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Updated: May 24, 2026

Blast Quantification Using Hopkinson Pressure Bars

Blast Quantification Using Hopkinson Pressure Bars

Published on: July 5, 2016

A numerical solution of the linear Boltzmann equation using cubic B-splines.

Saheba Khurana¹, Mark Thachuk

¹Department of Chemistry, University of British Columbia, 2036 Main Mall, Vancouver V6T 1Z1, Canada.

The Journal of Chemical Physics

|March 10, 2012

Summary

A novel numerical method using cubic B-splines accurately solves the linear Boltzmann equation. This approach efficiently predicts distribution functions and moments, even in higher dimensions.

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Last Updated: May 24, 2026

Blast Quantification Using Hopkinson Pressure Bars

Blast Quantification Using Hopkinson Pressure Bars

Published on: July 5, 2016

Area of Science:

Computational physics
Numerical analysis
Kinetic theory

Background:

The linear Boltzmann equation is fundamental in kinetic theory.
Solving this equation often requires complex numerical methods.
The Wigner-Wilkins collision kernel is a standard model for certain systems.

Purpose of the Study:

To present a new numerical method for solving the linear Boltzmann equation.
To evaluate the accuracy and efficiency of the proposed method.
To explore the method's applicability to different physical parameters.

Main Methods:

Utilizing cubic B-splines for discretizing the distribution function.
Employing the Wigner-Wilkins collision kernel.
Calculating eigenvalues, eigenfunctions, and moments of the collision matrix.

Main Results:

The numerical method demonstrates high accuracy and stability.
Eigenvalues and eigenfunctions align with known theoretical values.
Accurate prediction of distribution functions and moments is achieved with minimal data points.
The method generates sparse matrices suitable for parallel computation.

Conclusions:

The cubic B-spline method provides an accurate and efficient solution for the linear Boltzmann equation.
The method is robust across various mass and temperature ratios.
Its ability to generalize to higher dimensions and parallelize makes it a valuable tool for computational physics.