The Team for Advanced Flow Simulation and Modeling (T☆FSM) at Rice University specializes in developing fluid-structure interaction (FSI) modeling techniques for several classes of challenging problems including geometrically complex parachutes. Current modeling technologies are expanded upon with emphasis placed on more realistic FSI modeling of the Orion spacecraft ringsail parachutes. A method for generating a starting condition that matches NASA drop test data and allows for a fair comparison of design variations is introduced. The effect of the geometric porosity distribution on parachute performance and stability is analyzed for three parachute configurations. Rotationally periodic computations that model flow past the complex canopy geometry are presented. Fabric and geometric porosity coefficients are calculated for an improved FSI porosity model. A spatially multiscale technique is used to compare fabric stresses with and without a vent hoop.