A Fast Pressure-Correction Method for Incompressible Flows Over Curved Walls

Speaker: Antonino Ferrante, Department of Aeronautics and Astronautics, University of Washington
February 21, 2019

Presentation

Abstract

We have developed a new pressure-correction method for simulating incompressible flows over curved walls. We chose the orthogonal formulation of the Navier-Stokes equations in curvilinear coordinates vs the generalized curvilinear coordinates because the computational cost of advancing the numerical solution of the governing equations in time is substantially reduced as the orthogonal formulation does not contain cross-derivatives in the advection, diffusion, Laplacian, and gradient operators. As a result, the numerical stencils of the finite difference approximations to these operators mirror that of the Cartesian formulation. This also allows us to develop an FFT-based Poisson solver for pressure, called FastPoc, for the cases where the grid is uniform in one spatial direction: surfaces of revolution (e.g., axisymmetric ramps) and surfaces of linear translation (e.g., curved ramps, and curved bumps). Further, we have developed an explicit, three-stage, third-order accurate Runge-Kutta based projection method to advance the velocity field in time which requires solving the Poisson equation for pressure only once per time step. Thus, given that the computational mesh satisfies the property of orthogonality, our numerical method can simulate flows over curved wall surfaces with second-order accuracy in space and third-order accuracy in time. The new FFT-based Poisson solver, FastPoc, is thirty to sixty times faster than multigrid (depending on the tolerance set for multigrid), and the new flow solver, called FastRK3, is overall four to seven times faster when we used FastPoc instead of multigrid. Verification and validation test-cases and applications of separated flows will be presented. FastRK3 is applicable to DNS, LES and RANS.

Biography

Antonino Ferrante is an Associate Professor of the William E. Boeing Department of Aeronautics & Astronautics at the University of Washington (UW), Seattle, where he leads the Computational Fluid Mechanics Lab. In 1996, he received his B.S. in Aeronautical Engineering from Universita’ di Napoli, Federico II (Italy). In 1997, he received his M.S. in Aeronautics & Astronautics and the Belgian Government Prize from the von Karman Institute. In 2004, he received his Ph.D. in Mechanical and Aerospace Engineering from the University of California, Irvine, where he continued his research as Postdoctoral Scholar until 2007. From 2007 to 2009, he was Postdoctoral Scholar at the Graduate Aeronautical Laboratories of the California Institute of Technology (GALCIT). In 2009, he joined the UW as Assistant Professor where was tenured in 2015. Ferrante is recipient of the NSF CAREER Award (2011). Ferrante’s research is mainly focused on understanding the physical mechanisms and modeling of complex flows, e.g. multiphase and wall-bounded turbulent flows, by developing new computational methodologies for DNS and LES apt to performing simulations on high-performance supercomputers.