Chunhua Sheng

An investigation of parallel implicit solution algorithms for incompressible flows on multielement unstructured topologies

The primary objective of this study is to develop an efficient incompressible flow solver capable of performing viscous, high Reynolds number flow simulations for complex geometries using general unstructured grids. This parallel flow solver is demonstrated for large-scale meshes with viscous sublayer resolution (p+ N 1) and approximately lo6 points or more. Primary issues addressed in this work are 1) treatment of the connectivity between subdomain interfaces, 2) proper definition of the iteration hierarchy, and 3) methods for coupling of subdomains. The present parallel unstructured viscous flow solver is based on a domain decomposition for concurrent solution within subdomains assigned to multiple processors. The solution algorithm employs iterative solution of the implicit approximation, with coupling between subdomains according to several schemes that are a primary focus of the study. MPI message passing is used for interprocessor communication. Applications include 1) a full-scale ship hull, 2) the SUBOFF model hull with stern appendages, and 3) a fully-configured high-lift transport. Introduction Implicit algorithms for flows on unstructured grids have been investigated extensively by a variety of authors [l] [2] [3] [4]. However, implicit algorithms are much more difficult to) parallelize, because of their inherent global dependencies. As such, the parallelization of unstructured Euler solvers [5] [S] [7] and Navier-Stokes solvers [S] [9] [lo] have been previously investigated. This work seeks to examine a relaxation-type algorithm *Research Assistant I, Member ASME *Research Engineer I, Member AIAA SProfessor, Member AIAA §Distinguished Professor, Member AIAA Copyright@2000 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. in depth to provide insight concerning issues that arise in the parallelization of implicit solution algorithms on unstructured topologies. In general, the parallelization of an existing validated flow solver should satisfy several constraints. First and most important; the accuracy of the overall numerical scheme must not be compromised; i.e., the solution computed in parallel must have a oneto-one correspondence with the solution computed in serial mode. Also, the code must be efficient irrits use of computational resources. This characteristic is measured in terms of memory usage and scalability, as well as the fact that the parallel code should degenerate to the serial version if only one processor is available. Finally, the consequences of the inevitable domain decomposition should not seriously compromise the convergence rate of the iterative,algorithm. The present parallel unstructured viscous flow solver is based on a coarse-grained domain decomposition for concurrent solution within subdomains assigned to multiple processors. The solver also has the capability to map an arbitrary number of subdomains to a physical processor; thus, some flexibility is available to leverage available memory should memory resources be scarce. The present solution algorithm is related to several previous efforts. The approach is an evolution of the implicit flow solver and code of Anderson et al. [ll] [12] [13]; the solver developed in this series of works demonstrates 3D, implicit, high Reynolds number solution capability. Also, this work follows the unstructured multiblock solver of Sheng and Whitfield [14] [15] which uses the same core solver but employs a multiblock technique to reduce memory consumption by 70%. These studies are in turn related to the multiblock structured solvers originating from Taylor, Whitfield, and Sheng [16] [17] [18]. Elements of the present approach to parallel solution are related to the parallel multiblock structured grid solver of Pankajakshan and Briley [19].

Efficient Mesh Deformation Using Radial Basis Functions on Unstructured Meshes

An efficient mesh-deformation algorithm has been developed within an unstructured-grid computational-fluid-dynamics solver framework based on a radial-basis-function volume-interpolation method. The data-transfer problem between fluid and structural solvers is simplified here using a beam structural representation, with surface mesh deformation given directly via translational and rotational deformations. The volume mesh deformation is then performed using a radial-basis-function method, which requires no mesh-connectivity information and allows straightforward implementation in an unstructured computational-fluid-dynamics solver in a parallel fashion. However, the pure method is impractical for large meshes, and a novel “greedy” data-reduction algorithm is presented here to select an optimum reduced set of surface mesh points, which makes the mesh-deformation method extremely efficient. Several two- and three-dimensional test cases are presented to validate the algorithm performance, including a realisti...

Multigrid algorithm for three-dimensional incompressible high-Reynolds number turbulent flows

A robust multigrid algorithm is presented for solving three-dimensional incompressible high-Reynolds number turbulent flows on high aspect ratio grids. The artificial compressibility form of the Navier-Stokes equations is discretized in a cell-centered finite volume form on a time-dependent curvilinear coordinate system, and the so-called discretized Newton-relaxation scheme is used as the iterative procedure for the solution of the system of equations. A nonlinear multigrid scheme (full approximation scheme [FAS]) is applied to accelerate the convergence of the time-dependent equations to a steady state. Two methods for constructing the coarse grid operator, the Galerkin coarse grid approximation and the discrete coarse grid approximation have also been investigated and incorporated into the FAS. A new procedure, called implicit correction smoothing that leads to high efficiency of the multigrid scheme by allowing large Courant-Friedrichs-Lewy numbers, is introduced in this work. Numerical solutions of high-Reynolds number turbulent flows for practical engineering problems are presented to illustrate the efficiency and accuracy of the current multigrid algorithm.

Multiblock approach for calculating incompressible fluid flows on unstructured grids

A multiblock approach is presented for solving two-dimensional incompressible turbulent flows on unstructured grids. The artificial compressibility form of the governing equations is solved by a vertex-centered, finite-volume implicit scheme which uses a backward Euler time discretization. Point Gauss-Seidel relaxations are used to solve the linear system of equations at each time step. This work introduces a multiblock strategy to the solution procedure, which greatly improves the efficiency of the algorithm by significantly reducing the memory requirements while not increasing the CPU time. Results presented in this work shows that the current multiblock algorithm requires 70% less memory than the single block algorithm.

A preconditioned method for rotating flows at arbitrary mach number

An improved preconditioning is proposed for viscous flow computations in rotating and nonrotating frames at arbitrary Mach numbers. The key to the current method is the use of both free stream Mach number and rotating Mach number to construct a preconditioning matrix, which is applied to the compressible governing equations written in terms of primitive variables. A Fourier analysis is conducted that reveals the efficacy of the modified preconditioning. Numerical approximations for the convective and diffusive fluxes are detailed based on the preconditioned system of equations. A set of boundary conditions using characteristic variables are described for internal and external flow computations. Numerical validations are performed on four realistic viscous flows in both fixed and rotating frames. The results indicated that the modified preconditioning has a superior performance compared to the original method to predict flows from extremely low to supersonic Mach numbers.

Three-Dimensional Incompressible Navier-Stokes Flow Computations about Complete Configurations Using a Multiblock Unstructured Grid Approach

A multiblock unstructured grid approach is presented for solving three-dimensional incompressible inviscid and viscous turbulent flows about complete configurations. The artificial compressibility form of the governing equations is solved by a node-based, finite volume implicit scheme which uses a backward Euler time discretization. Point Gauss-Seidel relaxations are used to solve the linear system of equations at each time step. This work employs a multiblock strategy to the solution procedure, which greatly improves the efficiency of the algorithm by significantly reducing the memory requirements by a factor of 5 over the single-grid algorithm while maintaining a similar convergence behavior. The numerical accuracy of solutions is assessed by comparing with the experimental data for a submarine with stem appendages and a high-lift configuration.

LARGE-SCALE SIMULATIONS FOR MANEUVERING SUBMARINES AND PROPULSORS *

This paper describes an emerging computational capability for physics—based flow simulation and maneuvering predictions for appended submarine/propulsor geometries. The solution methodology for the unsteady Reynolds-averaged Navier—Stokes equations is summarized, including the transition of this capability from single—processor to scalable parallel computing. The current status of validation efforts for this methodology is discussed, including comparisons for appended—hull force and moment coefficients andpropulsor thrust and torque coefficients. Results are given from several simulations related to maneuvering of appended submarines with rotating propulsors. This capability will enable new complex simulations in computational naval hydrodynamics that can support the submarine design process as well as provide understanding leading to improved safety margins in submarines undergoing complicated maneuvers. To illustrate the impact of the scalable parallel code, a submarine maneuver requiring 3 million grid points and covering a distance of five hull lengths can be run in less than two days on 80 T3Eprocessors, as compared with over four months on a single processor.

VERIFICATION AND VALIDATION OF FORCES GENERATED BY AN UNSTRUCTURED FLOW SOLVER

A primary goal of computational fluid dynamics is the accurate prediction of the forces and moments on ships, aircraft, turbines and similar complicated geometries, especially when viscous effects are important. By using unstructured grids, much of the detail of these complicated geometries can be captured with the grid and hopefully with the solution generated by the flow solver. As unstructured flow solvers mature, the forces predicted by them should become more accurate. For unsteady maneuvering cases, the accuracy of the forces and moments is critical for accurate predictions of the location and orientation of the body in motion, because errors tend to accumulate and grow as the maneuver proceeds. Accurate simulations of maneuvers have been obtained with the structured flow solver UNCLE. However, its unstructured equivalent, U 2 NCLE, has produced anomalies that are not fully understood. In an effort to isolate and identify potential inaccuracies in the unstructured flow solver, the flow solver has undergone a thorough re-evaluation of each component and the interactions between the components. Particular attention has been paid to the effects of discretization error. The unstructured flow solver uses mixed element types to resolve the boundary, so the discretization error for the non-simplical element types was investigated. Several methods to discretize the viscous terms have been investigated, to determine whether they are linearity preserving. A new inviscid variable extrapolation method (Unstructured MUSCL) has been developed, which has a smaller discretization error than the previous method. Finally, effects of asymmetries in the grid and in the solution algorithm have been investigated.

Computational Aerodynamic Analysis of Offshore Upwind and Downwind Turbines

Aerodynamic interactions of the model NREL 5 MW offshore horizontal axis wind turbines (HAWT) are investigated using a high-fidelity computational fluid dynamics (CFD) analysis. Four wind turbine configurations are considered; three-bladed upwind and downwind and two-bladed upwind and downwind configurations, which operate at two different rotor speeds of 12.1 and 16 RPM. In the present study, both steady and unsteady aerodynamic loads, such as the rotor torque, blade hub bending moment, and base the tower bending moment of the tower, are evaluated in detail to provide overall assessment of different wind turbine configurations. Aerodynamic interactions between the rotor and tower are analyzed, including the rotor wake development downstream. The computational analysis provides insight into aerodynamic performance of the upwind and downwind, two- and three-bladed horizontal axis wind turbines.

A Preconditioned Arbitrary Mach Number Scheme Applied to Rotating Machinery

It is well known that the compressible flow equations face difficulties at low Mach numbers due to the large ratio of the acoustic and convective time scales, which leads to an illconditioned system when solving low-speed or incompressible flows. The time-dependent system of the Euler and Navier-Stokes equations exhibits stiffness that is strongly dependent on the Mach number and the Reynolds number. In this regard, Briley et al. (Briley et al., 1983) first introduced the preconditioning method using a simple constant preconditioning matrix added to a non-dimensional form of the isoenergetic equations. This generally improved convergence for a test case with reference Mach number Mr = 0.05 using the ADI factorization scheme in primitive variables. However, when applying this preconditioning to rotating flows in either fixed or rotating frame formulation, Sheng, et al. (Sheng & Wang, 2006; Wang & Sheng, 2005) observed the instability of the scheme due to the large variation of rotating speeds across the computational domain. Furthermore, it was found that the convergence of the preconditioned equations is sensitive to the selection of the reference Mach number, especially in rotating flows with a wide range of radial speeds and physical time scales. It was later proved using the Fourier footprint analysis (Wang & Sheng, 2005) that the eigensystem of the compressible governing equations can be significantly affected by both free stream and rotating speeds in rotating flows. A modified preconditioning scheme was thus proposed (Sheng & Wang, 2006; Wang & Sheng, 2005), in which both the global reference Mach number and the rotating Mach number are considered in the formulation of the preconditioning matrix. In general, this modified preconditioning scheme has improved the convergence and accuracy of compressible flows in subsonic, transonic and supersonic Mach number regimes. In this study, the modified preconditioning is further investigated and validated for predicting incompressible viscous flows in rotating machinery, such as a marine propeller P5168. One of the most important characters for marine propellers is the cavitation observed in high speed flows, which is of vital importance because of the damage of metal surfaces and degradation of performance of lifting surfaces. It is also a source of high-frequency noise in connection with acoustic detection of ships and submarines. Cavitation would take place when the local pressure drops to the vapor pressure. Therefore, accurate prediction of the velocity and pressure field is essential for understanding the process of cavitation inception and improving the hydrodynamic performance of the marine propeller. Since the condition for cavitation inception is related to the tip-vortex location, strength, convection, cavitation