Flow Simulation Using Generalized Static and Dynamic Grids

Abstract

A new approach is presented for a e ow simulation system using generalized grids. In a generalized grid, the physical domain of interest is decomposed into cells with an arbitrary number of edges or faces. The grid can be of structured, unstructured, or hanging node type or an arbitrary combination of the types. A cell-face-based data structure is used to storethegrid information. A e ow simulation system is developed forgeneralized gridsthat can handle static and dynamic grids. The full Navier ‐Stokes equations, in the integral form, are taken as the relations that govern the e uid e ow. A cell-centered e nite volume scheme is developed for solving these governing equations. The numerical e ux across the cell faces is evaluated by an upwind scheme based on Roe’ s approximate Riemann solver. A higher-order scheme is formulated by utilizing Taylor’ s series expansion and Green’ s theorem. Limiter functions are used to preserve monotonocity. The skin-friction coefe cient is used to evaluate the accuracy of the limiterfunctions. Thegeneralized minimalresidualmethod isutilized tosolvethesparselinearsystem ofequations resulting from thelinearization of the e ux vectors. TheSpalart ‐Allmaras one-equation turbulence model has been implemented for the generalized grids and is used to evaluate the turbulent viscosity. For dynamically moving bodies, the equations of classical mechanics are used to predict the trajectory based on the external aerodynamic and body forces. A variety of computational examples are presented to demonstratethe wide rangeof applications, and the results are compared with experimental data whenever available.