HyQMOM.jl

3D Hyperbolic Quadrature Method of Moments (HyQMOM) solver for the Boltzmann equation with BGK collision operator, featuring MPI parallelization and interactive visualization.

Overview

HyQMOM.jl is a high-performance computational fluid dynamics solver that implements the Hyperbolic Quadrature Method of Moments (HyQMOM) for solving multidimensional kinetic equations. The solver extends the one-dimensional HyQMOM closure to handle 2D and 3D velocity distribution functions using up to 35 fourth-order velocity moments.

The method provides closures for higher-order moments without requiring quadrature points or velocity distribution function reconstruction. Instead, it uses orthogonal polynomials constructed directly from known moments to define the unclosed moments needed for the hyperbolic flux terms. This approach ensures global hyperbolicity and moment realizability across arbitrary Knudsen and Mach number regimes.

Key features include:

• 3D moment-based kinetic solver for Boltzmann-BGK equation
• MPI parallelization with domain decomposition
• Interactive 3D visualization with GLMakie (time-series animation)
• Flexible parameter control via command-line arguments
• Serial or parallel execution (automatic detection)
• Snapshot collection for time evolution analysis

Quick Navigation

• Quickstart Guide
• • Installation
  • Your First Simulation
  • Quick Parameter Adjustments
  • MPI Parallel Execution
  • Visualizing Saved Results
  • Headless/HPC Systems
  • Next Steps
  • Troubleshooting
• HyQMOM.jl User Guide
• • Table of Contents
  • Prerequisites
  • Installing Julia
  • Getting the Code
  • Setting Up the Environment
  • Running Your First Simulation
  • Understanding the Output
  • Customizing Parameters
  • Running with MPI (Parallel)
  • Visualization Options
  • Troubleshooting
  • Advanced Usage
  • Summary: Quick Reference
  • Further Resources
  • Tips for Success
• MPI & Parallelization
• • Overview
  • Quick Start
  • Domain Decomposition
  • Performance Guidelines
  • MPI Configuration
  • Visualization in Parallel
  • Performance Scaling
  • HPC and Batch Systems
  • Debugging Parallel Runs
  • Advanced Topics
  • Performance Monitoring
• Interactive 3D Visualization Tutorial
• • Overview
  • Basic Usage
  • Step-by-Step Walkthrough
  • Advanced Features
  • Parallel Visualization
  • Troubleshooting
  • Tips and Best Practices
  • Next Steps
• API Reference
• • All Exported Functions and Types
• Developer Guide
• • Project Structure
  • Architecture Principles
  • Adding New Features
  • Code Style and Conventions
  • Performance Optimization
  • MPI Development
  • Visualization Development
  • Contributing Guidelines
  • Release Process

Getting Started

The fastest way to get started is with our Quickstart Guide, which will have you running your first simulation in minutes.

For a comprehensive overview of all features and capabilities, see the User Guide.

Key Features

High-Performance Computing

• MPI domain decomposition for scalable parallel execution
• Optimized numerical algorithms for kinetic equations
• Support for both serial and parallel workflows

Interactive Visualization

• Real-time 3D isosurface visualization with GLMakie
• Time-series animation with interactive controls
• Multiple physical quantities (density, velocity, pressure, temperature)
• Works seamlessly with both serial and MPI parallel simulations

Flexible Configuration

• Command-line parameter control for all simulation aspects
• Predefined initial condition configurations
• Easy customization for new physical scenarios

Citation

If you use HyQMOM.jl in your research, please cite:

@software{hyqmom_jl,
  title = {HyQMOM.jl: 3D Hyperbolic Quadrature Method of Moments},
  author = {Spencer H. Bryngelson and contributors},
  year = {2024},
  url = {https://github.com/comp-physics/HyQMOM.jl}
}

License

See the license file for licensing information.