Combining the monotonic Lagrangian grid with direct simulation Monte Carlo; a new approach for low-density flows

Accurate and affordable numerical methods play a vital role in the design and development of practical hypersonic vehicles. Existing analysis tools that provide aerothermodynamic properties for the high-altitude portion of a hypersonic vehicle's flight path are capable but expensive. This dissertation describes the development, validation, and application of a new tool aimed at expanding the practical analysis envelope of high Knudsen number flows.; The present work is the first to combine the Direct Simulation Monte Carlo (DSMC) methodology with a Lagrangian data structure, the Monotonic Lagrangian Grid (MLG). The result is a numerical approach for transition regime flows that automatically adjusts grid resolution to time-varying densities in the flow. The DSMC method is a direct particle simulation technique widely used in predicting flows of dilute gases. The MLG algorithm combines an efficient tracking and sorting scheme with a monotonic data structure for indexing and storing physical attributes of the moving particles. Monotonicity features of the MLG ensure that particles close in physical space are stored in adjacent array locations so that particle interactions may be restricted to a 'template' of near neighbors. The MLG templates provide a time-varying grid network that automatically adapts to local number densities within the flowfield. The majority of MLG and DSMC logic is inherently parallel, enabling extremely efficient application on parallel computer architectures.; Computational advantages and disadvantages of this new MLG-based implementation are demonstrated by a series of test problems. The effects of MLG sorting parameters on computational performance are investigated, and results from sensitivity studies on grid size and template size are presented. The combination of DSMC and MLG results in a new tool with several significant benefits, including an automatically adapting grid, improved prediction accuracy for a given grid size, and decreased computational requirements through efficient parallelization. Extensions to massively parallel computers offer significant advances in what can be computed.