TY - GEN
T1 - High-Order Accurate Incompressible Navier-Stokes Solver Based on Vorticity-Velocity Formulation for Orthogonal Curvilinear Grids
AU - Hosseinverdi, Shirzad
AU - Fasel, Hermann F.
N1 - Funding Information:
This work was supported by the Air Force Office of Scientific Research (AFOSR) under grant number FA9550-19-1- 0174, with Dr. Gregg Abate serving as the program manager. Computer time for numerical simulations was provided by the University of Arizona High Performance Computing center.
Funding Information:
This work was supported by the Air Force Office of Scientific Research (AFOSR) under grant number FA9550-19-1-0174, with Dr. Gregg Abate serving as the program manager. Computer time for numerical simulations was provided by the University of Arizona High Performance Computing center.
Publisher Copyright:
© 2021, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
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U2 - 10.2514/6.2021-2741
DO - 10.2514/6.2021-2741
M3 - Conference contribution
AN - SCOPUS:85123585335
SN - 9781624106101
T3 - AIAA Aviation and Aeronautics Forum and Exposition, AIAA AVIATION Forum 2021
BT - AIAA Aviation and Aeronautics Forum and Exposition, AIAA AVIATION Forum 2021
PB - American Institute of Aeronautics and Astronautics Inc, AIAA
T2 - AIAA Aviation and Aeronautics Forum and Exposition, AIAA AVIATION Forum 2021
Y2 - 2 August 2021 through 6 August 2021
ER -