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A high-order, degree-adaptive hybridizable discontinuous Galerkin (HDG)method is presented for two-fluid incompressible Stokes flows, with boundariesand interfaces described using NURBS. The NURBS curves are embedded in a fixedCartesian grid, yielding an unfitted HDG scheme capable of treating the exactgeometry of the boundaries/interfaces, circumventing the need for fitted,high-order, curved meshes. The framework of the NURBS-enhanced finite elementmethod (NEFEM) is employed for accurate quadrature along immersed NURBS and inelements cut by NURBS curves. A Nitsche's formulation is used to enforceDirichlet conditions on embedded surfaces, yielding unknowns only on the meshskeleton as in standard HDG, without introducing any additional degree offreedom on non-matching boundaries/interfaces. The resulting unfitted HDG-NEFEMmethod combines non-conforming meshes, exact NURBS geometry and high-orderapproximations to provide high-fidelity results on coarse meshes, independentof the geometric features of the domain. Numerical examples illustrate theoptimal accuracy and robustness of the method, even in the presence of badlycut cells or faces, and its suitability to simulate microfluidic systems fromCAD geometries.

An unfitted high-order HDG method for two-fluid Stokes flow with exact NURBS geometries