The book presents a practical, computation‑oriented path to solving the Boltzmann equation. This work equips readers with numerical methods used to model shock waves and other kinetic features, translating complex theory into actionable algorithms.

Grounded in a structured approach, the text shows how to represent the distribution function with moment expansions, and how to evaluate the collision term using Gaussian quadrature and Monte‑Carlo techniques. It discusses how to set up simulations, monitor conservation laws, and interpret results for different Mach numbers and flow conditions. The material is framed to illustrate both the method’s capabilities and its limitations, with comparisons to other theories and numerical approaches.

Representation of the kinetic function via Hermite-based expansions and how many moments to keep for accuracy.

Practical use of Gauss–Hermite quadrature and Monte‑Carlo methods to compute collision terms.

How shocks behave under varying Mach numbers and how to assess shock thickness and oscillations.

Techniques to verify conservation laws and track numerical errors during simulations.

Ideal for readers of computational physics, kinetic theory, and numerical analysis looking for a concrete, paper‑based guide to implementing the Boltzmann solver.

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