Enhanced-discretization and solution techniques in flow simulations and parachute fluid-structure interactions

We present three innovative approaches for simulations of parachute fluid-structure interactions (FSI), which otherwise tend to be unstable because of extreme sensitivity of thin membrane structure to massive fluid dynamic forces. In the first approach, we use an iterative scheme in conjunction with augmented structural mass matrix to achieve convergence in coupling the fluid and the structure motion. In the second approach, we use a coupled formulation that includes the inter-dependence of fluid and structure motion. The dependence of flow on domain deformation is addressed iteratively in this approach. Finally in the third approach, we use a directly coupled formulation that fully incorporates the inter-dependence of fluid, structure and mesh motion. All the three approaches accurately predict parachute FSI and successful FSI simulations of soft landing of T-10, G-12 and G-11 parachutes are presented to provide corroborating evidence.; To further improve the quality of FSI simulations, carried out using any of the three coupling approaches, we present more enhanced-discretization and solution techniques. We present definitions of the stabilization parameters used in SUPG and PSPG formulations based on local length scales that are shown to be accurate and less dissipative. We also present an Enhanced-Discretization Space-Time Technique (EDSTT) that has tremendous potential in saving significant amount of computational time as it allows us to use different time-step sizes in different regions of a computational domain. Complementary to EDSTT, we propose an Enhanced-Discretization Successive Update Method (EDSUM) which resolves small scale information in flow simulations. We have also described a variation of EDSUM that gives dramatic rates of convergence in solving linear equation systems. Another effort toward accurately solving linear equation systems is the Enhanced-Approximation Linear Solution Technique (EALST) that we propose for improving the convergence in selected regions of the flow. All these techniques are successfully tested on a variety of problems and the results obtained are unequivocally satisfactory.