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Register a new userGlobally hyperbolic moment model of arbitrary order for three-dimensional special relativistic Boltzmann equation
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This paper extends the model reduction method by the operator projection to the three-dimensional special relativistic Boltzmann equation. The derivation of arbitrary order moment system is built on our careful study of infinite families of the complicate Grad type orthogonal polynomials depending on a parameter and the real spherical harmonics. We derive the recurrence relations of the polynomials, calculate their derivatives with respect to the independent variable and parameter respectively, and study their zeros. The recurrence relations and partial derivatives of the real spherical harmonics are also given. It is proved that our moment system is globally hyperbolic, and linearly stable. Moreover, the Lorentz covariance is also studied in the 1D space.
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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.
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