A three-dimensional spectral algorithm for simulations of transition and turbulence

A spectral algorithm for simulating three dimensional, incompressible, parallel shear flows is described. It applies to the channel, to the parallel boundary layer, and to other shear flows with one wall bounded and two periodic directions. Representative applications to the channel and to the heated boundary layer are presented

Guidance, flight mechanics and trajectory optimization. Volume 6 - The N-body problem and special perturbation techniques

Analytical formulations and numerical integration methods for many body problem and special perturbative technique

Surface-surface intersection with validated error bounds

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering; and, (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2005.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 97-100).This thesis presents a robust method for tracing intersection curve segments between continuous rational parametric surfaces, typically rational polynomial parametric surface patches. Using a validated ordinary differential equation (ODE) system solver based on interval arithmetic, we obtain a continuous, validated upper bound for the intersection curve segment in the parametric space of each surface. Application of the validated ODE solver in the context of eliminating the pathological phenomena of straying and looping is discussed. We develop a method to achieve a continuous gap-free boundary with a definite numerically verified upper bound for the intersection curve error in parameter space. This bound in parametric space is further mapped to an upper bound for the intersection curve error in 3D model space, denoted as model space error, which assists in defining robust boundary representation models of complex three-dimensional solids. In addition, we also discuss a method for controlling this model space error so that it takes values below a predefined threshold (tolerance). Application of the above method to various examples is further demonstrated.by Harish Mukundan.S.M

Lagrangian tracking of the cavitation bubble

In this thesis, the dynamics of an isolated cavitation bubble submerged in a steady flow is studied numerically. A Lagrangian-Eulerian approach is considered, in which properties of the fluid are computed first by means of Eulerian methods (in this study the commercial CFD software Ansys Fluent 19 was used) and the trajectory of the bubble is then computed in a Lagrangian fashion, i.e. the bubble is considered as a small particle moving relative to the fluid, due to the effect of several forces depending on fluid's pressure field, fluid's velocity field and bubble's radius. Bubble's radius dynamics, modeled by Rayleigh-Plesset equation, has a big influence on its kinetics, so a special attention is given to it. Two study cases are considered. The first one, motivated by acoustic cavitation is concerned with the response of the bubble's radius in a static flow under the influence of an oscillatory pressure field, the second one studies the trajectory of the bubble submerged in a fluid passing by a Venturi tube and a sharp-edged orifice plate.In this thesis, the dynamics of an isolated cavitation bubble submerged in a steady flow is studied numerically. A Lagrangian-Eulerian approach is considered, in which properties of the fluid are computed first by means of Eulerian methods (in this study the commercial CFD software Ansys Fluent 19 was used) and the trajectory of the bubble is then computed in a Lagrangian fashion, i.e. the bubble is considered as a small particle moving relative to the fluid, due to the effect of several forces depending on fluid's pressure field, fluid's velocity field and bubble's radius. Bubble's radius dynamics, modeled by Rayleigh-Plesset equation, has a big influence on its kinetics, so a special attention is given to it. Two study cases are considered. The first one, motivated by acoustic cavitation is concerned with the response of the bubble's radius in a static flow under the influence of an oscillatory pressure field, the second one studies the trajectory of the bubble submerged in a fluid passing by a Venturi tube and a sharp-edged orifice plate.