Numerical simulation of flow through two biofluid devices

摘要

The results of a numerical simulation of flow through an artificial heart and through an artificial tilting disk heart valve are presented. The simulation involves solving the incompressible Navier-Stokes equations; the solution process is described. The details and difficulties of modeling these geometries are discussed. The artificial heart involves a piston-type action with a moving solid wall. A single H grid is fitted inside the heart chamber. The grid is continuously compressed and expanded (the number of grid points remains constant) to accommodate the moving piston. The valve geometry involves a tilting disk inside a cylindrical chamber. An overlaid-grid approach is used to simulate this geometry. The equations must be solved iteratively for each discrete time step of the computations, thus a significant amount of computing time is required. Approximately four hours on a supercomputer are needed for one period of the artificial heart's piston motion. It is particularly difficult to analyze and illustrate the fluid physics represented by these calculations because of the time-varying nature of the flow, and because the flows are internal. Three-dimensional graphics and scientific visualization techniques have become instrumental in solving these problems.