Space-Time NURBS-Enhanced Finite Elements for Solving the Compressible Navier-Stokes Equations
For computational fluid dynamics researchers, this is an incremental extension of NEFEM to a new equation class.
The paper applies NURBS-Enhanced Finite Element Method (NEFEM) to compressible Navier-Stokes equations, showing improved accuracy over conventional FEM in numerical examples, though no concrete performance numbers are provided.
This article considers the NURBS-Enhanced Finite Element Method (NEFEM) applied to the compressible Navier-Stokes equations. NEFEM, in contrast to conventional finite element formulations, utilizes a NURBS-based computational domain representation. Such representations are typically available from Computer-Aided-Design tools. Within the NEFEM, the NURBS boundary definition is utilized only for elements that are touching the domain boundaries. The remaining interior of the domain is discretized using standard finite elements. Contrary to isogeometric analysis, no volume splines are necessary. The key technical features of NEFEM will be discussed in detail, followed by a set of numerical examples that are used to compare NEFEM against conventional finite element methods with the focus on compressible flow.