A shifted boundary method for thermal flows

We present an implementation of the Shifted Boundary Method (Octree-SBM) on incomplete Octree meshes for multiphysics simulations of coupled flow and heat transfer. Specifically, a semi-implicit formulation of the thermal Navier-Stokes equations is used to accelerate the simulations while maintaining accuracy. The SBM enables precise enforcement of field and derivative boundary conditions on cut (intercepted) elements, allowing for accurate flux calculations near complex geometries, when using meshes that are not fitted to the boundary. Both Dirichlet and Neumann boundary conditions are implemented within the SBM framework, with numerical results demonstrating their accuracy in the context of Octree-based meshes. We illustrate this approach by simulating flows across different regimes, spanning several orders of magnitude in both Rayleigh number ( Ra ∼ 10³–10⁹) and Reynolds number ( Re ∼ 10⁰–10⁴), and covering the laminar, transitional, and turbulent flow regimes. Coupled thermal-flow phenomena and their statistics across all these regimes are accurately captured without any additional numerical treatments, beyond a Residual-based Variational Multiscale formulation (RB-VMS). This approach offers a reliable and efficient solution for complex geometries, boundary conditions and flow regimes in computational multiphysics simulations.

Duke Scholars

Author Guglielmo Scovazzi Civil and Environmental Engineering