Development of Reduced-Order Meshless Solutions of Three-Dimensional Navier Stokes Transport Phenomena
Advisor:McGee, Oliver G. III
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Publisher:The Ohio State University
Series/Report no.:The Ohio State University. Department of Civil and Environmental Engineering and Geodetic Science Honors Theses; 2006
Emerging meshless technologies are very promising for numerically solving Euler and Navier-Stokes transport systems in one-, two-, and three-dimensions (3-D). The Reduced-Order Meshless (ROM) technique developed in this work is applicable to a wide array of transport physics systems (i.e., fluid flow, heat transfer, gas dynamics, internal combustion flow and chemical reactions, and solid-liquid mixture flow) with various types of boundary and initial conditions. Such applications to be benchmarked in this work include one- and two-dimensional advection, and two- and three-dimensional convection-diffusion problems (Burgers’ equation). Computational solutions to these boundary-value problems will be demonstrated using the ROM approach and the predicted solutions will be posted against the Meshless Local Petrov-Galerkin (MLPG) method and exact solutions to these problems when they exist. Extensions to 3-D phenomenology will be attempted based on the conclusions obtained from computational studies to establish the existence, smoothness, and boundedness of 3-D Navier-Stokes transport systems. An approximated benchmark solution of the Navier-Stokes equations is also developed in this work using a linearized perturbation analysis. The classical paper on gas turbine throughflow, Three Dimensional Flows in Turbomachines (Marble, 1964), outlines this procedure for approximation, and produces solutions for a class of axisymmetric problems. An investigation into the behavior of these solutions uncovered a series of inconsistencies in the paper, which are outlined in detail and corrected when known to be in error.
This research was supported by The Ohio State University College of Engineering.
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