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4 results

  • Numerical analysis of modular regularization methods for the BDF2 time discretization of the Navier-Stokes equations∗

  • William Layton, Nathaniel Mays, Monika Neda, Catalin Trenchea
  • Journal:
    ESAIM: Mathematical Modelling and Numerical Analysis / Volume 48 / Issue 3 / May 2014
    Published online by Cambridge University Press:
    01 April 2014, pp. 765-793
    Print publication:
    May 2014

  • We consider an uncoupled, modular regularization algorithm for approximation of the Navier-Stokes equations. The method is: Step 1.1: Advance the NSE one time step, Step 1.1: Regularize to obtain the approximation at the new time level. Previous analysis of this approach has been for specific time stepping methods in Step 1.1 and simple stabilizations in Step 1.1. In this report we extend the mathematical support for uncoupled, modular stabilization to (i) the more complex and better performing BDF2 time discretization in Step 1.1, and (ii) more general (linear or nonlinear) regularization operators in Step 1.1. We give a complete stability analysis, derive conditions on the Step 1.1 regularization operator for which the combination has good stabilization effects, characterize the numerical dissipation induced by Step 1.1, prove an asymptotic error estimate incorporating the numerical error of the method used in Step 1.1 and the regularizations consistency error in Step 1.1 and provide numerical tests.

  • A Hybrid Immersed Interface Method for Driven Stokes Flow in an Elastic Tube

  • Yi Li, Sarah A. Williams, Anita T. Layton
  • Journal:
    Numerical Mathematics: Theory, Methods and Applications / Volume 6 / Issue 4 / November 2013
    Published online by Cambridge University Press:
    28 May 2015, pp. 600-616-
    Print publication:
    November 2013

  • We present a hybrid numerical method for simulating fluid flow through a compliant, closed tube, driven by an internal source and sink. Fluid is assumed to be highly viscous with its motion described by Stokes flow. Model geometry is assumed to be axisymmetric, and the governing equations are implemented in axisymmetric cylindrical coordinates, which capture 3D flow dynamics with only 2D computations. We solve the model equations using a hybrid approach: we decompose the pressure and velocity fields into parts due to the surface forcings and due to the source and sink, with each part handled separately by means of an appropriate method. Because the singularly-supported surface forcings yield an unsmooth solution, that part of the solution is computed using the immersed interface method. Jump conditions are derived for the axisymmetric cylindrical coordinates. The velocity due to the source and sink is calculated along the tubular surface using boundary integrals. Numerical results are presented that indicate second-order accuracy of the method.

  • Failure to Control an Outbreak of Multidrug-Resistant Streptococcus pneumoniae in a Long-Term–Care Facility Emergence and Ongoing Transmission of a Fluoroquinolone-Resistant Strain

  • Rosalind J. Carter, Genevieve Sorenson, Richard Heffernan, Julia A. Kiehlbauch, John S. Kornblum, Robert J. Leggiadro, Lucia J. Nixon, William A. Wertheim, Cynthia G. Whitney, Marcelle Layton, MDRSP Working Group
  • Journal:
    Infection Control & Hospital Epidemiology / Volume 26 / Issue 3 / March 2005
    Published online by Cambridge University Press:
    21 June 2016, pp. 248-255
    Print publication:
    March 2005
  • Objectives:

    To characterize risk factors associated with pneumococcal disease and asymptomatic colonization during an outbreak of multidrug-resistant Streptococcus pneumoniae (MDRSP) among AIDS patients in a long-term–care facility (LTCF), evaluate the efficacy of antimicrobial prophylaxis in eliminating MDRSP colonization, and describe the emergence of fluoroquinolone resistance in the MDRSP outbreak strain.

    Design:

    Epidemiologic investigation based on chart review and characterization of SP strains by antimicrobial susceptibility testing and PFGE and prospective MDRSP surveillance.

    Setting:

    An 80-bed AIDS-care unit in an LTCF.

    Participants:

    Staff and residents on the unit.

    Results:

    From April 1995 through January 1996, 7 cases of MDRSP occurred. A nasopharyngeal (NP) swab survey of all residents (n = 65) and staff (n = 70) detected asymptomatic colonization among 6 residents (9%), but no staff. Isolates were sensitive only to rifampin, ofloxacin, and vancomycin. A 7-day course of rifampin and ofloxacin was given to eliminate colonization among residents: NP swab surveys at 1, 4, and 10 weeks after prophylaxis identified 1 or more colonized residents at each follow-up with isolates showing resistance to one or both treatment drugs. Between 1996 and 1999, an additional 6 patients were diagnosed with fluoroquinolone-resistant (FQ-R) MDRSP infection, with PFGE results demonstrating that the outbreak strain had persisted 3 years after the initial outbreak was recognized.

    Conclusions:

    Chemoprophylaxis likely contributed to the development of a FQ-R outbreak strain that continued to be transmitted in the facility through 1999. Long-term control of future MDRSP outbreaks should rely primarily on vaccination and strict infection control measures.