Scholarly Works, Interdisciplinary Center for Applied Mathematics (ICAM)

Permanent URI for this collection

https://hdl.handle.net/10919/47108

Browse

Browsing Scholarly Works, Interdisciplinary Center for Applied Mathematics (ICAM) by Author "Interdisciplinary Center for Applied Mathematics (ICAM)"

Now showing 1 - 4 of 4
  • Thumbnail Image
    Comment on "A numerical study of periodic disturbances on two-layer Couette flow" [Phys. Fluids 10, 3056 (1998)]
    Renardy, Yuriko Y.; Li, Jie (AIP Publishing, 1999-10)
    The flow of fluids with different viscosities, subjected to an interfacial perturbation, can lead to fingering and migration...
  • Thumbnail Image
    Model Reduction for DAEs with an Application to Flow Control
    Borggaard, Jeffrey T.; Gugercin, Serkan (Springer-Verlag Berlin, 2015-01-01)
  • Thumbnail Image
    A new wavelet family based on second-order LTI-systems
    Abuhamdia, Tariq; Taheri, Saied; Burns, John A. (SAGE, 2016)
    In this paper, a new family of wavelets derived from the underdamped response of second-order Linear-Time-Invariant (LTI) systems is introduced. The most important criteria for a function or signal to be a wavelet is the ability to recover the original signal back from its continuous wavelet transform. We show that it is possible to recover back the original signal once the Second-Order Underdamped LTI (SOULTI) wavelet is applied to decompose the signal. It is found that the SOULTI wavelet transform of a signal satisfies a linear differential equation called the reconstructing differential equation, which is closely related to the differential equation that produces the wavelet. Moreover, a time-frequency resolution is defined based on two different approaches. The new transform has useful properties; a direct relation between the scale and the frequency, unique transform formulas that can be easily obtained for most elementary signals such as unit step, sinusoids, polynomials, and decaying harmonic signals, and linear relations between the wavelet transform of signals and the wavelet transform of their derivatives and integrals. The results obtained are presented with analytical and numerical examples. Signals with constant harmonics and signals with time-varying frequencies are analyzed, and their evolutionary spectrum is obtained. Contour mapping of the transform in the time-scale and the time-frequency domains clearly detects the change of the frequency content of the analyzed signals with respect to time. The results are compared with other wavelets results and with the short-time fourier analysis spectrograms. At the end, we propose the method of reverse wavelet transform to mitigate the edge effect.
  • Thumbnail Image
    A numerical study of periodic disturbances on two-layer Couette flaw
    Li, Jie; Renardy, Yuriko Y.; Renardy, Michael J. (AIP Publishing, 1998-12)
    The flow of two viscous liquids is investigated numerically with a volume of fluid scheme. The scheme incorporates a semi-implicit Stokes solver to enable computations at low Reynolds numbers, and a second-order velocity interpolation. The code is validated against linear theory for the stability of two-layer Couette flow, and weakly nonlinear theory for a Hopf bifurcation. Examples of long-time wave saturation are shown. The formation of fingers for relatively small initial amplitudes as well as larger amplitudes are presented in two and three dimensions as initial-value problems. Fluids of different viscosity and density are considered, with an emphasis on the effect of the viscosity difference. Results at low Reynolds numbers show elongated fingers in two dimensions that break in three dimensions to form drops, while different topological changes take place at higher Reynolds numbers. (C) 1998 American Institute of Physics. [S1070-6631(98)00612-6].