A strategy to interface isogeometric analysis with Lagrangian finite elements—Application to incompressible flow problems. (20th March 2016) - Rasool, Raheel; Corbett, Callum J.; Sauer, Roger A.
Highlights: A strategy to interface isogeometric analysis (IGA) with Lagrangian finite elements. Enriched finite elements are used to obtain a localized IGA-based enrichment for CFD. Provides similar accuracy as IGA at a cost similar to Lagrangian finite elements. Provides more accurate representation of the boundary surfaces. Provides higher-order evaluation of integrals only at regions where it is desired. Abstract: Motivated by the superior accuracy and better stability of isogeometrically enriched finite elements — when compared to standard Lagrangian finite elements for problems involving contact and debonding [15, 16] — we extend their applicability to fluid flow problems. Internal and external flow involving incompressible Newtonian fluids is analyzed in the framework of the Finite Element Method (FEM). The concept of isogeometric analysis is applied only at certain localized regions while the bulk fluid is modeled with Lagrangian finite elements. This is achieved by using isogeometrically enriched finite elements that have a NURBS surface representation on one face while all other basis functions are represented by Lagrange polynomials. In this manner an enriched representation and analysis of the near surface region is possible, resulting in an approach that shows similar accuracy as the isogeometric analysis (IGA) while at the same time incurring similar cost as the standard FEM. This is demonstrated through several numerical examples involving laminar fluid flow.