**Prof. David A. Caughey**

Sibley School of Mechanical and Aerospace Engineering

Cornell University

**"Implicit Multigrid Computation of Unsteady Flows with Applications to Aeroelasticity"**

**Abstract:**

Unsteady fluid flows often are characterized by time scales that are large compared to those governing the stability of the numerical methods used to solve the equations of motion, especially when the equations of compressible
flow are used. This fact has provided motivation for the development of implicit methods that have relaxed stability criteria, relative to explicit methods.

While early versions of implicit schemes used linearization of the equations to avoid iteration on the nonlinear terms within each time step, a number of researchers have found it useful to embrace the concept of iteration (or subiteration) within the time step. A number of advantages accrue by this approach, including the elimination of factorization error in factored implicit schemes, the elimination of errors due to approximations made in the implicit operator to improve numerical efficiency, the elimination of errors due to lagged boundary conditions at both solid and internal fluid boundaries, and the ability to use non-physical, pre-conditioned iterative methods for more efficient convergence of the subiterations.

In this talk I will describe an implicit, multigrid scheme that has been extended to treat unsteady flows using the concept of subiteration. The scheme is applied to compute the unsteady flow past fixed and moving circular cylinders at moderate Reynolds numbers. The observed pattern of periodic vortex shedding is computed for fixed cylinders, and the corresponding Strouhal numbers are compared with experimentally measured values. Flow
patterns for cylinders having prescribed motions are then computed as well as the coupled problem in which the motion of the cylinder is determined by the aerodynamic forcing. Finally, the efficiency of the sub-iterated, multigrid approach will be discussed.

#### Friday, February 25, 2000

3:00 PM in 335 Jabara Hall

Please join us for refreshments before the lecture at 2:30p.m. in room 353 Jabara Hall.

[ Spring 2000]