Leveraging Truncated Hierarchical B-splines for Efficient Stokes Solutions
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Computational fluid dynamics (CFD) plays an increasingly important role in engineering design and analysis. However, with the increasingly optimized and complex designs, there is a need for high-fidelity simulations with reduced computational expense. This research aims to begin addressing these challenges by introducing a geometrically flexible, locally refinable, high-order approach centered around the use of truncated hierarchical B-splines applied to the de Rham complex of discrete differential forms. Our investigation discusses the computational stability achieved by truncated hierarchical B-splines, particularly examining their effectiveness in ensuring mass conservation. Analyses are performed for both steady Stokes flow, as well as in more generalized solutions of the Navier-Stokes equations in two dimensions. Results indicate that the methods show promise for yielding highly accurate results at reduced computational expense compared to alternative methods.