Kidambi Sreenivas

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].

DOE's Effort to Reduce Truck Aerodynamic Drag Through Joint Experiments and Computations

Class 8 tractor-trailers are responsible for 11-12% of the total US consumption of petroleum. Overcoming aero drag represents 65% of energy expenditure at highway speeds. Most of the drag results from pressure differences and reducing highway speeds is very effective. The goal is to reduce aerodynamic drag by 25% which would translate to 12% improved fuel economy or 4,200 million gal/year. Objectives are: (1) In support of DOEs mission, provide guidance to industry in the reduction of aerodynamic drag; (2) To shorten and improve design process, establish a database of experimental, computational, and conceptual design information; (3) Demonstrate new drag-reduction techniques; and (4) Get devices on the road. Some accomplishments are: (1) Concepts developed/tested that exceeded 25% drag reduction goal; (2) Insight and guidelines for drag reduction provided to industry through computations and experiments; (3) Joined with industry in getting devices on the road and providing design concepts through virtual modeling and testing; and (4) International recognition achieved through open documentation and database.

Aerosol Propagation in an Urban Environment

The objective of this study is to demonstrate the capability of an arbitrary mach number algorithm to predict aerosol propagation in an urban environment. A preconditioned approach is applied to an unstructured mesh to determine accurately the highly unsteady turbulent flow field about the urban setting. DES modifications are implemented into a hybrid k − , k − ω turbulence model and evaluated. A scalar transport model is used to release and to advect the aerosol agent through the urban landscape. Comparisons between RANS and DES turbulence modeling are presented for multiple agent release scenarios.

A Generalized, Unstructured Interpolative Interface Method for Rotor-Stator Interactions

A generalized interpolative interface is developed to provide interdomain and intradomain coupling between multielement unstructured grids, including those that require highly stretched anisotropic meshes. The method centers around an extruded interpolative interface that does not require matched unstructured grids on the corresponding surfaces. In the context of rotor/stator interactions, this generalized interpolative interface is utilized between the rotor and stator sections, so that each can be solved within its own frame of reference. The interpolative interface supports the sliding of the rotor relative to the stator, such that variables are transmitted from one domain to the other accordingly. Coupling between the rotor and stator sections is accomplished via solution interpolations from mesh extrusions constructed from the interpolative interface. Further, the same interpolative interface technology is utilized to implement an axisymmetric boundary condition that also does not require matching surface grids on the periodic surfaces. Given that these axisymmetric boundary conditions intersect with the rotor/stator interface, special consideration is required in these areas, and the techniques applied are explained in this work in detail. This interpolative interface scheme is tested and applied via a performance mapping of the SDT2-R4 rotor/stator configuration as documented in Hughes, 1 simulated as a 2 rotor/5 stator passage. Results for this configuration are compared to available experimental data as well as full-wheel simulations of the same, in order to determine the eect of the axisymmetric interfaces on the overall solution. Overall agreement with experimental performance mappings is excellent.

Unstructured Nonlinear Free Surface Flow Solutions: Validation and Verification

A nonlinear free surface solution methodology is incorporated within an existing three-dimensional, unstructured Navier-Stokes solver, . This portable, parallel solver uses a node-based finite volume method to solve the incompressible Reynolds-averaged NavierStokes equations on mixed element high-aspect ratio grids, includes several turbulence models to simulate the affects of turbulence within the boundary layer, and has the capability to simulate flow through rotating propellers accurately. To obtain a nonlinear free surface, the kinematic free surface equation is solved at each time level via a finite element implementation, valid on both triangles and quadrilaterals; after several time steps (approximately 200), the grid is moved to match the free surface elevations while conforming to the geometry. Robust grid movement is achieved by using a three-dimensional extension of Farhat’s torsional spring analogy. Validation studies include a grid refinement for the free surface on a circle based on a prescribed velocity field, and of flow around a submerged NACA0012 hydrofoil. For the NACA0012 hydrofoil, for the viscous and inviscid Wigley hull and for the DTMB Model 5415 series hull, wave profiles along the hull are compared against available experimental results as well as numerical results from a more mature structured nonlinear free surface code UNCLE.

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.

Investigation of Two Analytical Wake Models Using Data From Wind Farms

A code ‘Wind Farm Optimization using a Genetic Algorithm’ (referred as WFOG) was developed for optimizing the placement of wind turbines in large wind farms. It utilizes an analytical wake model (by Jensen et al.) to minimize the cost per unit power for the wind farm. In this study, a new wake model by Ishihara et al. is tested in WFOG. The wake model takes into account the effect of atmospheric turbulence and rotor generated turbulence on the wake recovery. Results of the two wake models are compared with data from Horns Rev and Nysted wind farm. The maximum error (Horns Rev wind farm) for Ishihara’s wake model was 7% as compared to 15% for Jensen’s wake model. The optimal results obtained in earlier studies (using Jensen’s wake model) are compared to wind farm configurations obtained for Ishihara’s wake model. The optimization is carried out for the simplest wind regime: Constant wind speed and fixed wind direction.Copyright

Aerodynamic Simulation of Heavy Trucks with Rotating Wheels

Aerodynamic simulations were carried out for the Ground Transportation System model, a 1/8 th scale tractor-trailer model, that was tested in the NASA Ames 7’x10’ tunnel. The computed forces and pressure coefficients are compared to experiment. Detailed comparisons are also carried out for the wake in the symmetry plane of the model. A DES version of the two equation k-e/k-ω ω ω ω hybrid turbulence model is shown to predict the single vortex structure observed in the experiment. Simulations are also carried out for an isolated rotating wheel and the results are compared to experiment data. A theoretically predicted jet arising at the contact patches was observed computationally with its magnitude matching the theoretical predictions. Representative simulations were also carried out for a tractortrailer model with rotating wheels.

A Generalized Interpolative Interface for Parallel Unstructured Field Solvers

A generalized interpolative interface is developed to provide a coupling between multielement unstructured grids potentially in relative motion, including those that require highly stretched anisotropic meshes. The method centers around an extruded interpolative interface that does not require matched unstructured grids on the corresponding surfaces. The method is also constructed such that is generally applicable to any data that must be transported between the adjacent solution domains; as such, the same mechanism can be used regardless of the underlying governing equations of the field. This feature is utilized in the current work by using dierent sets of governing equations for the presented solutions, as well as using the same interpolative procedure in the process of solving the turbulence models. Mesh extrusions are constructed from the interpolative interface, which allow for closure and the solution of control volumes that lie on the interface. For each extruded point, a corresponding virtual point is created in order to control the exact location at which the client data interpolations are performed. This allows interpolation from locations that are reflective of the physics of the problem. Special procedures, such as utilization of surface projections and parallel boundary layer displacement algorithms, are required for support of highly stretched anisotopic grids commonly used in the resolution of large gradients most common in fluid flow solvers. All algorithms used to extrude the interpolative surface, place virtual points, and interpolate for the client data must be parallelized for compatibility with modern parallel field solvers. To this end, fully general parallel mechanisms are implemented in order to transport data from its native storage to a possibly remote location. Interpolation also requires a parallel unstructured multielement search algorithm, which is a concerted eort by itself, and is the subject of an upcoming paper. This interpolative interface scheme is validated on a ramp immersed in supersonic flow, where the shock passes through the interface; comparisons with the theoretical solution for an oblique shock are excellent. Also, an unsteady pitching airfoil in which the airfoil is pitched with the aid of a surrounding interpolative interface is examined and compared against experimental data and a baseline case where the entire grid is pitched; comparisons here are excellent as well. The NASA SDT2-R4 turbofan stage is also presented as a demonstration of capability of the interpolative interface in real-world problems. Agreement with experimental data for demonstrated case at 100% speed is good.

Turbulence Modeling For Highly Separated Flows

The objective of this study is to investigate the Detached Eddy Simulation (DES) modifications to the hybrid k , k ! (kk! ) turbulence model and the Scale Adaptive Simulation (SAS) modifications to the one-equation k (1k ) turbulence model. Additionally, modifications to the damping functions to the baseline 1k model are presented and validated for a variety of test cases. Further, the Stress-! (S!) Reynolds stress model is tested alongside the 1k and kk! models. A blended dissipation equation is implemented into the S! model and validated for a variety of test cases. A surface-mounted cube is chosen as the primary test case to examine specifically the highly separated wake flow. Multiple grid levels are used to identify the grid requirements necessary for accurate computations with the kk! DES and 1k SAS models.