Extending the cell‐based smoothed finite element method into strongly coupled fluid–thermal–structure interaction

• Published in: International journal for numerical methods in fluids Vol. 93; no. 4; pp. 1269 - 1291
• Main Author: He, Tao
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.04.2021
• Subjects: Algorithms; Approximation; Aquatic reptiles; arbitrary Lagrangian–Eulerian; Boussinesq approximation; CS‐FEM; Deformation; Elastodynamics; Finite element analysis; Finite element method; Flexible bodies; Fluid dynamics; Fluid flow; Fluid-structure interaction; fluid–thermal–structure interaction; Incompressible flow; Mathematical analysis; Navier-Stokes equations; partitioned strong coupling; smoothed finite element method; thermal buoyancy
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.4928

This work generalizes the cell‐based smoothed finite element method (CS‐FEM) into fluid–thermal–structure interaction (FTSI) analysis under the arbitrary Lagrangian–Eulerian description. The thermal buoyancy is included with the incompressible Navier–Stokes equations through the Boussinesq approximation. The combined fluid flow and energy equations are solved by a smoothed characteristics‐based split algorithm that incorporates equal low‐order interpolations for the three primitive variables. The structural motions involving both oscillating rigid and flexible bodies are advanced by the generalized‐α method. Moreover, the nonlinear elastodynamics equations discretized with the CS‐FEM are linearized by the modified Newton–Raphson method. An efficient two‐level mesh updating scheme is subsequently discussed to account for large structural displacement and finite solid deformation. The cell‐based smoothing concept is then adopted to evaluate fluid forces acting on the immersed structure. The smoothed FTSI system is iteratively solved by the block‐Gauss–Seidel procedure. Transient FTSI examples are tested to demonstrate the effectiveness and robustness of the CS‐FEM. The cell‐based smoothed finite element method (CS‐FEM) is extended to unsteady strongly coupled fluid–thermal–structure interaction (FTSI) through the arbitrary Lagrangian–Eulerian description and Boussinesq approximation. The combined fluid flow and energy equations are solved by a smoothed characteristics‐based split algorithm. The cell‐based smoothing concept is also adopted to impose interface conditions. Transient FTSI examples are tested to demonstrate the effectiveness and robustness of the CS‐FEM.