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NASA NTRS1995

Floating shock fitting via Lagrangian adaptive meshes

In recent work we have formulated a new approach to compressible flow simulation, combining the advantages of shock-fitting and shock-capturing. Using a cell-centered on Roe scheme discretization on unstructured meshes, we warp the mesh while marching to steady state, so that mesh edges align with shocks and other discontinuities. This new algorithm, the Shock-fitting Lagrangian Adaptive Method (SLAM), is, in effect, a reliable shock-capturing algorithm which yields shock-fitted accuracy at convergence.

Vanrosendale, John↗

NASA NTRS1995

Parallel adaptive mesh refinement within the PUMAA3D Project

To enable the solution of large-scale applications on distributed memory architectures, we are designing and implementing parallel algorithms for the fundamental tasks of unstructured mesh computation. In this paper, we discuss efficient algorithms developed for two of these tasks: parallel adaptive mesh refinement and mesh partitioning. The algorithms are discussed in the context of two-dimensional finite element solution on triangular meshes, but are suitable for use with a variety of element types and with h- or p-refinement. Results demonstrating the scalability and efficiency of the refinement algorithm and the quality of the mesh partitioning are presented for several test problems on the Intel DELTA.

Freitag, Lori↗

NASA NTRS1995

Auto-adaptive finite element meshes

Accurate capturing of discontinuities within compressible flow computations is achieved by coupling a suitable solver with an automatic adaptive mesh algorithm for unstructured triangular meshes. The mesh adaptation procedures developed rely on non-hierarchical dynamical local refinement/derefinement techniques, which hence enable structural optimization as well as geometrical optimization. The methods described are applied for a number of the ICASE test cases are particularly interesting for unsteady flow simulations.

Richter, Roland↗

NASA NTRS1995

Adaptive Mesh Refinement in Curvilinear Body-Fitted Grid Systems

To be truly compatible with structured grids, an AMR algorithm should employ a block structure for the refined grids to allow flow solvers to take advantage of the strengths of unstructured grid systems, such as efficient solution algorithms for implicit discretizations and multigrid schemes. One such algorithm, the AMR algorithm of Berger and Colella, has been applied to and adapted for use with body-fitted structured grid systems. Results are presented for a transonic flow over a NACA0012 airfoil (AGARD-03 test case) and a reflection of a shock over a double wedge.

Steinthorsson, Erlendur↗

NASA NTRS1994

Sonic boom predictions using a solution-adaptive full-potential code

The TranAir full-potential code, which utilizes a solution-adaptive, unstructured Cartesian grid, was used to compute near-field pressure signatures of three generic geometries: (1) a cone-cylinder; (2) a low aspect ratio rectangular wing; and (3) a delta-wing/body. Pressure signatures computed by TranAir are extrapolated to near- and midfield distances using a quasilinear extrapolation technique. Results are compared with wind-tunnel data and, where possible, with extrapolated wind-tunnel data and Whitham-method results. In general, extrapolated TranAir data is in good agreement with experimental and Whitham-method pressure signatures, but peak pressures are slightly underpredicted. It is felt that data computed too close to the model caused some of the discrepancies. The flowfield grid structure was also found to be an important issue in obtaining accurate off-body data. Results were encouraging enough to proceed with the application of TranAir to conceptual configurations in support of the NASA high speed research program (HSRP).

Madson, Michael D.↗

NASA NTRS1996

Refinement Of Hexahedral Cells In Euler Flow Computations

Topologically Independent Grid, Euler Refinement (TIGER) computer program solves Euler equations of three-dimensional, unsteady flow of inviscid, compressible fluid by numerical integration on unstructured hexahedral coordinate grid refined where necessary to resolve shocks and other details. Hexahedral cells subdivided, each into eight smaller cells, as needed to refine computational grid in regions of high flow gradients. Grid Interactive Refinement and Flow-Field Examination (GIRAFFE) computer program written in conjunction with TIGER program to display computed flow-field data and to assist researcher in verifying specified boundary conditions and refining grid.

Melton, John E.↗

NASA NTRS1995

Large-scale variations of solar wind elemental composition and charge states with heliospheric latitude

The Solar Wind Ion Composition Spectrometer (SWICS) onboard Ulysses allows determination of the elemental composition of the solar wind and the charge states of all major solar wind ion species. Ulysses left the ecliptic plane in early 1992, crossed the Sun's south polar region in late 1994 and made a fast approach back towards the ecliptic in the first half of 1995. Data from this period were investigated for long-term variations in the solar wind composition. At midlatitudes Ulysses encountered periodically the fast solar wind stream emerging from the south coronal hole. As a consequence, dramatic variations in the charge-states arise, between high charge-states dominating in the current sheet solar wind and low charge states in the coronal hole stream. However, the initial analysis indicates that from midlatitudes onwards, with Ulysses permanently immersed in the coronal hole stream, the charge state and elemental abundance ratios of the major solar wind ion species stayed essentially constant. This implies that the temperature profile in the coronal hole at solar wind source altitudes exhibit no variation with solar latitude. It confirms that the south coronal hole is essentially unstructured down to scale lengths of several degrees in solar latitude.

Woch, J.↗

NASA NTRS1995

Simulating the interaction of the heliosphere with the local interstellar medium: MHD results from a finite volume approach, first bidimensional results

We have designed a full compressible MHD code working on unstructured meshes in order to be able to compute accurately sharp structures embedded in large scale simulations. The code is based on a finite volume method making use of a kinetic flux splitting. A bidimensional version of the code has been used to simulate the interaction of a moving interstellar medium, magnetized or unmagnetized with a rotating and magnetized heliopspheric plasma source. Being aware that these computations are not realistic due to the restriction to two dimensions, we present it to demonstrate the ability of this new code to handle this problem. An axisymetric version, now under development, will be operational in a few months. Ultimately we plan to run a full 3d version.

Chanteur, G.↗

NASA NTRS1996

Global Load Balancing with Parallel Mesh Adaption on Distributed-Memory Systems

Dynamic mesh adaption on unstructured grids is a powerful tool for efficiently computing unsteady problems to resolve solution features of interest. Unfortunately, this causes load imbalance among processors on a parallel machine. This paper describes the parallel implementation of a tetrahedral mesh adaption scheme and a new global load balancing method. A heuristic remapping algorithm is presented that assigns partitions to processors such that the redistribution cost is minimized. Results indicate that the parallel performance of the mesh adaption code depends on the nature of the adaption region and show a 35.5X speedup on 64 processors of an SP2 when 35% of the mesh is randomly adapted. For large-scale scientific computations, our load balancing strategy gives almost a sixfold reduction in solver execution times over non-balanced loads. Furthermore, our heuristic remapper yields processor assignments that are less than 3% off the optimal solutions but requires only 1% of the computational time.

Biswas, Rupak↗

NASA NTRS1996

Practical Aspects of Krylov Subspace Iterative Methods in CFD

Implementation issues associated with the application of Krylov subspace iterative methods, such as Newton-GMRES, are presented within the framework of practical computational fluid dynamic (CFD) applications. This paper categorizes, evaluates, and contrasts the major ingredients (function evaluations, matrix-vector products, and preconditioners) of Newton-GMRES Krylov subspace methods in terms of their effect on the local linear and global nonlinear convergence, memory requirements, and accuracy. The discussion focuses on Newton-GMRES in both a structured multi-zone incompressible Navier-Stokes solver and an unstructured mesh finite-volume Navier-Stokes solver. Approximate versus exact matrix-vector products, effective preconditioners, and other pertinent issues are addressed.

Pulliam, Thomas H.↗

NASA NTRS1996

Computational Study of a McDonnell Douglas Single-Stage-to-Orbit Vehicle Concept for Aerodynamic Analysis

This paper presents the results of a computational flow analysis of the McDonnell Douglas single-stage-to-orbit vehicle concept designated as the 24U. This study was made to determine the aerodynamic characteristics of the vehicle with and without body flaps over an angle of attack range of 20-40 deg. Computations were made at a flight Mach number of 20 at 200,000 ft. altitude with equilibrium air, and a Mach number of 6 with CF4 gas. The software package FELISA (Finite Element Langley imperial College Sawansea Ames) was used for all the computations. The FELISA software consists of unstructured surface and volume grid generators, and inviscid flow solvers with (1) perfect gas option for subsonic, transonic, and low supersonic speeds, and (2) perfect gas, equilibrium air, and CF4 options for hypersonic speeds. The hypersonic flow solvers with equilibrium air and CF4 options were used in the present studies. Results are compared with other computational results and hypersonic CF4 tunnel test data.

Prabhu, Ramadas K.↗

NASA NTRS1996

A Genuinely Two-Dimensional Scheme for the Compressible Euler Equations

We present a new genuinely multidimensional discretization for the compressible Euler equations. It is the only high-resolution scheme known to us where Gauss-Seidel relaxation is stable when applied as a smoother directly to the resulting high-resolution scheme. This allows us to construct a very simple and highly efficient multigrid steady-state solver. The scheme is formulated on triangular (possibly unstructured) meshes.

Sidilkover, David↗

NASA NTRS1996

An Algebraic Multigrid Solver for Navier-Stokes Problems in the Discrete Second-Order Approximation

An algebraic multigrid scheme is presented for solving the discrete Navier-Stokes equations to second-order accuracy using the defect-correction method. Solutions have been obtained for problems involving both structured and unstructured meshes, with the resolution and resolution grading controlled by global and local mesh refinements. The solver is efficient and robust to the extent that no underrelaxation of variables has been required to ensure convergence, but rates of convergence can be improved with small amounts of underrelaxation of the velocity-pressure coupling. Provided that the computational mesh can resolve the flow field, convergence characteristics are almost mesh independent. Rates of convergence actually improve with refinement, asymptotically approaching mesh independent values. For extremely coarse meshes where dispersive truncation errors would be expected to prevent convergence (or even induce divergence), solutions can still be obtained by using explicit underrelaxation in the iterative cycle.

Webster, R.↗

NASA NTRS1996

Global Load Balancing with Parallel Mesh Adaption on Distributed-Memory Systems

Dynamic mesh adaptation on unstructured grids is a powerful tool for efficiently computing unsteady problems to resolve solution features of interest. Unfortunately, this causes load inbalances among processors on a parallel machine. This paper described the parallel implementation of a tetrahedral mesh adaption scheme and a new global load balancing method. A heuristic remapping algorithm is presented that assigns partitions to processors such that the redistribution coast is minimized. Results indicate that the parallel performance of the mesh adaption code depends on the nature of the adaption region and show a 35.5X speedup on 64 processors of an SP2 when 35 percent of the mesh is randomly adapted. For large scale scientific computations, our load balancing strategy gives an almost sixfold reduction in solver execution times over non-balanced loads. Furthermore, our heuristic remappier yields processor assignments that are less than 3 percent of the optimal solutions, but requires only 1 percent of the computational time.

Biswas, Rupak↗

NASA NTRS1996

Research in Parallel Algorithms and Software for Computational Aerosciences

Phase 1 is complete for the development of a computational fluid dynamics CFD) parallel code with automatic grid generation and adaptation for the Euler analysis of flow over complex geometries. SPLITFLOW, an unstructured Cartesian grid code developed at Lockheed Martin Tactical Aircraft Systems, has been modified for a distributed memory/massively parallel computing environment. The parallel code is operational on an SGI network, Cray J90 and C90 vector machines, SGI Power Challenge, and Cray T3D and IBM SP2 massively parallel machines. Parallel Virtual Machine (PVM) is the message passing protocol for portability to various architectures. A domain decomposition technique was developed which enforces dynamic load balancing to improve solution speed and memory requirements. A host/node algorithm distributes the tasks. The solver parallelizes very well, and scales with the number of processors. Partially parallelized and non-parallelized tasks consume most of the wall clock time in a very fine grain environment. Timing comparisons on a Cray C90 demonstrate that Parallel SPLITFLOW runs 2.4 times faster on 8 processors than its non-parallel counterpart autotasked over 8 processors.

Domel, Neal D.↗

NASA NTRS1996

Flows in Pinned Arrays Simulating Brush Seals

Flows through idealized pin arrays were investigated using an unstructured grid finite difference model and the simplified Ergun model to predict leakage flows and pressure drops in brush seals. The models are in good agreement in the laminar region with departures in the laminar-turbulent transition region defined by the simplified Ergun model. No local disturbances in the velocity or pressure fields, symptomatic of turbulence were found in the numerical results. The simplified model failed to predict the pressure drop of a 32-pin anisotropic array. Transitional and anisotropic behavior requires

Hendricks, R.C.↗

NASA NTRS1997

Sensitivity Analysis and Optimization of Aerodynamic Configurations with Blend Surfaces

A novel (geometrical) parametrization procedure using solutions to a suitably chosen fourth order partial differential equation is used to define a class of airplane configurations. Inclusive in this definition are surface grids, volume grids, and grid sensitivity. The general airplane configuration has wing, fuselage, vertical tail and horizontal tail. The design variables are incorporated into the boundary conditions, and the solution is expressed as a Fourier series. The fuselage has circular cross section, and the radius is an algebraic function of four design parameters and an independent computational variable. Volume grids are obtained through an application of the Control Point Form method. A graphic interface software is developed which dynamically changes the surface of the airplane configuration with the change in input design variable. The software is made user friendly and is targeted towards the initial conceptual development of any aerodynamic configurations. Grid sensitivity with respect to surface design parameters and aerodynamic sensitivity coefficients based on potential flow is obtained using an Automatic Differentiation precompiler software tool ADIFOR. Aerodynamic shape optimization of the complete aircraft with twenty four design variables is performed. Unstructured and structured volume grids and Euler solutions are obtained with standard software to demonstrate the feasibility of the new surface definition.

Thomas, A. M.↗

NASA NTRS1996

Optimal and robust control of transition

Optimal and robust control theories are used to determine feedback control rules that effectively stabilize a linearly unstable flow in a plane channel. Wall transpiration (unsteady blowing/suction) with zero net mass flux is used as the control. Control algorithms are considered that depend both on full flowfield information and on estimates of that flowfield based on wall skin-friction measurements only. The development of these control algorithms accounts for modeling errors and measurement noise in a rigorous fashion; these disturbances are considered in both a structured (Gaussian) and unstructured ('worst case') sense. The performance of these algorithms is analyzed in terms of the eigenmodes of the resulting controlled systems, and the sensitivity of individual eigenmodes to both control and observation is quantified.

Bewley, T. R.↗