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          Resources/ServicesACMD Seminar: On convergence analysis of an IEQ-based numerical scheme for hydrodynamical Q-tensor model

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Yukun Yue*Ph.D. Student, Mathematical Sciences, Carnegie Mellon University*

Tuesday, May 16, 2023, 3:00-4:00 PM ET (1:00-2:00 PM MT)

**A video of this talk will be made available to NIST staff in the Math channel on NISTube, which is accessible from the NIST internal home page. It will be taken down from NISTube after 12 months at which point it can be requested by emailing the ACMD Seminar Chair.**

**Abstract:** This talk will focus on a numerical approach based on the Invariant Quadratization Method(IEQ) to find solutions for a hydrodynamical system. We start with a toy model concerned with the parabolic type Q-tensor equations, numerical design schemes that keep energy dissipation law discretely, and analyze its properties. Then we present a convergence analysis of an unconditional energy-stable first-order semi-discrete numerical method intended for the hydrodynamic Q-tensor model. This model couples a Navier-Stokes system for the fluid flows and a parabolic type Q-tensor system governing the nematic liquid crystal director fields. We prove the stability properties of the scheme and show convergence to weak solutions of the coupled fluid crystal system. We will also be able to give you a brief overview of recent results on the existence and regularity of Beris-Edwards systems and other related models.

**Bio:**Yukun Yue is a fifth-year graduate student at Carnegie Mellon University working in partial differential equations and numerical analysis. He is working under the supervision of Prof. Franziska Weber and Prof. Noel Walkington.

**Host:** Ryan Evans / Tony Kearsley

**Note**: This talk will be recorded to provide access to NIST staff and associates who could not be present to the time of the seminar. The recording will be made available in the Math channel on NISTube, which is accessible only on the NIST internal network. This recording could be released to the public through a Freedom of Information Act (FOIA) request. Do not discuss or visually present any sensitive (CUI/PII/BII) material. Ensure that no inappropriate material or any minors are contained within the background of any recording. (To facilitate this, we request that cameras of attendees are muted except when asking questions.)

**Note**: Visitors from outside NIST must contact Lochi Orr; at least 24 hours in advance.
  Mathematics and statistics

    
    Contacts
      
        

Ryan Evans
    
      
  ryan.evans@nist.gov
  (301) 975-5456

  Zachary Grey
    
      
  zachary.grey@nist.gov
  (303) 497-5920

  Lochi Orr
    
      
  lochi.orr@nist.gov
  (410) 598-6986

Created February 9, 2023, Updated May 19, 2023
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