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

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

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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