Numerical Solution of Three-Dimensional Unsteady Viscous Flows

Abstract

Abstract : In many fluid dynamics problems, the flows are three-dimensional, unsteady and turbulent. Flow past submarine configurations, flow through marine propellers and turbomachinery are examples of such flows. Numerical procedures for accurate and efficient computations of such flows are presently not possible due to mixed elliptic-parabolic nature of the governing equations. Indeed, methods for 3-D incompressible flows lag behind 3-D compressible flows by several years. Until accurate and efficient methods for 3-D incompressible, unsteady flows become available, it will be possible to attempt challenging problems such as first principles based direct simulations of turbulent flow over marine vehicles. The long term objective of the present effort is the development of solution techniques for direct numerical simulation of unsteady 3-D incompressible turbulent flows. The kinetic aspects of this problem are governed by a set of parabolic partial differential equations, which may be efficiently integrated by a variety of time marching schemes. The kinematic aspects of this flow such as the relationship between velocity and vorticity, and the relationship between velocity and pressure are governed by elliptic partial differential equations, which can be solved at any instance in time, only by iterative techniques. Direct and/or large eddy simulation of turbulent flows over submarine configurations, turbomachinery, pumps, ducts and other configurations of interest to the U.S. Navy require efficient solution methods for solving the governing equations.