The goal of the Physics/Fields Colloquium is to feature scientists whose work is of interest to both the physics and the mathematical science community. The series has been running since the Spring of 2007. Usually there is one speaker per semester. Each speaker gives a primary, general talk in the regular physics colloquium venue and, whenever possible, a second, more specialised talk at the Fields Institute.

This seminar takes place Wednesdays at 3:10pm at the Fields Institute **AND** Thursdays at 4:10pm in MP 102

Our interest in computing the Navier-Stokes equations coupled to moving boundaries is directed toward understanding the unsteady aerodynamics of insect flight and fluttering and tumbling objects. While many interesting fluid phenomena originate near a moving sharp interface, computational schemes typically encounter great difficulty in resolving them. We have been designing efficient computational codes that are aimed at resolving the moving sharp interfaces in flows at Reynolds number relevant to insect flight. The first set of codes are Navier-Stokes solvers for simulating a 2D rigid flapping wing, which are based on high-order schemes in vorticity-stream function formulation. In these solvers we take advantage of coordinate transformations and 2D conformal mapping to resolve the sharp wing tips so as to avoid grid-regeneration. These methods were used to elucidate the unsteady aerodynamics of forward and hovering flight. They were also used to examine the aerodynamics of the fluttering and tumbling of plates falling through fluids. To go beyond 2D simulations of rigid objects, we recently developed a more general- purpose code for simulating 3D flexible wing flight, based on immersed interface method. The main improvement is to obtain the 2nd order accuracy along the sharp moving surface. To avoid introducing ad-hoc boundary conditions at the moving interface, we employ a systematic method to derive from the 3D Navier-Stokes equation the jump conditions on the fluid variables caused by the singular force. In addition, the temporal jump conditions must be included in order to have a correct scheme. To handle the spatial and temporal jump conditions in the finite difference scheme, we derive generalized Taylor expansions for functions with discontinuities of arbitrary order.

- · Wednesday, Mar. 24, 2010: Computing Insect Flight and Falling Paper (Jane Wang)
- · Thursday, Mar. 25, 2010: How Insects Fly and Turn (Jane Wang)
- · Wednesday, Mar. 09, 2011: Some Issues in Bipedal locomotion (Andy Ruina)
- · Thursday, Mar. 10, 2011: Rotation with zero angular momentum: Demonstrations of the falling cat phenomenon go sour (Andy Ruina)
- · Thursday, Oct. 27, 2011: Wave-particle duality at the macroscopic scale (Yves Couder)