Space–time fluid mechanics computation of heart valve models

Abstract

Fluid mechanics computation of heart valves with an interface-tracking (moving-mesh) method was one of the classes of computations targeted in introducing the space---time (ST) interface tracking method with topology change (ST-TC). The ST-TC method is a new version of the Deforming-Spatial-Domain/Stabilized ST (DSD/SST) method. It can deal with an actual contact between solid surfaces in flow problems with moving interfaces, while still possessing the desirable features of interface-tracking methods, such as better resolution of the boundary layers. The DSD/SST method with effective mesh update can already handle moving-interface problems when the solid surfaces are in near contact or create near TC, if the "nearness" is sufficiently "near" for the purpose of solving the problem. That, however, is not the case in fluid mechanics of heart valves, as the solid surfaces need to be brought into an actual contact when the flow has to be completely blocked. Here we extend the ST-TC method to 3D fluid mechanics computation of heart valve models. We present computations for two models: an aortic valve with coronary arteries and a mechanical aortic valve. These computations demonstrate that the ST-TC method can bring interface-tracking accuracy to fluid mechanics of heart valves, and can do that with computational practicality.