American Institute of Aeronautics and Astronautics 1 Development of High-Order Realizable Finite-Volume Schemes for Quadrature-Based Moment Method V. Vikas 1 and Z. J. Wang 2 Department of Aerospace Engineering, Iowa State University, Ames, IA, 50011 A. Passalacqua 3 and R. O. Fox 4 Department of Chemical and Biological Engineering, Iowa State University, Ames, IA, 50011 Kinetic equations containing terms for spatial transport, gravity, fluid drag and particle- particle collisions can be used to model dilute gas-particle flows. However, the enormity of independent variables makes direct numerical simulation of these equations almost impossible for practical problems. A viable alternative is to reformulate the problem in terms of moments of velocity distribution. Recently, a quadrature-based moment method was derived by Fox for approximating solutions to kinetic equation for arbitrary Knudsen number. Fox also described 1 st - and 2 nd -order finite-volume schemes for solving the equations. The success of the new method is based on a moment-inversion algorithm that is used to calculate non-negative weights and abscissas from moments. The moment-inversion algorithm does not work if the moments are non-realizable, meaning they do not correspond to a distribution function. Not all the finite-volume schemes lead to realizable moments. Desjardins et al. showed that realizability is guaranteed with the 1 st -order finite-volume scheme, but at the expense of excess numerical diffusion. In the present work, the non- realizability of the standard 2 nd -order finite-volume scheme is demonstrated and a generalized idea for the development of high-order realizable finite-volume schemes for quadrature-based moment methods is presented. This marks a significant improvement in the accuracy of solutions using the quadrature-based moment method as the use of 1 st -order scheme to guarantee realizability is no longer a limitation. I. Introduction AS-PARTICLE flows are ubiquitous in aerospace, mechanical, chemical and many other engineering disciplines. One finds such flows in automotive and aircraft engines, snow and sand storms, helicopter brownout phenomenon, and many other critical situations. The understanding of the flow characteristics is crucial in improving the performance of gas-turbine engines, or mitigating the harmful effects of helicopter brownout. The numerical simulation of gas-particle flows is complicated by the wide range of phenomena that can occur in real applications [1, 2, 3, 4, 5, 6, 7, 8, 9]. In the case of helicopter brownout, the number of particles is so large that it is impossible to track the motion of each one. In addition, these particles may have very different sizes and shapes. It is well known that the traditional multiphase flow solvers based on the volume-of-fluid (VOF) method [15, 16, 17] or the level-set method [18, 19, 20 , 21] are hopeless for such applications, and Lagrangian particle tracking methods [22, 23, 24] are also very inefficient. In many other applications, physical complexities may include particle breaking, merging (or coalescence), and evaporation [25]. It appears, the only method that can handle these physical complexities is a kinetic-based method that solves for the moments of the velocity distribution function. Fox [5, 10, 11, 12, 13] developed a quadrature-based moment method (QMOM) to solve for a set of moments of the velocity distribution function. The success of this method is based on a moment-inversion algorithm that is used to calculate non-negative weights and abscissas from moments. The moment-inversion algorithm does not work if 1 Graduate Research Assistant, Department of Aerospace Engineering, 2271 Howe Hall, AIAA Member. 2 Professor of Aerospace Engineering, 2271 Howe Hall, Associate Fellow of AIAA. 3 Postdoctoral Research Fellow, Department of Chemical and Biological Engineering, 2114 Sweeney Hall 4 Professor of Chemical and Biological Engineering, 2114 Sweeney Hall. . G 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition 4 - 7 January 2010, Orlando, Florida AIAA 2010-1080 Copyright © 2010 by V. Vikas, Z. J. Wang, A. Passalacqua, R. O. Fox. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.