Development of Reduced-order Meshless Solutions of Three-dimensional Navier Sokes Transport Phenomena
Author: Daniel Benjamin Work
Publisher:
Published: 2006
Total Pages:
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DOWNLOAD EBOOKAbstract: 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.