Lattice Boltzmann methods for solids: Difference between revisions

Revision as of 22:48, 30 November 2022

Revision as of 22:48, 30 November 2022

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{{Short description|definition of the lattice Boltzmann methods for solids}}

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The '''Lattice Boltzmann methods for solids (LBMS)''' are specific methods based on the [[lattice Boltzmann methods]] (LBM). LBM are a group of numerical methods that are used to solve [[Partial differential equation|partial differential equations]] (PDE). These methods themselves relying on a discretization of the [[Boltzmann equation]] (BE). When the PDE at stake are related to solid mechanics, this subset of LBM is called lattice Boltzmann methods for solids. The main categories of LBMS are relying on:

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=== Wave solvers ===

Another approach consists in using LBM as acoustic solvers to capture waves propagation in solids.<ref name="geo2011wave"/><ref name="xia07"/><ref name="Guangwu_2000a"/><ref name="obr12"/>.

=== Force tuning ===

==== Introduction ====

This idea consists of introducing a modified version of the forcing term:<ref name="guo2002force"/> (or equilibrium distribution<ref name="noel2019"/>) into the LBM as a stress divergence force. This force is considered space-time dependent and contains solid properties<ref group="Note" name="notesolidproperties"/>:

::<math>\vec{g} = \frac{1}{\rho} \vec{\mathbf{\nabla}_{x}} \cdot \overline{\overline{\sigma}}</math>,

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== References ==

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[[Category:Biomechanics]]

[[Category:Fluid dynamics]]

[[Category:Thermodynamics]]