A chronological catalog of methods and solutions in the Space–Time Computational Flow Analysis: I. Finite element analysis

The Space–Time Computational Flow Analysis (STCFA) started in 1990 with the inception of the Deforming-Spatial-Domain/Stabilized Space–Time (DSD/SST) method. The DSD/SST was introduced as a moving-mesh method for flows with moving boundaries and interfaces, which is a wide class of problems that includes fluid–particle interactions, fluid–structure interactions (FSI), and free-surface and multi-fluid flows. The first 3D computations were reported in 1992. The original DSD/SST method is now called “ST-SUPS,” reflecting its stabilization components. As the STCFA evolved, advanced mesh moving methods, FSI coupling methods, and problem-class-specific methods were introduced to increase its scope and the ST Variational Multiscale was introduced to upgrade its stabilization components to the VMS. Complementary general-purpose methods developed in the evolution of the STCFA include the ST Isogeometric Analysis (ST-IGA) and the ST Slip Interface (ST-SI) and ST Topology Change (ST-TC) methods. The ST-IGA delivers superior accuracy through IGA basis functions not only in space but also in time. The ST-SI enables high-fidelity moving-mesh computations even over meshes made of patches with nonmatching meshes at the interfaces between those patches. The ST-TC enables high-fidelity moving-mesh computations even in the presence of topology changes in the fluid mechanics domain, such as an actual contact between moving solid surfaces. The STCFA brought first-of-its-kind solutions in many classes of problems, ranging from fluid–particle interactions in particle-laden flows to FSI in parachute aerodynamics, flapping-wing aerodynamics of an actual locust to ventricle-valve-aorta flow analysis to car and tire aerodynamics with near-actual geometries, road contact, and tire deformation. With the success we see in so many classes of problems, we can conclude that the STCFA has reached a level of remarkable sophistication, scope, and practical value. We present a chronological catalog of the methods and solutions in the STCFA. In Part I of this two-part article, we focus on the methods and solutions in finite element analysis.