# Space-Time NURBS-Enhanced Finite Elements for Solving the Compressible Navier-Stokes Equations

## TL;DR

This paper introduces NEFEM, a finite element method that uses NURBS for boundary representation, improving the simulation of compressible Navier-Stokes equations by integrating CAD data directly into the analysis.

## Contribution

The paper presents NEFEM, a novel finite element approach that incorporates NURBS boundary representations from CAD tools without requiring volume splines, enhancing compressible flow simulations.

## Key findings

- NEFEM accurately models boundary conditions using CAD-based NURBS.
- NEFEM shows improved accuracy over conventional FEM in compressible flow problems.
- Numerical examples demonstrate NEFEM's efficiency and precision.

## Abstract

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.