Globally hyperbolic moment model of arbitrary order for one-dimensional special relativistic Boltzmann equation
This provides a novel theoretical framework for efficiently approximating the relativistic Boltzmann equation, which is important for applications in astrophysics and high-energy physics.
This work extends the operator projection model reduction method to the one-dimensional special relativistic Boltzmann equation, deriving globally hyperbolic moment systems of arbitrary order. Numerical results demonstrate that solutions of the hyperbolic moment system converge to the solution of the relativistic Boltzmann equation as the order increases.
This paper extends the model reduction method by the operator projection to the one-dimensional special relativistic Boltzmann equation. The derivation of arbitrary order globally hyperbolic moment system is built on our careful study of two families of the complicate Grad type orthogonal polynomials depending on a parameter. We derive their recurrence relations, calculate their derivatives with respect to the independent variable and parameter respectively, and study their zeros and coefficient matrices in the recurrence formulas. Some properties of the moment system are also proved. They include the eigenvalues and their bound as well as eigenvectors,hyperbolicity, characteristic fields, linear stability, and Lorentz covariance. A semi-implicit numerical scheme is presented to solve a Cauchy problem of our hyperbolic moment system in order to verify the convergence behavior of the moment method. The results show that the solutions of our hyperbolic moment system can converge to the solution of the special relativistic Boltzmann equation as the order of the hyperbolic moment system increases.