Anisotropic adaptive finite element method for modelling blood flow

Abstract

In this study, we present an adaptive anisotropic finite element method (FEM) and demonstrate how computational efficiency can be increased when applying the method to the simulation of blood flow in the cardiovascular system. We use the SUPG formulation for the transient 3D incompressible Navier–Stokes equations which are discretised by linear finite elements for both the pressure and the velocity field.

 Given the pulsatile nature of the flow in blood vessels we have pursued adaptivity based on the average flow over a cardiac cycle. Error indicators are derived to define an anisotropic mesh metric field. Mesh modification algorithms are used to anisotropically adapt the mesh according to the desired size field. We demonstrate the efficiency of the method by first applying it to pulsatile flow in a straight cylindrical vessel and then to a porcine aorta with a stenosis bypassed by a graft. We demonstrate that the use of an anisotropic adaptive FEM can result in an order of magnitude reduction in computing time with no loss of accuracy compared to analyses obtained with uniform meshes.

Keywords:

• Finite element method
• Navier–Stokes equations
• Blood flow
• anisotropic adaptive techniques

Acknowledgements

We gratefully acknowledge the support of this work by NSF grant ACI-0205741. This work was facilitated through an allocation of advanced computing resources by NPACI (NRAC program) through the support of the National Science Foundation. The solutions presented herein made use of the linear algebra solution library provided by AcuSim Software.