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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.
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 compl
We consider a mono-dimensional two-velocities scheme used to approximate the solutions of a scalar hyperbolic conservative partial differential equation. We prove the convergence of the discrete solution toward the unique entropy solution by first es
We prove the global existence of smooth solution to the relativistic string equation in a class of data that is not small. Our solution admits the feature that the right-travelling wave can be large and the left-travelling wave is sufficiently small,
In order to solve the Boltzmann equation numerically, in the present work, we propose a new model equation to approximate the Boltzmann equation without angular cutoff. Here the approximate equation incorporates Boltzmann collision operator with angu
This paper develops the high-order accurate entropy stable finite difference schemes for one- and two-dimensional special relativistic hydrodynamic equations. The schemes are built on the entropy conservative flux and the weighted essentially non-osc