Local Metrics for Exact Streaming on Curvilinear Lattices: A Curvilinear D3Q27 Cumulant Lattice-Boltzmann Method
Abstract
A three-dimensional curvilinear lattice-Boltzmann method is introduced for simulations on smoothly deformed grids while retaining exact one-to-one streaming on a uniform computational lattice. The coordinate transformation is represented locally through a metric-Gaussian equilibrium and a Christoffel-connection source in moment space. A dynamically reconstructed homogeneous-state perturbation streaming procedure preserves homogeneous physical states on warped meshes without interpolation in the advection step. The method is implemented on a D3Q27 lattice with a cumulant collision operator, while the geometric construction remains compatible with other local collision models. The formulation is assessed using two sets of tests. First, static non-orthogonal warped-cube cases validate the bulk curvilinear solver through a convected helical shear wave, the Taylor--Green vortex, and Arnold--Beltrami--Childress flow. These tests verify viscous decay, clean freestream preservation, vortex-breakdown dynamics, and the nonlinear inertial--pressure balance induced by geometric acceleration. Second, wall-bounded and moving-boundary demonstrations assess the boundary-compatible extension through warped plane Poiseuille flow, arbitrary Lagrangian--Eulerian (ALE) peristaltic pumping, and a two-way fluid--structure interaction (FSI) case with added-mass frequency shift. The results show that the proposed curvilinear LBM avoids interpolation-based transport, reduces geometry-locked numerical modes, preserves global mass and momentum to round-off accuracy in the tested warped periodic cases, and extends to wall-bounded ALE/FSI configurations with conservative treatment of mass and physically consistent momentum exchange.
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BibTeX
@misc{sawaf2026local,
title = {{Local Metrics for Exact Streaming on Curvilinear Lattices: A Curvilinear D3Q27 Cumulant Lattice-Boltzmann Method}},
author = {Maher Sawaf and Jonas Latt and Nikolaus A. Adams and Mostafa S. Shadloo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36971},
eprint = {2610.36971},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36971},
}
RIS
TY - UNPB
TI - Local Metrics for Exact Streaming on Curvilinear Lattices: A Curvilinear D3Q27 Cumulant Lattice-Boltzmann Method
AU - Maher Sawaf
AU - Jonas Latt
AU - Nikolaus A. Adams
AU - Mostafa S. Shadloo
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.36971
UR - https://arxiv.org/abs/2610.36971
AB - A three-dimensional curvilinear lattice-Boltzmann method is introduced for simulations on smoothly deformed grids while retaining exact one-to-one streaming on a uniform computational lattice. The coordinate transformation is represented locally through a metric-Gaussian equilibrium and a Christoffel-connection source in moment space. A dynamically reconstructed homogeneous-state perturbation streaming procedure preserves homogeneous physical states on warped meshes without interpolation in the advection step. The method is implemented on a D3Q27 lattice with a cumulant collision operator, while the geometric construction remains compatible with other local collision models. The formulation is assessed using two sets of tests. First, static non-orthogonal warped-cube cases validate the bulk curvilinear solver through a convected helical shear wave, the Taylor--Green vortex, and Arnold--Beltrami--Childress flow. These tests verify viscous decay, clean freestream preservation, vortex-breakdown dynamics, and the nonlinear inertial--pressure balance induced by geometric acceleration. Second, wall-bounded and moving-boundary demonstrations assess the boundary-compatible extension through warped plane Poiseuille flow, arbitrary Lagrangian--Eulerian (ALE) peristaltic pumping, and a two-way fluid--structure interaction (FSI) case with added-mass frequency shift. The results show that the proposed curvilinear LBM avoids interpolation-based transport, reduces geometry-locked numerical modes, preserves global mass and momentum to round-off accuracy in the tested warped periodic cases, and extends to wall-bounded ALE/FSI configurations with conservative treatment of mass and physically consistent momentum exchange.
ER -