A Nitsche stabilized finite element method: Application for heat and mass transfer and fluid-structure interaction

A Nitsche stabilized finite element method is proposed for heat & mass transfer and fluid-structure interaction. The GLS/PSPG stabilization is employed to stabilize the finite element formulation. The Nitsche's methods are employed to weakly impose the Dirichlet condition for heat & mass transfer. An upwind term is included in Nitsche's methods to enhance the stability for fast moving interfaces. The Ghost penalty method is employed to control the jumps across the cut cells. The projection-based adaptive Gauss quadrature (PAGQ) scheme is used for the numerical integration of the discontinuous function. The nonlinear advection-diffusion equations are linearized by Newton procedure. The second-order accurate unconditionally stable generalized-a time integration is implemented to march the solution in time. The fluid and the structure equations are weakly coupled by a second-order accurate staggered-partitioned scheme. Numerical examples include the cases of fixed/vibrating/rotating cylinder(s) for heat & mass transfer and fluid-structure interaction in enclosure and external flow. The obtained numerical results match well with the experiments, the empirical correlation and the numerical simulations in literature. This methodology efficiently and accurately simulates the complex physics of heat & mass transfer. (C) 2021 Elsevier B.V. All rights reserved.