Isogeometric analysis in computation of complex-geometry flow problems with moving boundaries and interfaces

Abstract

Flows with moving boundaries and interfaces (MBI) are a large class of problems that include fluid–particle and fluid–structure interactions, and in broader terms, moving solid surfaces. They also include multi-fluid flows, and as a special case of that, free-surface flows, sometimes in combination with moving solid surfaces. In some classes of MBI problems the solid surfaces could be in fast, linear or rotational relative motion or could come into contact. In almost all real-world applications, the solid surfaces would have complex geometries. All these problems are frequently encountered in engineering analysis and design, pose some of the most formidable computational challenges, and have a common core computational technology need. Bringing solution and analysis to them motivated the development of a good number of core computational methods and special methods targeting specific classes of MBI problems. This paper is an overview of some of those core and special methods. The focus is on isogeometric analysis, complex geometries, incompressible-flow Space–Time Variational Multiscale (ST-VMS) and Arbitrary Lagrangian–Eulerian VMS (ALE-VMS) methods, compressible-flow ST Streamline-Upwind/Petrov–Galerkin (ST-SUPG) and ALE-SUPG methods, and some of the special methods developed in connection with these core ST and ALE methods. The incompressible-flow ST-VMS and ALE-VMS and compressible-flow ST-SUPG and ALE-SUPG are moving-mesh methods, where the mesh moves to have mesh-resolution control near the fluid–solid interfaces, enabling high-resolution boundary-layer representation, an essential feature when the accuracy in representing the boundary layer is a priority. The computational examples presented are car and tire aerodynamics with road contact and tire deformation, ventricle–valve–aorta flow, and gas turbine flow.