A generalized difference method for hyperbolic equations on arbitrary grids

Many engineering problems of interest are governed by systems of hyperbolic equations. Among these equations are the Euler equations for inviscid fluid flow, the acoustic equations for aero-acoustic wave propagation, and Maxwell's equations for electromagnetic wave propagation. These different physical problems have been approached from different perspectives in the past despite their mathematical similarities. The result has been the development of computational methods that are applicable only to limited classes of problems.; This thesis addresses the solution of hyperbolic equations in a general way that allows for a more straight forward extension to different systems of governing equations. Adapting this computational method to a new set of governing equations simply requires that information on the physics of the problem be defined in a code object separate from the governing equation solver.; Another issue addressed by this work is the large amount of user time devoted to applying existing computational methods to geometrically complex problems. This thesis addresses this issue by developing a method that is applicable to any grid, structured, unstructured, or completely arbitrary. This computational method is independent of grid node location and connectivity. For solutions of geometrically complex problems, the use of arbitrary types of grids, such as unstructured grids, can be the only practical means of generating a computational solution.; The generalized difference method has been validated for the solution of Maxwell's equations and the Euler equations. The solution of Maxwell's equations represents a test of the numerical accuracy of this method. The solution of the Euler equations represents a test of the application of this method to nonlinear equations. Comparisons have been made for the solution of both systems of governing equations to analytical, experimental, and other computational solutions. Several cases have been computed to demonstrate the versatility of this approach and ease with which it can be applied to the solution of different goveming equations for a range of geometric problems.