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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2401.04017 |
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| _version_ | 1866917770485039104 |
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| author | Ambruş, Victor E. Wagner, David |
| author_facet | Ambruş, Victor E. Wagner, David |
| contents | 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 $ρ_r^{μ_1 \cdots μ_\ell}$ 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 $λ_{Ππ}$ in the frame of the Bjorken flow of massive particles, as well as the diffusion-shear transport coefficients $\ell_{Vπ}$, $\ell_{πV}$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04017 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | High-order Shakhov-like extension of the relaxation time approximation in relativistic kinetic theory Ambruş, Victor E. Wagner, David Nuclear Theory Fluid Dynamics 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 $ρ_r^{μ_1 \cdots μ_\ell}$ 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 $λ_{Ππ}$ in the frame of the Bjorken flow of massive particles, as well as the diffusion-shear transport coefficients $\ell_{Vπ}$, $\ell_{πV}$ 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. |
| title | High-order Shakhov-like extension of the relaxation time approximation in relativistic kinetic theory |
| topic | Nuclear Theory Fluid Dynamics |
| url | https://arxiv.org/abs/2401.04017 |