High-Order Accurate Incompressible Navier-Stokes Solver Based on Vorticity-Velocity Formulation for Orthogonal Curvilinear Grids

Shirzad Hosseinverdi, Hermann F. Fasel

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations

Abstract

The development of a high-order accurate incompressible Navier-Stokes solver based on the vorticity-velocity formulation for orthogonal curvilinear grids is presented and discussed. The solver is written in Fortran 90, and it is parallelized using a hybrid MPI-OpenMP strategy. State-of-the-art numerical algorithms have been incorporated that are especially designed for direct numerical simulations of transitional and turbulent flows. Towards this end, sixorder split and central compact-difference discretizations are employed for the computation of spatial derivatives in the streamwise and wall-normal directions together with a pseudo spectral treatment of the spanwise direction. The governing equations are integrated in time using a strong stability preserving form of the explicit four-stage Runge–Kutta scheme. A highly efficient, high-order accurate Poisson solver, based on a combination of the fourth-order compact finite-difference scheme and a multiscale multigrid method, was developed for solving the (steady) convection-diffusion type equation with variable coefficients for the velocity Poisson equations that result from the vorticity-velocity formulation of the Navier-Stokes equations. An efficient approach is employed that guarantees the divergence-free condition for the velocity and vorticity fields. In addition, a new hybrid approach for generating structured grids with high orthogonality and smoothness, while achieving a desired wall-normal distance required for turbulent boundary layers, is implemented. In this strategy, orthogonal grids are generated first by solving a set of Poisson equations, then the grids are modified by using the orthogonality constraint and a general form of Cauchy–Riemann relations for conformal mapping. In the present paper, results obtained from the new Navier-Stokes solver are compared with benchmark solutions for the flow past a circular cylinder. Furthermore, the new solver was employed for a three-dimensional direct numerical simulation of the uncontrolled flow for a modified NACA 643-618 airfoil at a chord Reynolds number of '4 = 200: And zero angle of attack.

Original languageEnglish (US)
Title of host publicationAIAA Aviation and Aeronautics Forum and Exposition, AIAA AVIATION Forum 2021
PublisherAmerican Institute of Aeronautics and Astronautics Inc, AIAA
ISBN (Print)9781624106101
DOIs
StatePublished - 2021
Externally publishedYes
EventAIAA Aviation and Aeronautics Forum and Exposition, AIAA AVIATION Forum 2021 - Virtual, Online
Duration: Aug 2 2021Aug 6 2021

Publication series

NameAIAA Aviation and Aeronautics Forum and Exposition, AIAA AVIATION Forum 2021

Conference

ConferenceAIAA Aviation and Aeronautics Forum and Exposition, AIAA AVIATION Forum 2021
CityVirtual, Online
Period8/2/218/6/21

ASJC Scopus subject areas

  • Aerospace Engineering
  • Energy Engineering and Power Technology
  • Nuclear Energy and Engineering

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