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An immersogeometric variational framework for CFD and FSI with application to aortic valves

The aim of this work is to develop a geometrically flexible technique for computational fluid dynamics (CFD) and fluid–structure interaction (FSI). The motivating application is the simulation of aortic valve function over the complete cardiac cycle. Due to the complex motion of the heart valve leaflets, the fluid domain undergoes large deformations, including changes of topology. We propose an immersogeometric method that directly analyzes an isogeometric surface representation of the structure by immersing it into a non-boundary-fitted discretization of the surrounding fluid domain. The variational formulation for immersogeometric FSI is derived using an augmented Lagrangian approach. The framework also includes a penalty-based dynamic contact algorithm for shell structures represented by isogeometric surfaces. To evaluate the accuracy of the proposed methods, we test them on benchmark problems and compare the results with those of established boundary-fitted techniques. We then simulate the coupling of the aortic valve and the surrounding blood flow under physiological conditions, demonstrating the effectiveness of the proposed techniques in practical computations. An arbitrary Lagrangian–Eulerian/immersogeometric hybrid methodology is also developed under the augmented Lagrangian framework for FSI. A single computation combines a boundary-fitted, deforming-mesh treatment of some fluid–structure interfaces with a non-boundary-fitted treatment of others. This approach enables us to also simulate the FSI of a bioprosthetic aortic valve implanted in a flexible artery through the entire cardiac cycle.

Author(s):

Ming-Chen Hsu    
Iowa State University
United States

David Kamensky    
The University of Texas at Austin
United States

Michael C. H. Wu    
Iowa State University
United States

Fei Xu    
Iowa State University
United States

Vasco Varduhn    
University of Minnesota
United States

Dominik Schillinger    
University of Minnesota
United States