Lattice Boltzmann methods for solids: Difference between revisions

Revision as of 14:06, 25 August 2022

Revision as of 14:46, 25 August 2022

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{{AfC submission|t||ts=20220824221323|u=YetAnotherScientist|ns=118|demo=}}<!-- Important, do not remove this line before article has been created. -->

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:

* Vectorial distributions

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* Force tuning<ref name="mnnclbms"/>

The LBMS subset remains highly challenging from a computational aspect as much as from a theoretical point of view. Solving solid equations within the LBM framework is still a very active area of research. If solids are solved, this shows that the [[Boltzmann equation]] (BE) is capable to describe solids motions as well as fluids and gases: thus unlocking complex physics to be solved such as [[Fluid–structure interaction|fluid-structure interaction]] (FSI) in biomechanics.

== Proposed insights ==

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==== Some results ====

[[File:LBMS solid displacement.png|thumb|2D displacement magnitude on a solid system using force tuning. Obtained field is in accordance with [[Finite element method|finite element methods]] results.]]

Force tuning<ref name="mnnclbms"/> has recently proven its efficiency with a maximum error of 5% in comparison with standard [[Finite element method|finite element]] solvers in mechanics. Accurate validation of results can be also a tedious task since these methods are very different, common issues are: