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A differential equation is obtained for the smoothed “overall” pressure distribution around a herringbone-grooved, gas-lubricated journal bearing operating with a variable film thickness. The equation is based on the limiting case of an idealized bearing for which the number of grooves approaches an infinite number. A numerical solution to the differential equation is obtained valid for small eccentricities. This solution includes the case where the journal is undergoing steady circular whirl. In addition to the usual plain bearing parameters L/D, Λ, and whirl speed ratio ω3/(ω1 + ω2), the behavior of a grooved bearing also depends on four additional parameters: The groove angle β, the relative groove width α, the relative groove depth H0, and a compressibility number, Λs, which is based on the relative speed between the grooved and smooth members of the bearing. Results are presented showing bearing radial force and attitude angle as functions of β, α, H0, Λs, Λ, and whirl speed ratio.

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-

A nontraditional numerical method for solving conservation laws is being developed. The new method is designed from a physicist's perspective, i.e., its development is based more on physics than numerics. Even though it uses only the simplest approximation techniques, a 2D time-marching Euler solver developed recently using the new method is capable of generating nearly perfect solutions for a 2D shock reflection problem used by Helen Yee and others. Moreover, a recent application of this solver to computational aeroacoustics (CAA) problems reveals that: (i) accuracy of its results is comparable to that of a 6th order compact difference scheme even though nominally the current solver is only of 2nd-order accuracy; (ii) generally, the non-reflecting boundary condition can be implemented in a simple way without involving characteristic variables; and (iii) most importantly, the current solver is capable of handling both continuous and discontinuous flows very well and thus provides a unique numerical tool for solving those flow problems where the interactions between sound waves and shocks are important, such as the noise field around a supersonic over-or under-expansion jet. *Graduate student, Student member AIAA. tProfessor, Associate Fellow AIAA.