Space–time computational flow analysis: Unconventional methods and first-ever solutions

Abstract

The Deforming-Spatial-Domain/Stabilized Space–Time (DSD/SST) method was introduced in 1990 as a moving-mesh method for computational analysis of flows with moving boundaries and interfaces (MBI), which is a wide class of problems that includes fluid–particle and fluid–structure interactions and free-surface and multi-fluid flows. The method was inspired by Thomas Hughes’s 1987 work on space–time finite element methods for elastodynamics. The original DSD/SST method is now called “ST-SUPS”, reflecting its stabilization components, which are the Streamline-Upwind/Petrov–Galerkin (SUPG) method, pioneered by Hughes, and the Pressure-Stabilizing/Petrov–Galerkin (PSPG) method, inspired by Hughes’s work on a Stokes-flow Petrov–Galerkin formulation allowing equal-order interpolations for velocity and pressure. Hughes’s work on the residual-based variational multiscale (RBVMS) method inspired the ST-VMS method, which is the VMS version of the DSD/SST. A number of special methods were introduced in connection with the core methods ST-SUPS and ST-VMS. Hughes’s work on isogeometric analysis (IGA) inspired one of those special methods, the “ST-IGA”, with IGA basis functions not only in space but also in time. The core and special ST methods enabled first-ever solutions in some of the most challenging classes of MBI problems, including particle-laden flows, spacecraft parachute fluid–structure interactions, and car and tire aerodynamics. We provide an overview of the ST methods inspired by Hughes’s work and highlight some of the first-ever solutions in these three classes of MBI problems.