High-order Shakhov-like extension of the relaxation time approximation in relativistic kinetic theory
| Autor: | Ambruş, Victor E., Wagner, David |
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| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Phys. Rev. D 110 (2024) 056002 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevD.110.056002 |
| Popis: | In this paper we present a relativistic Shakhov-type generalization of the Anderson-Witting relaxation time model for the Boltzmann collision integral. The extension is performed by modifying the path on which the distribution function $f_{\mathbf{k}}$ is taken towards local equilibrium $f_{0\mathbf{k}}$, by replacing $f_{\mathbf{k}} - f_{0\mathbf{k}}$ via $f_{\mathbf{k}} - f_{{\rm S}\mathbf{k}}$. The Shakhov-like distribution $f_{{\rm S} \mathbf{k}}$ is constructed using $f_{0\mathbf{k}}$ and the irreducible moments $\rho_r^{\mu_1 \cdots \mu_\ell}$ of $f_\mathbf{k}$ and reduces to $f_{0\mathbf{k}}$ in local equilibrium. Employing the method of moments, we derive systematic high-order Shakhov extensions that allow both the first- and the second-order transport coefficients to be controlled independently of each other. We illustrate the capabilities of the formalism by tweaking the shear-bulk coupling coefficient $\lambda_{\Pi \pi}$ in the frame of the Bjorken flow of massive particles, as well as the diffusion-shear transport coefficients $\ell_{V\pi}$, $\ell_{\pi V}$ in the frame of sound wave propagation in an ultrarelativistic gas. Finally, we illustrate the importance of second-order transport coefficients by comparison with the results of the stochastic BAMPS method in the context of the one-dimensional Riemann problem. Comment: 38 pages, 8 figures, 2 tables |
| Databáze: | arXiv |
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