Abstract
This is an overview of some of the new directions we have taken the space–time (ST) computational methods since 2010 in bringing solution and analysis to different classes of challenging engineering problems. The new directions include the variational multiscale (VMS) version of the Deforming-Spatial-Domain/Stabilized ST method, using NURBS basis functions in temporal representation of the unknown variables and motion of the solid surfaces and fluid mechanics meshes, ST techniques with continuous representation in time, ST interface-tracking with topology change, and the ST-VMS method for flow computations with slip interfaces. We describe these new directions and present a few examples.
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