| Advanced time-marching algorithms are designed to compute steady-state solutions of the Euler equations. These algorithms include the implicit ADI and the explicit Runge-Kutta multi-stage schemes that utilize central differencing in space. Additional implicit schemes such as the full implicit, diagonal ADI, and various LU schemes are also explored. The computations are made on a body-fitted, generalized coordinate system.;The present work proceeds by first studying the implicit ADI and explicit Runge-Kutta schemes on one- and two-dimensional, incompressible and compressible problems. The results show that the implicit scheme is overwhelmingly superior to the explicit scheme in one dimension, is only slightly more efficient than the explicit scheme in two dimensions, and is less efficient than the explicit scheme in three dimensions.;The Euler equations are hyperbolic or can be made hyperbolic in time. It is well-known that the system of equations governing the inviscid compressible flows is hyperbolic. The inviscid incompressible system of equations is also made hyperbolic by the concept of pseudocompressibility. These two systems are then solved in a generalized fashion.;The boundary conditions for these hyperbolic systems are implemented based on the theory of characteristics. Substitutional boundary-condition procedures known as the explicit boundary procedures are presented as well for comparisons.;The calculations for three-dimensional incompressible Euler equations and their stability analysis are presented in the last chapter. As an example of engineering applications, flows passing a propeller behind a ship hull are calculated. |
