Immersed boundary finite element method for blood flow simulation

Abstract

We present an efficient and accurate immersed boundary (IB) finite element (FE) solver for numerically solving incompressible Navier-Stokes equations. Particular emphasis is given to internal flows with complex geometries (blood flow in the vasculature system). IB methods are computationally costly for internal flows, mainly due to the large percentage of grid points that lie outside the flow domain. In this study, we apply a local refinement strategy, along with a domain reduction approach in order to reduce the grid that covers the flow domain and increase the percentage of the grid nodes that fall inside the flow domain. The proposed method utilizes an efficient and accurate FE solver with the incremental pressure correction scheme (IPCS), along with the boundary condition enforced IB method to numerically solve the transient, incompressible Navier-Stokes flow equations. We verify the accuracy of the numerical method using the analytical solution for Poiseuille flow in a cylinder. We further examine the accuracy and applicability of the proposed method by considering flow within complex geometries, such as blood flow in aneurysmal vessels and the aorta, flow configurations which would otherwise be extremely difficult to solve by most IB methods. Our method offers high accuracy, as demonstrated by the verification examples, and high efficiency, as demonstrated through the solution of blood flow within complex geometry on an off-the-shelf laptop computer.

Simulation of intracranial hemodynamics by an efficient and accurate immersed boundary scheme

“…Figure 2 shows the computed axial velocity plotted along with the experimental data [30], measured at the central cross-section at the end of the tube's curved section (tube outlet). The numerical results obtained using the linear (𝑃 1 /𝑃 1 ) elements are in good agreement the experimental data, highlighting the accuracy of the proposed scheme [27].…”

“…The IB methodology used in this study, has been discussed in detail in a recent publication by Bourantas et al [27], demonstrating the accuracy of the IB method. The IB combines the FE and the BCE-IB methods for internal flows, emphasizing in blood flow simulations.…”

“…In the present work, we highlight the applicability of the immersed boundary N-S solver [27] on internal flow problems with complex geometry. The numerical scheme combines the finite element (FE) method for the numerical solution of Navier-Stokes equations and the IB method to simulate fluid flow problems.…”

“…The IB combines the FE and the BCE-IB methods for internal flows, emphasizing in blood flow simulations. Herein, we replace the incremental pressure correction scheme (IPCS) flow solver used in Bourantas et al [27] (IPCS is a modified version of projection method, which provides improved accuracy at little extra computational cost), to the verified [26] and validated [28] finite element CFD solver Oasis, which is a high fidelity finite element Navier-Stokes solver using building blocks from the FEniCS project [29]. In Oasis, special care has been taken to ensure a kinetic energy-preserving and minimally-dissipative numerical solution of the Navier-Stokes equation.…”

“…In the this study, we examine the applicability of the previously developed and validated finite element (FE) [26] boundary condition enforced immersed boundary method [27], to simulate blood flow in patient-specific ICAs. We utilize Cartesian Eulerian grids for the solution of the flow field and Lagrangian points to represent the immersed object.…”