DRAFT: NEXT GENERATION EXASCALE CAPABLE MULTIPHASE SOLVER WITH TRILINOS

A framework is developed to integrate the existing MFiX (Multiphase Flow with Interphase eXchanges) flow solver with state-of-the-art linear equation solver packages in Trilinos. The integrated solver is tested on various flow problems. The performance of the solver is evaluated on fluidized bed problems and observed that the integrated flow solver performs better compared to the actual solver. INTRODUCTION Multiphase flow systems have found diverse applications in fluid engineering, micro fluidics and bio-fluids in recent endeavors[1][2][3]. In this regard accurate models of multiphase systems have become a need of the day, as has been shown in various literatures. Past work have put in considerable effort in building semi-analytical models of multiphase flow, for example in heterogeneous permeable media[4], in carbondioxide sequestration[5], multiphase heat transfer applications[6], soil characteristic investigation[7]. A considerable development in solving fluidized bed problems from a theoretical point of view have been noticed in recent literature owing to a multitude of fluidized bed experiments performed over the years[8][9][10][11][12][[13] in terms of gas extraction, bio-mass air steam gasification and many more. Robust numerical models have been developed in order to study these processes in[8] where a discrete particle simulation has been performed on a 2-D fluidized bed or in [14] where a numerical model to study cohesive powder behavior has been developed. Cluster patterns in circulating fluidized beds has been studied with a comparison between a discrete particle simulation and two-fluid model in [15]. Discrete particle simulation have found application in bubble and slug formation in [16] where a hard sphere approach has been adopted where as multiscale modeling strategies can also be seen in [17] . In each of these applications one has to solve the Navier Stokes equation in multiphase systems using some numerical techniques as has been reported in[18] where a lattice bolzmann model has been used and in several other literatures that has numerically modeled the Navier Stoke’s equation based on various algorithms such as phase field modeling [19], fronttracking method[20] and fictitious domain approach[21]. In these applications MFiX have provided legacy codes developed in FORTRAN for a very long time to facilitate research in multiphase system. MFiX [22] has capabilities to model these complex multi-physics systems providing sub-routines to solve these large fluid engineering problems on massively parallel computers, using efficient data decomposition techniques and linear and non-linear solvers such as GMRES, Conjugate Gradient etc. Over the years this particular open source library have become an industry standard to solve multiphase fluid mechanics problems such as the fluidized bed reactor problem[23][24][25] combustion problems [26] core-annulus flow problems[27] and many more. However, as we go on increasing the size of the problem, especially in case of a 3-D multiphase problem, the efficiency of the linear and especially the non-linear solvers tends to decrease thus creating a need for more sophisticated and faster state-of-the-art solvers. Sandia National Labs in the recent years, have developed a state-of-theart library Trilinos[28] equipped with an object oriented framework enabling generic programming with faster and efficient solvers thus paving way to true exascale computing(10 floating point operations per second). The framework for this library has been developed in C++ and thus has an object oriented structure and allows inherent parallelism