A new spline space, the hierarchical structure-preserving B-spline space, is introduced and implemented in the analysis of Stokes flow. The space, when properly constrained, is shown to be stable and to have at least optimal convergence rates in the velocity field and suboptimal convergence rates in the pressure field. However, results show that superoptimal convergence can often be expected in the pressure field, likely due to error reduction in the velocity field. Like other hierarchical spline spaces, these splines are shown to greatly increase accuracy and to drastically lower computation times for analyses on domains whose solution fields have singularities or could otherwise benefit from local refinement. With the advent of this adaptive, locally-refineable, high-fidelity technology, isogeometric methods can become more feasible for use in fluid analyses.
College and Department
Ira A. Fulton College of Engineering and Technology; Civil and Environmental Engineering
BYU ScholarsArchive Citation
Shepherd, Kendrick Monroe, "Modeling Stokes Flow Using Hierarchical Structure-Preserving B-Splines" (2015). Theses and Dissertations. 5581.
B-splines, NURBS, isogeometric analysis, finite element analysis, Stokes flow, hierarchical splines, structure-preserving splines