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

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.(c) 2023 Elsevier B.V. All rights reserved.

Automated summary

The DSD/SST method is a moving-mesh method used for computational analysis of flows with moving boundaries and interfaces. It combines different stabilization components, such as SUPG and PSPG methods, to enable fluid analysis. Special methods, such as ST-IGA, were also introduced. These methods allow for the solution of challenging fluid flow problems.