Speaker
Description
Recent modeling frameworks to predict the mechanics of additive manufacturing processes involve both fluid and solid mechanics, with the former often described adopting the lattice Boltzmann method. Motivated by the wish to model all physics with the same method, we proposed a novel lattice Boltzmann formulation to solve the equations of linear elastostatics [1,2] and we now aim at extending the scope to elastodynamics [3]. In comparison to previous attempts in the same direction, our approach aims at higher accuracy and efficiency, as well as at retaining the computational benefits of the lattice Boltzmann method.
In this contribution we outline the systematic construction of a second-order consistent lattice Boltzmann formulation to solve the equations of linear elastodynamics with Dirichlet and Neumann boundary conditions. To this end, we reformulate the target equation as first-order hyperbolic system and use the so-called vectorial LBM for its numerical approximation [3]. Using the asymptotic expansion technique [4] we formally show second-order consistency. Additionally, we establish a CFL-like stability criterion based on the notion of so-called pre-stability structures [5]. Lastly, we propose novel second-order consistent and stable boundary formulations for Dirichlet and Neumann boundary conditions.
All derivations are verified by numerical experiments using manufactured solutions and standard benchmark test cases.
References
[1] Boolakee, O., Geier, M. and De Lorenzis, L. A new lattice Boltzmann scheme for linear elastic solids: periodic problems. Comp. Meth. Appl. Mech. Eng. (2023) 404:115756.
[2] Boolakee, O., Geier, M. and De Lorenzis, L. Dirichlet and Neumann boundary conditions for a lattice Boltzmann scheme for linear elastic solids on arbitrary domains. Comp. Meth. Appl. Mech. Eng. (2023) 415:116225.
[3] Boolakee, O., Geier, M. and De Lorenzis, L. Lattice Boltzmann for linear elastodynamics: Periodic problems and Dirichlet boundary conditions. Comp. Meth. Appl. Mech. Eng. (2024) 433:117469.
[4] Junk, M., Klar, A. and Lou, L. S. Asymptotic analysis of the lattice Boltzmann equation. J. Comp. Phys. (2005) 210:676–704.
[5] Banda, M. K., Yong, W. A., Klar, A. A stability notion for lattice Boltzmann equations. SIAM J. Sci. Comput. (2006) 27:2098–2111.
