Parallel Pseudo-spectral Method for Two-phase Flows

INTRODUCTION Flows involving two phases can be found in many industrial applications. Models that can accurately predict the behaviour of these ows in complex physical situations such as turbulent ow with rotation, and unsteady turbulent two-phase ows, are lacking. Numerical simulation of the detailed behaviour of the drops or bubbles in a complex and unsteady turbulent ow can provide a fundamental understanding of the mechanisms involved in such ows, and provide valuable data for the development and validation of new models. Such simulations require the space and time accurate integration of the turbulent ow eld in the two phases and additionally model accurately the eeects due to the interface. Esmaeeli and Tryggvason 1] performed numerical simulations of several buoyant bubbles in two-dimensional periodic domains that show the formation of ow structures much larger than the bubble size, and a continuous increase in energy of the low-wavenumber velocity modes. However, their results are restricted to relatively low-Reynolds-number bubbly ows. Since such simulations are very computationally intensive, higher Reynolds-number bubbly ow simulations could proot from the scalable performance available on parallel arqui-tectures. Pseudo-spectral methods, due to their high accuracy and performance when used in simple domains, and their intrinsic parallelism, can be applied successfully for the simulation of two phase ows in distributed memory computers. In this work we describe a new parallel pseudo-spectral code designed to perform high resolution, space and time accurate simulation of two-phase ows on various current distributed memory architectures. The parallel algorithm explores the intrinsic parallelism of the pseudo-spectral method and it is based on a domain decomposition approach. The remainder of this paper is organized as follows. In the next section we brieey review the governing equations of two-phase bubbly ows. The section that follows details our pseudo-spectral method, based on Fourier expansions. The next section presents the parallel implementation, designed to achieve high performance, while retaining portability across diierent platforms. The following section shows the numerical results for a test case and discusses the parallel performance of the code on several computers. Finally, the paper ends with a summary of the main conclusions of this work.