Scan-based immersed isogeometric flow analysis

TL;DR

This paper reviews innovative methods for scan-based immersed isogeometric flow analysis, enabling stable, efficient, and detailed simulations directly from complex scan data, with applications to patient-specific cases.

Contribution

It introduces new techniques for geometry extraction, stabilization, adaptive integration, and mesh refinement tailored for scan-based immersed isogeometric analysis.

Findings

Stable results achieved on immersed domains

Enhanced computational efficiency through adaptive quadrature

Successful simulation of flow on complex scan data

Abstract

This chapter reviews the work conducted by our team on scan-based immersed isogeometric analysis for flow problems. To leverage the advantageous properties of isogeometric analysis on complex scan-based domains, various innovations have been made: (i) A spline-based segmentation strategy has been developed to extract a geometry suitable for immersed analysis directly from scan data; (ii) A stabilized equal-order velocity-pressure formulation for the Stokes problem has been proposed to attain stable results on immersed domains; (iii) An adaptive integration quadrature procedure has been developed to improve computational efficiency; (iv) A mesh refinement strategy has been developed to capture small features at a priori unknown locations, without drastically increasing the computational cost of the scan-based analysis workflow. We review the key ideas behind each of these innovations, and illustrate these using a selection of simulation results from our work. A patient-specific scan-based analysis case is reproduced to illustrate how these innovations enable the simulation of flow problems on complex scan data.