Abstract. In numerical computations, unstructured grids can be used easily to fit computational domains involving complex geometries. The method of spacetime conservation element and solution element (CE/SE method) [i,2] can be used in conjunction with unstructured grids. In this paper, the procedure of developing a non-splitting unstructured-triangular-mesh Euler solver based on the CE/SE method is described. Numerical examples involving complex features of shock waves are presented to show that the CE/SE method works very well even for unstructured triangular grids. IntroductionThe CE/SE method is a new numerical framework that was conceived and formulated from basic physical principles to overcome several major limitations of the traditional methods, i.e., finite difference, finite volume, finite element, and spectral methods. It was built from ground zero and aimed to be a simple, coherent, robust, and general-purpose numerical method for accurate and efficient simulation of CFD problems. Various flow problems have previously been solved by using the CE/SE method. For example, some complex physical phenomena that involve shock waves and their reflections, rarefactions, and interactions with bodies or other waves have been successfully simulated using CE/SE Euler solvers based on structured grids(uniform or nonuniform) [3,4]. Previous work in the application of the CE/SE method to computational aeroacoustics [5], chemical reacting flows [6], and dam-break and hydraulic jump [7] has demonstrated the robustness and efficiency of this method.To further broaden the applicability of the CE/SE method, the 2-D CE/SE Euler solver based on an unstructured mesh is developed in this paper. The major difference between the CE/SE Euler solver based on structured and unstructured meshes is described. Two representative numerical results are presented and compared with experimental data to show the per-

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AbetractA quastthree-dimensional rotor/statcr analysis has been developed for blade-teblade flows in turbomachinery. The analysis solves the unsteady M e r OT thin-layer Navier-Stokes equations in a body-fitted coordinate system. It accounts for the effects of rotation, radiw change, and stream-surface thickness. The Baldwirr Lomax eddy-viscosity model is used for turbulent flows. The equations are integrated in time using a four-stage RungeKutta scheme with a constant time step. Results are shown for the first stage of the Space Shuttle Main Engine high pressure fuel turbopump. M e r and Navier-Stokes results are compared on the scaled singleand multi-passage machine. The method is relatively fast and the quastthree-dimensional fmmulation is a p plicable to a wide range of turbomachinery geometries.