University of Illinois Urbana-Champaign

A high-order Legendre-WENO numerical scheme for the non-conservative kernel density equations modeling particle-laden flows

Smith, Timothy Andrew

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SMITH-DISSERTATION-2019.pdf

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https://hdl.handle.net/2142/106183

Description

Title
A high-order Legendre-WENO numerical scheme for the non-conservative kernel density equations modeling particle-laden flows
Author(s)
Smith, Timothy Andrew
Issue Date
2019-11-22
Director of Research (if dissertation) or Advisor (if thesis)
Pantano, Carlos
Doctoral Committee Chair(s)
Fischer, Paul
Committee Member(s)
  • Ewoldt, Randy
  • Bodony, Daniel
Department of Study
Mechanical Sci & Engineering
Discipline
Theoretical & Applied Mechans
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Date of Ingest
2020-03-02T21:58:08Z
Keyword(s)
  • dispersed flows
  • essentially non-oscillatory
  • finite volume
Abstract
A numerical scheme is developed to integrate the kernel density equations for the particle phase of disperse flows. The kernel density equations arise from least squares minimization of the approximation of the position-velocity phase-space particle distribution by a sum of kernel density functions. For concreteness in this work, Gaussian kernel density functions are used in approximating the particle distribution. The resulting kernel density equations form a non-conservative, hyperbolic system of PDE’s. The basic numerical scheme is a Roe method that has been generalized to non-conservative systems. The kernel density equations can become weakly hyperbolic; in this case an asymptotic expansion is introduced and singular terms are handled analytically. High-order spatial accuracy is achieved using a novel hybrid essentially non-oscillatory scheme with a Legendre basis. A standard WENO scheme is used by default, and a nonlinear mapping is introduced when needed to enforce physically relevant bounds in the solution, especially in areas of particle depletion. The strong stability preserving RK3 scheme is used to obtain high temporal accuracy. The new scheme has been applied to direct numerical simulation of particles in homogeneous turbulence.
Graduation Semester
2019-12
Type of Resource
text
Permalink
http://hdl.handle.net/2142/106183
Copyright and License Information
Copyright 2019 Timothy Andrew Smith

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Dissertations and Theses - Mechanical Science and Engineering