Space-Time Computational Techniques for the Aerodynamics of Flapping Wings

Abstract

We present the special space-time computational techniques we have introduced recently for computation of flow problems with moving and deforming solid surfaces. The techniques have been designed in the context of the deforming-spatial-domain/stabilized space-time formulation, which was developed by the Team for Advanced Flow Simulation and Modeling for computation of flow problems with moving boundaries and interfaces. The special space-time techniques are based on using, in the space-time flow computations, non-uniform rational B-splines (NURBS) basis functions for the temporal representation of the motion and deformation of the solid surfaces and also for the motion and deformation of the volume meshes computed. This provides a better temporal representation of the solid surfaces and a more effective way of handling the volume-mesh motion. We apply these techniques to computation of the aerodynamics of flapping wings, specifically locust wings, where the prescribed motion and deformation of the wings are based on digital data extracted from the videos of the locust in a wind tunnel. We report results from the preliminary computations.

A numerical study of linear and nonlinear kinematic models in fish swimming with the DSD/SST method

“…Some examples of these applications are animal swimming and flight [13,22,[60][61][62][63][64][65][66], flag flapping [28], spacecraft parachutes [67][68][69][70][71][72][73][74][75][76][77], cardiovascular fluid mechanics [78][79][80][81][82], wind-turbine aerodynamics [83][84][85][86], and non-Newtonian flow [87].…”

Space–time computations in practical engineering applications: a summary of the 25-year history

“…The computations reported in 2012 were for detailed analysis of parachute FSI [85][86][87][88], arterial FSI [89,90], flow in aneurysms blocked with stent [91], wind-turbine aerodynamics [92], and bioinspired flapping-wing aerodynamics [18,93,94]. The detailed parachute studies, all for the Orion spacecraft parachutes, were for different designs of the suspension lines and overinflation control line, reefed parachute stages, different trial canopy design configurations, different payload models, 2-parachute clusters, FSIbased dynamical analysis of single parachutes and parachute clusters, disreefing of single parachutes and parachute clusters, parachutes with modified geometric porosity, and Stage 2 shape determination for the modified-geometric-porosity parachute.…”

“…These special ST methods include the ST Slip Interface (ST-SI) [14,15] and ST Topology Change (ST-TC) [16,17] methods. The ST-SUPS and ST-VMS computations started with finite element discretization, but with the ST Isogeometric Analysis (ST-IGA) [7,18,19], they are now also with isogeometric discretization in space and time. When we summarize the ST computations in practical engineering applications, we will focus on the application, rather than the precise nature of the ST computational framework.…”

Space–time SUPG finite element computation of shallow-water flows with moving shorelines

“…The stabilization techniques used in the DSD/SST formulation are the SUPG and PSPG methods. A number of advanced mesh update methods [5,18,22,24,38,82,94] have been developed in conjunction with the DSD/SST formulation. The DSD/SST formulation has been applied successfully to several different classes of problems involving moving boundaries and interfaces (see, for example, [5,7-9, 11,12,14-19,22,24,26-29,34,35,38,82,95,96]), including free-surface and two-fluid flows, fluid-particle and fluidstructure interactions, and flows with mechanical components in fast, linear or rotational relative motion.…”

“…Here we will call that formulation "(SU PG) 82 ". Later, (SU PG) 82 was recast in entropy variables and supplemented with a shock-capturing term [101,102], which yielded better shock profiles.…”