Kopriva The investigator develops and implements a flexible multidomain spectral collocation method for the solution of time dependent compressible flows. Two particular areas are emphasized. The first is the study of time accurate interface conditions for the Euler gas-dynamics equations and the advective terms of the Navier-Stokes equations. The second is the development of a non-conforming interface condition for the Navier-Stokes equations that allows flexible local refinement of the subdomains in viscous flows. The result of this work is a means to solve accurately problems such as the interaction of free-stream turbulence and bodies in a supersonic flow, with or without viscous effects. This project is part of an effort to develop high accuracy numerical methods, suitable for use on high performance computers, to solve high speed fluid flow problems. Efficient, high accuracy numerical methods are needed to compute detailed solutions of complex fluid flows at a reasonable cost. Increasingly, detailed solutions, and the understanding of the flow physics that follows from them, are required by industry for engineering design applications.
