A high-order incompressible flow solver with WENO

Authors:
Ju Zhang;Thomas L. Jackson
Affiliations:
Computational Science and Engineering, University of Illinois at Urbana-Champaign, 3243 Digital Computer Laboratory, 1304 West Springfield Avenue, Urbana, IL 61801, USA;Computational Science and Engineering, University of Illinois at Urbana-Champaign, 3243 Digital Computer Laboratory, 1304 West Springfield Avenue, Urbana, IL 61801, USA
Venue:
Journal of Computational Physics
Year:
2009

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Abstract

A numerical method for solving the incompressible Navier-Stokes equations with a 5th-order weighted essentially non-oscillatory (WENO) scheme is presented. The method is not based on artificial compressibility and is free of tunable parameters such as the artificial compressibility parameter. The method makes use of the fractional-step method in conjunction with the low-dissipation and low-dispersion Runge-Kutta (LDDRK) scheme to improve temporal accuracy of the scheme. The use of a WENO scheme makes it possible to obtain stable solutions for discontinuous initial data and resolve difficult applications with strong shear such as Kelvin-Helmholtz instability or turbulence. Good convergence rate is established for the velocity variables and numerical solutions of the present method compare well with exact solutions and other numerical results.