Space–Time Flow Computation with Contact Between the Moving Solid Surfaces

In computation of flow problems with moving boundaries and interfaces, including fluid–structure interaction, moving the fluid mechanics mesh to follow the fluid–solid interface enables mesh-resolution control near the interface. Therefore moving-mesh methods, such as the Space–Time Variational Multiscale (ST-VMS) method, enable high-resolution boundary-layer representation near fluid–solid interfaces and thus higher accuracy in such critical flow regions. In flow problems with contact between solid surfaces, until recently, one had to either give up on representing the actual contact and leave a small gap or give up on using a moving-mesh method and thus give up on having high-fidelity flow solution near the solid surfaces. The ST Topology Change (ST-TC) method changed all that. Now we can both represent the actual contact and have high-fidelity flow solution near the solid surfaces. With the ST-VMS, which serves as the core method, and the ST-TC and two other special methods, the ST Slip Interface method and ST Isogeometric Analysis, we have created a powerful computational framework. The new framework is enabling high-fidelity computational flow analysis of some of the most complex problems, such as the ventricle-valve-aorta sequence. This chapter is a description and demonstration of that framework.