Composite Solution Procedure for 3-D Flow Simulations on a Multi-Box Grid

Fluid flows in biological systems are typically complex, due to factors such as non-Newtonian behavior of biochemical fluids and complex geometry, as well as the interaction of muscles and fluid. With the advent of modern computational technology, these problems are gradually resolved. The present research illustrates two such examples. Grid generation is essential for conducting numerical simulation of fluid flow. In the present research, a new grid generation technique is developed and implemented into a flow solver. This technique enables one to create a grid for complex geometry using only a single computational zone. The flow field can therefore be analyzed without iteration between zones. The numerical scheme developed for solving the grid generation equations is an extension of the traditional three-dimensional Douglass-Gunn Alternating-Direction Implicit (ADI) scheme. A unique feature of the demonstrated grid generation scheme is the concept of multi-box computational domains. In this scheme, the physical domain is mapped onto a multi-box geometry in the computational space, rather than a single box as the traditional methods do. Therefore, the numerical scheme is adjusted accordingly. Flow simulations were performed using the software INS3D, which employs the method of artificial compressibility. This method transforms the Navier-Stokes equations into a system of hyperbolic-parabolic equations, and then marches along the pseudo-time axis until the velocity field becomes divergence-free. Two biological flow problems were analyzed using the aforementioned method. The flow field in an arterial graft as well as in the Left atrium (LA) of the human heart was studied. The effect of Reynolds number and flow-division ratio is examined in the graft problem. The Reynolds number effect is demonstrated via the presence of a helical flow structure and the overall pressure drop. The flow-division ratio alters the flow field in a way that moves the stagnation points. The simulated flow field closely resembles that observed clinically. The steady-state simulation of the flow field in the left atrium of the human heart provided information about the long-term performance of the heart chamber. The simulation demonstrates the existence of low wall shear region, which is therefore susceptible to blood clot formation. This observation also agrees with the clinical findings. In summary, the present research demonstrates application of CFD techniques in the analysis of flow in a biological system. A new grid generation technique is realized, and proved to be useful in simulating these flows. The flow simulation results provide insights into the system, and may be useful for clinical reference.