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

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Theoretical & Applied Mechans

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2020

Author dc:creator

• Smith, Timothy Andrew

Contributors dc:contributor

• Pantano, Carlos
• Fischer, Paul
• Ewoldt, Randy
• Bodony, Daniel

• dispersed flows
• essentially non-oscillatory
• finite volume

Statement dc:rights

• Copyright 2019 Timothy Andrew Smith

Language dc:language

en

Handle dc:identifier

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

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/106183