# A Liquid-Solid Coupling Hemodynamic Model with Microcirculation Load
## 2 Model and Methods
### 2.2. Simulate Method  
In order to comprehensively show the properties of the model, this paper selected the entire blood circulation system starting from the aorta as a study subject. The whole aorta has a straight tube of about 1 m. Because of the scale and strain rate of the aorta, the fluid was simplified as the Newtonian fluid [13]. The straight tube was set with a length of 1000 mm, diameter of 20 mm, and wall thickness  
Figure 1: Calculation model and schematic of measuring point distribution.  
of 2 mm, which accords with the aortal physiological parameters. The tube with porous media for seepage had a length of 300 mm, ensuring its internal flow developing completely. As the power source of the blood circulation system, the inlet took velocity as its boundary condition. Outlet was set as free outlet, located at the end of the tube with porous media for seepage.  
The Computational methodology process of the hemodynamic model is shown in Figure 2. On the liquid-solid interface, fluid applied the calculated wall pressure on the solid; after the solid was deformed due to the pressure, the flow field grid was rebuilt. Then, after several iterations, a convergent result was obtained. Notably, due to the change in the flow field region, the fluid would be temporarily stored in the deformation; when the pressure in the tube dropped, the deformation would decrease and those stored fluids would reenter the flow field to flow. On the fluid-porous media seepage interface, fluid provided the pressure on interface. Under this pressure, the total fluid amount allowed to go through the seepage tube could be calculated. In this system, though solid and porous media seepage did not interact directly on an interface, they were connected together by the flow field. Therefore, the three parts operate synergistically, creating a complex multi-directional coupling relationship.  
This paper divided the model into a structural grid. As shown in Figure 3, the tube cross-section was divided into butterfly grids. The model finally consisted of 84,728 cells, with 107,850 nodes. Therein, the fluid region had 52,668 cells, the solid region had 16,632 cells, and the tube with porous media for seepage had 15,428 cells. CFD-ACE SOLVER was chosen to carry out the entire calculation for this paper, and an arbitrary Lagrangian-Eulerian (ALE) method was employed. The first-order upwind difference scheme was used. A constant time step \(\Delta t=0.02\) s was employed in this study. When the program was running, corresponding physical quantities such as pressure and displacement transfer across fluid-structure interfaces through the coupling of the two sets of codes until a convergence criterion (\(10^{-4}\)) was reached for each time step. Repeated computations with a finer grid (253,800 nodes, 205,386 cells) and coarser grid (33,165 nodes, 24,220 cells) were carried out. Results showed that the alteration of maximum pressure at the same location of the fluid domain was 6% between the finer grid and the coarser grid, and alteration was 3% between the finer grid and the grid in this paper.  
Figure 2: Computational methodology.