Entropic lattice Boltzmann method for general anisotropic advection--diffusion
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911642919370752 |
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| author | Feng, Jingsen Leng, Jing Jiang, Jingchao Chu, Xu |
| author_facet | Feng, Jingsen Leng, Jing Jiang, Jingchao Chu, Xu |
| contents | Many transport processes exhibit direction-dependent diffusion, described macroscopically by the full-tensor anisotropic advection--diffusion equation (ADE). Numerical discretization is demanding when the principal axes are rotated relative to the mesh, since mixed derivatives and oblique fluxes amplify grid-orientation errors under large tensor contrasts. This paper develops a local entropic lattice Boltzmann discretization for the general anisotropic ADE. The non-equilibrium population is split into a first-order flux sector and a residual ghost sector. The diffusion tensor is imposed through local tensorial relaxation of the flux, while higher-order kinetic content is controlled by an ADE-corrected entropic stabilizer with positivity fallback. Chapman--Enskog analysis shows the scheme recovers the target full-tensor equation with a discrete-time diffusivity relation between the physical tensor and the flux-relaxation matrix. The update is local, matrix-free, and applies to rotated, spatially varying, heterogeneous, and dynamically coupled tensor transport. We validate it on 3D benchmarks--advected Gaussian plumes, decay of rotated Fourier modes, and source-driven transport with varying tensors--covering off-diagonal diffusion, high-Péclet advection, anisotropy ratios of O(104)O(10^4) O(104), and local contrasts up to $3\times10^4:1$. It is then applied to orientation-induced Taylor dispersion of Brownian rods, quantifying enhancement from shear-driven rotation. Heat-conduction tests include rotated thermal-conductivity measurements and effective conduction in heterogeneous porous media with anisotropy up to $10^4:1. Finally, anisotropic Rayleigh--Bénard convection is simulated to examine how plume morphology and heat transfer change over seven decades of anisotropy ratios, demonstrating an accurate, stable local solver for strongly anisotropic advection--diffusion. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_01774 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Entropic lattice Boltzmann method for general anisotropic advection--diffusion Feng, Jingsen Leng, Jing Jiang, Jingchao Chu, Xu Fluid Dynamics Many transport processes exhibit direction-dependent diffusion, described macroscopically by the full-tensor anisotropic advection--diffusion equation (ADE). Numerical discretization is demanding when the principal axes are rotated relative to the mesh, since mixed derivatives and oblique fluxes amplify grid-orientation errors under large tensor contrasts. This paper develops a local entropic lattice Boltzmann discretization for the general anisotropic ADE. The non-equilibrium population is split into a first-order flux sector and a residual ghost sector. The diffusion tensor is imposed through local tensorial relaxation of the flux, while higher-order kinetic content is controlled by an ADE-corrected entropic stabilizer with positivity fallback. Chapman--Enskog analysis shows the scheme recovers the target full-tensor equation with a discrete-time diffusivity relation between the physical tensor and the flux-relaxation matrix. The update is local, matrix-free, and applies to rotated, spatially varying, heterogeneous, and dynamically coupled tensor transport. We validate it on 3D benchmarks--advected Gaussian plumes, decay of rotated Fourier modes, and source-driven transport with varying tensors--covering off-diagonal diffusion, high-Péclet advection, anisotropy ratios of O(104)O(10^4) O(104), and local contrasts up to $3\times10^4:1$. It is then applied to orientation-induced Taylor dispersion of Brownian rods, quantifying enhancement from shear-driven rotation. Heat-conduction tests include rotated thermal-conductivity measurements and effective conduction in heterogeneous porous media with anisotropy up to $10^4:1. Finally, anisotropic Rayleigh--Bénard convection is simulated to examine how plume morphology and heat transfer change over seven decades of anisotropy ratios, demonstrating an accurate, stable local solver for strongly anisotropic advection--diffusion. |
| title | Entropic lattice Boltzmann method for general anisotropic advection--diffusion |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2605.01774 |