High Performance Solvers for Fluid Flow Simulations
Thursday, April 28, 3:00 – 4:00 PM
157 Benedum Hall
ABSTRACT: We present high performance solvers for two classes of flow problems: (1) those with smooth solutions but in complex geometries, and (2) those with a challenging combination of nonlinear discontinuities and smooth but complex structures. We focus on efficient numerical methods that display minimum computation and communication costs for a given engineering accuracy on the contemporary parallel computing platforms.
For the first class, we consider both incompressible and compressible flows governed by the Navier-Stokes equations in complex geometries. For the unsteady incompressible Navier-Stokes equations, we present an efficient parallel solver based on high-order discontinuous Galerkin (DG) methods using triangular and tetrahedral meshes in two and three space dimensions, respectively. In the context of a semi-explicit temporal discretization, we present an algorithm with compact stencil sizes for all discrete equations yielding minimum computation and communication costs. We show the accuracy, efficiency and the competitiveness of our algorithm in solving three dimensional test problems. For the compressible Navier-Stokes equations, we present scalable multigrid algorithms for systems arising from high-order DG discretizations on unstructured meshes. The algorithms are based on coupling both functional and geometric multigrid methods which are used as preconditioners to a Newton -Krylov solver.
For problems with a mix of discontinuities and smooth flow structures- a well-known example being the Richtmyer-Meshkov instabilities- challenges are twofold: the sharp and non-oscillatory resolution of shocks and other discontinuous features, and accurate propagation of the small smooth structures. We introduce a hybrid strategy in which the regions of discontinuities are treated using high-order weighted essentially non-oscillatory (WENO) finite difference methods and regions containing smooth solutions are discretized using a newly developed Fourier continuation method. Our Fourier-based approach enables high-order and non-oscillatory solution of system of nonlinear conservation laws, which enjoys essentially dispersionless, spectral character away from shocks. For the simulation of an early stage of two-dimensional Richtmyer-Meshkov instability in two space dimensions, we show that our hybrid solver is fourfold faster than the alternative based on the pure WENO method. The efficiency gain for three dimensional version of the problem with transition and turbulence mixing is expected to be much higher.
We finally highlight our ongoing and future research directions including the three-dimensional implementations of our hybrid solver for the Navier-Stokes equations on large scale parallel computers and on many core graphic processors, direct numerical simulations of high-speed multi-material flows, computational aeroacoustics, and simulations of physiological flows.
BIOGRAPHY: Khosro Shahbazi is currently a postdoctoral research associate in the Division of Applied Mathematics, Brown University. Before joining Brown, he held another postdoctoral position in the Computational Fluid Dynamics laboratory of Mechanical Engineering Department at the University of Wyoming. He obtained his PhD and Master’s degrees in Mechanical Engineering from the University of Toronto, and a Bachelor of Science degree in Mechanical Engineering from Sharif University of Technology. His general research area is computational fluid dynamics including discontinuous Galerkin solvers for compressible and incompressible Navier-Stokes equations in complex geometries, hybrid Fourier-WENO methods for conservation laws with discontinuous and smooth solutions, and multigrid solvers for nonlinear systems arising from discretizations of the Navier-Stokes equations.
Faculty Host: Peyman Givi