WEB-spline based isogeometric analysis for advection–diffusion and incompressible Navier–Stokes problems on implicitly trimmed geometries

This study explores the application of the weighted extended B-splines (WEB-splines) to the advection-diffusion and incompressible Navier-Stokes problems on implicitly trimmed domains, in the context of isogeometric analysis (IGA). The proposed methodology enables a single-patch parameterization for trimmed domains and allows for a natural imposition of Dirichlet boundary conditions on trimming boundaries. To mitigate spurious oscillations in advection-dominated flows, the Streamline-Upwind/Petrov-Galerkin (SUPG) technique is adapted to both the WEB-spline based isogeometric Galerkin method (WEB-IGA-G) and isogeometric Collocation method (WEB-IGA-C). For the Stokes and Navier–Stokes problems, a pair of inf–sup stable WEB-spline spaces is introduced, inspired by Taylor–Hood elements. We detail the discretization process for each unknown and, for the WEB-IGA-C scheme, specify the use of the penalty function method. Numerical experiments demonstrate the excellent performance of the WEB-IGA-G and WEB-IGA-C methods for the advection-diffusion equations, Stokes equations, and incompressible Navier–Stokes equations, with comprehensive comparisons highlighting their convergence characteristics and computational efficiency. Simulations of the dynamic problems on trimmed manifolds and the flow around a cylinder further demonstrate the robustness and applicability of the proposed schemes.