Hybridizable Discontinuous Galerkin Projection Methods For Navier–Stokes And Boussinesq Equations
Advanced Search
Select up to three search categories and corresponding keywords using the fields to the right. Refer to the Help section for more detailed instructions.

Search our Collections & Repository

For very narrow results

When looking for a specific result

Best used for discovery & interchangable words

Recommended to be used in conjunction with other fields

Dates

to

Document Data
Library
People
Clear All
Clear All

For additional assistance using the Custom Query please check out our Help Page

i

Hybridizable Discontinuous Galerkin Projection Methods For Navier–Stokes And Boussinesq Equations

Filetype[PDF-5.62 MB]


Select the Download button to view the document
This document is over 5mb in size and cannot be previewed
Details You May Also Like

Details:

  • Journal Title:
    Journal of Computational Physics
  • Personal Author:
  • NOAA Program & Office:
    Sea Grant
  • Sea Grant Program:
    MIT (MIT Sea Grant)
  • Description:
    Schemes for the incompressible Navier–Stokes and Boussinesq equations are formulated and derived combining the novel Hybridizable Discontinuous Galerkin (HDG) method, a projection method, and Implicit–Explicit Runge–Kutta (IMEX-RK) time-integration schemes. We employ an incremental pressure correction and develop the corresponding HDG finite element discretization including consistent edge-space fluxes for the velocity predictor and pressure correction. We then derive the proper forms of the element-local and HDG edge-space final corrections for both velocity and pressure, including the HDG rotational correction. We also find and explain a consistency relation between the HDG stability parameters of the pressure correction and velocity predictor. We discuss and illustrate the effects of the time-splitting error. We then detail how to incorporate the HDG projection method time-split within standard IMEX-RK time-stepping schemes. Our high-order HDG projection schemes are implemented for arbitrary, mixed-element unstructured grids, with both straight-sided and curved meshes. In particular, we provide a quadrature-free integration method for a nodal basis that is consistent with the HDG method. To prevent numerical oscillations, we develop a selective nodal limiting approach. Its applications show that it can stabilize high-order schemes while retaining high-order accuracy in regions where the solution is sufficiently smooth. We perform spatial and temporal convergence studies to evaluate the properties of our integration and selective limiting schemes and to verify that our solvers are properly formulated and implemented. To complete these studies and to illustrate a range of properties for our new schemes, we employ an unsteady tracer advection benchmark, a manufactured solution for the steady diffusion and Stokes equations, and a standard lock-exchange Boussinesq problem.
  • Keywords:
  • Source:
    Journal of Computational Physics 306: 390-421
  • DOI:
  • Document Type:
    Journal Article
  • Rights Information:
    Accepted Manuscript
  • Compliance:
    Library
  • Main Document Checksum:
  • Download URL:
  • File Type:

Supporting Files

  • No Additional Files
More +

You May Also Like

Checkout today's featured content at repository.library.noaa.gov

Version 3.27.1