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Full-Text Articles in Mathematics

Jet Noise Reduction: A Fresh Start, Christopher K. Tam, Fang Q. Hu Jan 2023

Jet Noise Reduction: A Fresh Start, Christopher K. Tam, Fang Q. Hu

Mathematics & Statistics Faculty Publications

Attempts to reduce jet noise began some 70 years ago. In the literature, there have been many publications written on this topic. By now, it is common knowledge that jet noise consists of a number of components. They possess different spectral and radiation characteristics and are generated by different mechanisms. It appears then that one may aim at the suppression of the noise of a single component instead of trying to reduce jet noise overall. The objective of the present project is to reduce large turbulence structures noise. It is the most dominant noise component radiating in the downstream direction. …


Stable And Convergent Difference Schemes For Weakly Singular Convolution Integrals, Wesley Davis, Richard D. Noren Jan 2021

Stable And Convergent Difference Schemes For Weakly Singular Convolution Integrals, Wesley Davis, Richard D. Noren

Mathematics & Statistics Faculty Publications

We obtain new numerical schemes for weakly singular integrals of convolution type called Caputo fractional order integrals using Taylor and fractional Taylor series expansions and grouping terms in a novel manner. A fractional Taylor series expansion argument is utilized to provide fractional-order approximations for functions with minimal regularity. The resulting schemes allow for the approximation of functions in Cγ [0, T], where 0 < γ <= 5. A mild invertibility criterion is provided for the implicit schemes. Consistency and stability are proven separately for the whole-number-order approximations and the fractional-order approximations. The rate of convergence in the time variable is shown …


Numerical Modeling Of Submicron Particles For Acoustic Concentration In Gaseous Flow, Jizhou Liu, Xiaodong Li, Fang Q. Hu Jan 2020

Numerical Modeling Of Submicron Particles For Acoustic Concentration In Gaseous Flow, Jizhou Liu, Xiaodong Li, Fang Q. Hu

Mathematics & Statistics Faculty Publications

This paper intends to explore the rationality and feasibility of modeling dispersed submicron particles in air by a kinetic-based method called the unified gas-kinetic scheme (UGKS) and apply it to the simulation of particle concentration under a transverse standing wave. A gas-particle coupling scheme is proposed where the gas phase is modeled by the two-dimensional linearized Euler equations (LEE) and, through the analogous behavior between the rarefied gas molecules and the air-suspended particles, a modified UGKS is adopted to estimate the particle dynamics. The Stokes' drag force and the acoustic radiation force applied on particles are accounted for by introducing …


Numerical Simulation For A Rising Bubble Interacting With A Solid Wall: Impact, Bounce, And Thin Film Dynamics, Changjuan Zhang, Jie Li, Li-Shi Luo, Tiezheng Qian Jan 2018

Numerical Simulation For A Rising Bubble Interacting With A Solid Wall: Impact, Bounce, And Thin Film Dynamics, Changjuan Zhang, Jie Li, Li-Shi Luo, Tiezheng Qian

Mathematics & Statistics Faculty Publications

Using an arbitrary Lagrangian-Eulerian method on an adaptive moving unstructured mesh, we carry out numerical simulations for a rising bubble interacting with a solid wall. Driven by the buoyancy force, the axisymmetric bubble rises in a viscous liquid toward a horizontal wall, with impact on and possible bounce from the wall. First, our simulation is quantitatively validated through a detailed comparison between numerical results and experimental data. We then investigate the bubble dynamics which exhibits four different behaviors depending on the competition among the inertial, viscous, gravitational, and capillary forces. A phase diagram for bubble dynamics has been produced using …