Chen, Hudong (2021) Volumetric Lattice Boltzmann Models in General Curvilinear Coordinates: Theoretical Formulation. Frontiers in Applied Mathematics and Statistics, 7. ISSN 2297-4687
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Abstract
A theoretical formulation of lattice Boltzmann models on a general curvilinear coordinate system is presented. It is based on a volumetric representation so that mass and momentum are exactly conserved as in the conventional lattice Boltzmann on a Cartesian lattice. In contrast to some previously existing approaches for arbitrary meshes involving interpolation approximations among multiple neighboring cells, the current formulation preserves the fundamental one-to-one advection feature of a standard lattice Boltzmann method on a uniform Cartesian lattice. The new approach is built on the concept that a particle is moving along a curved path. A discrete space-time inertial force is derived so that the momentum conservation is exactly ensured for the underlying Euclidean space. We theoretically show that the new scheme recovers the Navier-Stokes equation in general curvilinear coordinates in the hydrodynamic limit, along with the correct mass continuity equation.
Item Type: | Article |
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Subjects: | Euro Archives > Mathematical Science |
Depositing User: | Managing Editor |
Date Deposited: | 20 Apr 2023 04:43 |
Last Modified: | 04 Jun 2024 10:40 |
URI: | http://publish7promo.com/id/eprint/1216 |