Distributed Lagrange multiplier/fictitious domain method in the framework of lattice Boltzmann method for fluid–structure interactions

A new implementation of the lattice Boltzmann method (LBM) for fluid–structure interactions is presented. The idea of the distributed-Lagrange-multiplier/fictitious-domain method (DLM/FD) is introduced in the framework of the lattice Boltzmann algorithm. This implementation employs a fixed mesh for the solution of the fluid problem and a Lagrangian formulation for the solid problem. The main advantage of the method is that the re-meshing procedure normally required in the ALE method is circumvented. Numerical examples are provided to verify the algorithm and illustrate the capacity of the method to deal with the fluid/elastic–solid interactions.