A novel multiblock immersed boundary method for large eddy simulation of complex arterial hemodynamics

Abstract

Computational fluid dynamics (CFD) simulations are becoming a reliable tool to understand hemodynamics, disease progression in pathological blood vessels and to predict medical device performance. Immersed boundary method (IBM) emerged as an attractive methodology because of its ability to efficiently handle complex moving and rotating geometries on structured grids. However, its application to study blood flow in complex, branching, patient-specific anatomies is scarce. This is because of the dominance of grid nodes in the exterior of the fluid domain over the useful grid nodes in the interior, rendering an inevitable memory and computational overhead. In order to alleviate this problem, we propose a novel multiblock based IBM that preserves the simplicity and effectiveness of the IBM on structured Cartesian meshes and enables handling of complex, anatomical geometries at a reduced memory overhead by minimizing the grid nodes in the exterior of the fluid domain. As pathological and medical device hemodynamics often involve complex, unsteady transitional or turbulent flow fields, a scale resolving turbulence model such as large eddy simulation (LES) is used in the present work. The proposed solver (here after referred as WenoHemo), is developed by enhancing an existing in-house high order incompressible flow solver that was previously validated for its numerics and several LES models by Shetty et al. [Journal of Computational Physics 2010; 229 (23), 8802-8822]. In the present work, WenoHemo is systematically validated for additional numerics introduced, such as IBM and the multiblock approach, by simulating laminar flow over a sphere and laminar flow over a backward facing step respectively. Then, we validate the entire solver methodology by simulating laminar and transitional flow in abdominal aortic aneurysm (AAA). Finally, we perform blood flow simulations in the challenging clinically relevant thoracic aortic aneurysm (TAA), to gain insights into the type of fluid flow patterns that exist in pathological blood vessels. Results obtained from the TAA simulations reveal complex vortical and unsteady flow fields that need to be considered in designing and implanting medical devices such as stent grafts.

Multiblock high order Large Eddy Simulation of powered Fontan hemodynamics: Towards computational surgery

“…This model is easy to implement, efficient to use, and applicable to fully inhomogeneous turbulent flows[3, 13, 14, 49]. This model gives: $${\nu }_T=C{\mathrm{normal\Pi }}^g$$ $${\mathrm{normal\Pi }}^g=\sqrt{\frac{B_{\beta }}{{\alpha }_{ij}{\alpha }_{ij}}}$$ with…”

“…The diffusion terms and the sub-grid stress tensor arising from the filtering of the equations are computed using fourth order accurate centered difference schemes. The implementation of the methods were tested and validated in our previous studies[3, 13, 14]. …”

Unstructured Cartesian refinement with sharp interface immersed boundary method for 3D unsteady incompressible flows

“…In the overlapping decomposition methods, which include hierarchical adaptive mesh refinement (AMR) techniques [10,14,67] and overset grids [63,8,64,66,79], the sub-domains have interior points in common. On the other hand, multi-block [46,49,20,4] and patched grid techniques [52,28,9] are examples of non-overlapping decomposition or substructuring methods. An alternative to the domain decomposition techniques (DDM) is the implementation of monolithic structured or unstructured grids [18,7].…”

“…Darbandi and Naderi [20] proposed a hybrid multi-block finite volume method and demonstrated that their methodology is flexible in mesh generation and can satisfy the conservation properties through the block boundaries on laminar flows. In the more recent work of Anupindi et al [4] a multi-block approach was combined with an immersed boundary method to perform LES of arterial hemodynamics. In this study, only equal blocks with uniform meshes were utilized to avoid any interpolation at the block-interfaces and make the scheme conservative.…”

On parallel pre‐conditioners for pressure Poisson equation in LES of complex geometry flows

“…However, with recent developments in immersed boundary methods [25][26][27][28][29][30][31], structured Cartesian grid methods are back in favour. These methods have been extended for a wide variety of flow problems including moving boundary and fluid structure interaction problems [32][33][34][35]. Cartesian grid methods are very easy to parallelize using domain decomposition, and hence, these are especially suited for LES/DNS using massively parallel computers.…”