Development of non-boundary-fitted Cartesian grid method for numerical simulation of mechanical heart valve and the potential for blood clotting

Computational fluid dynamics (CFD) simulations are becoming a reliable tool in understanding disease progression, investigating blood flow patterns and evaluating medical device performance such as mechanical heart valves (MHV). Previous studies indicated that the non-physiological flow pattern (i.e. recirculation, stagnation, and vortex) might cause a trapped platelet and be responsible for the formation of blood clots in MHV. Accurate simulation of this flow requires a high order accuracy numerical scheme together with a scale resolving turbulence model such as large eddy simulation (LES). This requires the use of uniform orthogonal grids for the descretisation process, which is not able to handle complex branching arterial domains that contain MHV, where the generation are usually boundary-fitted (BF) grid with non-orthogonality and distortions. Therefore, nonboundary fitted (NBF) Cartesian grid method is an alternative solution. The objective of this study is to develop a new NBF method based on the volume of fluid (VOF), containing the colour function, namely NBF-VOF Cartesian grid method. A single set of governing equation is used for both solid and fluids identified by unity colour function and zero colour function respectively. The solid was treated as a fluid with very high viscosity to theoretically reduce its deformability, and subsequently satisfy a no-slip condition at the boundary. In the first attempt, we found that in prior, the treatment was not satisfied. To suppress the fluid velocities in the solid, we introduced the artificial term derived from the colour function into an algebraic system of momentum equations, which had a significant impact on the originality of this study. The developed solver, NBF-VOF, is then thoroughly validated using a variety of numerical and experimental results available in the literature which is Hagen-Poiseuille flow, lid-driven cavity, flow over a cylinder, 90o tube flow, and pulsatile flow through the real anatomic aorta. Opensource CFD software was used as our simulation platform. Although the second order method degenerates the spatial accuracy of convergence rate as function of the grid size from 2 to 1.5, an agreement was found for all cases qualitative and quantitatively. The grid uncertainty obtained was less than 5%, which was within the acceptable range. The computational time was lower when the viscosity of solid was higher. However, higher solid viscosity gives lagging in the result for transient cases. Despite this, using higher time step, until the maximum Courant number of 4.0, can speed up the simulation time and preserved the stability. Finally, another breakthrough in this study was the application of the solver to simulate pulsatile blood flow of MHV placed in an axisymmetric and real patient anatomic aorta with the sinus, which reveals complex blood flow patterns, shear stress loading, and history of particles age in the local domain, that consequently can identified the potential of blood clotting.

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