeroacoustics
Published in In the proceedings of Congrès Français d'Acoustique, 2022
Recommended citation: Manuel Diaz, Véronique Fortuné, David Marx, Christian Prax, "A High-Order Immersed Boundary Technique for Computational Aeroacoustics." In the proceedings of Congrès Français d'Acoustique, 2022.
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An efficient three-level weighted essentially non-oscillatory scheme for hyperbolic equations
Published in Computational and Applied Mathematics, 2023
Recommended citation: A Neelan, R Chandran, Manuel Diaz, Raimund Bürger, "An efficient three-level weighted essentially non-oscillatory scheme for hyperbolic equations." Computational and Applied Mathematics, 2023.
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Localizing aeroacoustic sources in complex geometries: A hybrid method coupling 3D microphone array and time-reversal
Published in Journal of Sound and Vibration, 2024
Recommended citation: Yinshi Zhou, Manuel Diaz, David Marx, Régis Marchiano, Christian Prax, Vincent Valeau, "Localizing aeroacoustic sources in complex geometries: A hybrid method coupling 3D microphone array and time-reversal." Journal of Sound and Vibration, 2024.
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talks
Asymptotic-Preserving WENO Schemes for Boltzmann Model Equations and Rarefied Gas Flow Simulation
Published:
Conference presentation on asymptotic-preserving WENO schemes for Boltzmann model equations and rarefied gas flows (with J.-Y. Yang, W.Y. Kang, and J.C. Huang).
Direct Modelling of Rarefied Quantum Gases in Arbitrary Flow Regimes with Semi-classical Boltzmann-BGK Equation
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Conference presentation on a direct approach to model Quantum rarefied gases using a Boltzmann-BGK model equation (with J.-Y. Yang, and J.C. Huang).
A Numerical investigation on the contribution of local nonlinear effects
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Conference presentation on a study of local nonlinear effects in acoustics (with D. Diaz, M.A. Solovchuka, and T.W.H. Sheu).
High-order Numerical Descriptions of Nonlinear Acoustics Propagations on Multiple GPUs
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Conference presentation on high-order numerical descriptions of nonlinear acoustics propagations on multiple GPUs (with M.A. Solovchuka, and T.W.H. Sheu).
Nonlinear Models for Describing Highly Nonlinear Acoustic Waves
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Summary talk on nonlinear acoustics models developed so far and how to use multi-GPU to solve nonlinear acoustics problems. The talk was awarded the Best Paper Presentation at NHRI Research Day.
teaching
Teaching Assistant — Nanoscale Energy Transport
Teaching assistant, Institute of Applied Mechanics, National Taiwan University (NTU), 2014
Supervised 18 hours of problem-solving sessions under Prof. Jaw-Yen Yang. Developed exercises on heat transfer and ideal plasma hydrodynamics. Reference: Jaw-Yen Yang.
Fluid Mechanics Lab Instructor
Laboratory, ENSIP — University of Poitiers, 2020
Taught 24 hours/year of fluid mechanics laboratory sessions for first-year engineering students. Covered basic measurement techniques (pressure, flow rate, viscosity, head losses, etc.). Reference: F. Margnat.
LaTeX Instructor
Certification course, Tecnológico Nacional de México, 2021
Taught a 16-hour online certification program: 8 hours on Beamer presentations and 8 hours on LaTeX document management for thesis writing. Reference: Hugo A. Carrillo.
Kinematics and Ordinary Differential Equations
Internship, Inspira STEM program, 2025
Taught a 32-hour online internship in Kinematics and Ordinary Differential Equations. Reference: Miguel Montalvo and Erick Urquilla.
Finite Difference Methods and Partial Differential Equations
Internship, Inspira STEM program, 2026
Taught a 32-hour online internship in Finite Difference Methods and Partial Differential Equations. Reference: Miguel Montalvo and Erick Urquilla.