An unfitted finite-element approach to simulating coupled fluid flow and heat transfer on meshes that do not conform to the geometry. Rather than integrating over awkward cut elements, the Shifted Boundary Method imposes boundary conditions on a nearby surrogate boundary and corrects for the shift with a Taylor expansion, enabling accurate enforcement of both temperature (Dirichlet) and heat-flux (Neumann) conditions near complex shapes. Combined with an Octree discretization and a semi-implicit flow / implicit heat coupling, it captures buoyancy-driven convection from laminar through turbulent regimes without bespoke meshing.
The Shifted Boundary Method (SBM) is an unfitted, immersed-boundary finite-element technique that avoids body-conforming meshes by integrating the weak form over a surrogate boundary shifted inward f…