Note: Different Date and Location
Abstract:
An algebraic approach to derivation of high-resolution schemes for convection-dominated flow problems is introduced. In the first part of the talk, the underlying design principles are explained in the context of a scalar transport equation. The discretization in space is performed using linear or bilinear finite elements. The standard Galerkin approximation is shown to possess unfavorable properties which are responsible for nonphysical oscillations that occur in the vicinity of steep gradients. A nonoscillatory low-order scheme is constructed by adding a discrete diffusion operator designed so as to enforce the algebraic positivity constraint. The resulting error is decomposed into skew-symmetric internodal fluxes, which makes it possible to remove excessive artificial diffusion. A family of fully multidimensional flux limiters is developed building on the flux-corrected transport (FCT) algorithm and total variation diminishing (TVD) schemes. In the case of an implicit time-stepping method, the nonlinearity of the discretized convective term is handled using iterative defect correction. In the second part of the talk, the new methodology is applied to nonlinear PDE systems including the compressible Euler equations, the incompressible Navier-Stokes equations, the k-epsilon turbulence model, and some advanced multiphase flow models. Two- and three-dimensional simulation results are presented to give a flavor of practical applications.
This seminar is easily accessible to persons with disabilities. For more information or for assistance, please contact the Mathematics Department at 743-3500.