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NASA NTRS1996

Research in Parallel Algorithms and Software for Computational Aerosciences

Phase I is complete for the development of a Computational Fluid Dynamics 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 NTRS1997

RIACS

Topics considered include: high-performance computing; cognitive and perceptual prostheses (computational aids designed to leverage human abilities); autonomous systems. Also included: development of a 3D unstructured grid code based on a finite volume formulation and applied to the Navier-stokes equations; Cartesian grid methods for complex geometry; multigrid methods for solving elliptic problems on unstructured grids; algebraic non-overlapping domain decomposition methods for compressible fluid flow problems on unstructured meshes; numerical methods for the compressible navier-stokes equations with application to aerodynamic flows; research in aerodynamic shape optimization; S-HARP: a parallel dynamic spectral partitioner; numerical schemes for the Hamilton-Jacobi and level set equations on triangulated domains; application of high-order shock capturing schemes to direct simulation of turbulence; multicast technology; network testbeds; supercomputer consolidation project.

Oliger, Joseph↗

NASA NTRS1995

A 3D High-Order Unstructured Finite-Volume Algorithm for Solving Maxwell's Equations

A three-dimensional finite-volume algorithm based on arbitrary basis functions for time-dependent problems on general unstructured grids is developed. The method is applied to the time-domain Maxwell equations. Discrete unknowns are volume integrals or cell averages of the electric and magnetic field variables. Spatial terms are converted to surface integrals using the Gauss curl theorem. Polynomial basis functions are introduced in constructing local representations of the fields and evaluating the volume and surface integrals. Electric and magnetic fields are approximated by linear combinations of these basis functions. Unlike other unstructured formulations used in Computational Fluid Dynamics, the new formulation actually does not reconstruct the field variables at each time step. Instead, the spatial terms are calculated in terms of unknowns by precomputing weights at the beginning of the computation as functions of cell geometry and basis functions to retain efficiency. Since no assumption is made for cell geometry, this new formulation is suitable for arbitrarily defined grids, either smooth or unsmooth. However, to facilitate the volume and surface integrations, arbitrary polyhedral cells with polygonal faces are used in constructing grids. Both centered and upwind schemes are formulated. It is shown that conventional schemes (second order in Cartesian grids) are equivalent to the new schemes using first degree polynomials as the basis functions and the midpoint quadrature for the integrations. In the new formulation, higher orders of accuracy are achieved by using higher degree polynomial basis functions. Furthermore, all the surface and volume integrations are carried out exactly. Several model electromagnetic scattering problems are calculated and compared with analytical solutions. Examples are given for cases based on 0th to 3rd degree polynomial basis functions. In all calculations, a centered scheme is applied in the interior, while an upwind matching scheme is employed at material interfaces and the Engquist-Majda non-reflecting boundary condition is implemented at the numerical outer boundaries. The staggered leapfrog scheme and the Runge-Kutta methods are utilized for the time integration. Excellent agreements are found between the numerical and analytical solutions.

Liu, Yen↗

NASA NTRS2011

Cartesian Off-Body Grid Adaption for Viscous Time- Accurate Flow Simulation

An improved solution adaption capability has been implemented in the OVERFLOW overset grid CFD code. Building on the Cartesian off-body approach inherent in OVERFLOW and the original adaptive refinement method developed by Meakin, the new scheme provides for automated creation of multiple levels of finer Cartesian grids. Refinement can be based on the undivided second-difference of the flow solution variables, or on a specific flow quantity such as vorticity. Coupled with load-balancing and an inmemory solution interpolation procedure, the adaption process provides very good performance for time-accurate simulations on parallel compute platforms. A method of using refined, thin body-fitted grids combined with adaption in the off-body grids is presented, which maximizes the part of the domain subject to adaption. Two- and three-dimensional examples are used to illustrate the effectiveness and performance of the adaption scheme.

Buning, Pieter G.↗

NASA NTRS1995

The adaptive, cut-cell Cartesian approach (warts and all)

Solution-adaptive methods based on cutting bodies out of Cartesian grids are gaining popularity now that the ways of circumventing the accuracy problems associated with small cut cells have been developed. Researchers are applying Cartesian-based schemes to a broad class of problems now, and, although there is still development work to be done, it is becoming clearer which problems are best suited to the approach (and which are not). The purpose of this paper is to give a candid assessment, based on applying Cartesian schemes to a variety of problems, of the strengths and weaknesses of the approach as it is currently implemented.

Powell, Kenneth G.↗

NASA NTRS2005

Reduced-Order Modeling of a Heaving Airfoil

A reduced-order model of a flapping airfoil is developed using Proper Orthogonal Decomposition (POD). The proper basis functions, developed from snapshots of full Navier-Stokes simulations, are used for a Galerkin projection of the governing equations. The resulting coupled, nonlinear ordinary di.erential equations have a low dimension because the first few basis members capture most of the energy of the flow. The reduced-order model is used to simulate heaving motions that are both similar to and different from the motion(s) used to generate the basis functions, and the errors in the model are quantified. Several methods are used to generate mode sets that can be used over a range of heaving parameters, including snapshots from one, two, and multiple Navier-Stokes simulations. As snapshots from additional simulations are added to the decomposition, the mode sets become richer and can simulate a wider range of parameter space, at some computational cost. Whereas the POD method is fully applicable in three dimensions, the simulation technique based on a body-fixed and body-fitted grid suffers large overhead when extended to three dimensions. To reduce the overhead, an embedding technique is discussed which embeds the solid wing into a fixed Cartesian grid. The wing, which can now have multiple pieces and also be flexible, is represented by a distribution of body forces. This distribution is determined to give exactly the flow around a flapping wing.

Haj-Hariri, H.↗

NASA NTRS1991

Multi-resolution analysis for ENO schemes

Given an function, u(x), which is represented by its cell-averages in cells which are formed by some unstructured grid, we show how to decompose the function into various scales of variation. This is done by considering a set of nested grids in which the given grid is the finest, and identifying in each locality the coarsest grid in the set from which u(x) can be recovered to a prescribed accuracy. This multi-resolution analysis was applied to essentially non-oscillatory (ENO) schemes in order to advance the solution by one time-step. This is accomplished by decomposing the numerical solution at the beginning of each time-step into levels of resolution, and performing the computation in each locality at the appropriate coarser grid. An efficient algorithm for implementing this program in the 1-D case is presented; this algorithm can be extended to the multi-dimensional case with Cartesian grids.

Harten, Ami↗

NASA NTRS1993

Multi-resolution analysis for ENO schemes

Given a function u(x) which is represented by its cell-averages in cells which are formed by some unstructured grid, we show how to decompose the function into various scales of variation. This is done by considering a set of nested grids in which the given grid is the finest, and identifying in each locality the coarsest grid in the set from which u(x) can be recovered to a prescribed accuracy. We apply this multi-resolution analysis to Essentially Non-oscillatory Schemes (ENO) schemes in order to reduce the number of numerical flux computations which is needed in order to advance the solution by one time-step. This is accomplished by decomposing the numerical solution at the beginning of each time-step into levels of resolution, and performing the computation in each locality at the appropriate coarser grid. We present an efficient algorithm for implementing this program in the one-dimensional case; this algorithm can be extended to the multi-dimensional case with cartesian grids.

Harten, Ami↗

NASA NTRS1998

Visual Methods for Model and Grid Validation

This joint research interchange proposal allowed us to contribute in two directions that are of interest to NASA. These are: (a) data level comparative visualization of experimental and computational fluid flow, and (b) visualization tools for analysis of adaptively refined Cartesian grids.

Pang, Alex↗

NASA NTRS1987

High resolution finite volume methods on arbitrary grids via wave propagation

A generalization of Godunov's method for systems of conservation laws has been developed and analyzed that can be applied with arbitrary time steps on arbitrary grids in one space dimension. Stability for arbitrary time steps is achieved by allowing waves to propagate through more than one mesh cell in a time step. The method is extended here to second order accuracy and to a finite volume method in two space dimensions. This latter method is based on solving one dimensional normal and tangential Riemann problems at cell interfaces and again propagating waves through one or more mesh cells. By avoiding the usual time step restriction of explicit methods, it is possible to use reasonable time steps on irregular grids where the minimum cell area is much smaller than the average cell. Boundary conditions for the Euler equations are discussed and special attention is given to the case of a Cartesian grid cut by an irregular boundary. In this case small grid cells arise only near the boundary, and it is desirable to use a time step appropriate for the regular interior cells. Numerical results in two dimensions show that this can be achieved.

Leveque, Randall J.↗

NASA NTRS1988

High resolution finite volume methods on arbitrary grids via wave propagation

A generalization of Godunov's method for systems of conservation laws has been developed and analyzed that can be applied with arbitrary time steps on arbitrary grids in one space dimension. Stability for arbitrary time steps is achieved by allowing waves to propagate through more than one mesh cell in a time step. The method is extended here to second order accuracy and to a finite volume method in two space dimensions. This latter method is based on solving one dimensional normal and tangential Rieman problems at cell interfaces and again propagating waves through one or more mesh cells. By avoiding the usual time step restriction of explicit methods, it is possible to use reasonable time steps on irregular grids where the minimum cell area is much smaller than the average cell. Boundary conditions for the Euler equations are discussed and special attention is given to the case of a Cartesian grid cut by an irregular boundary. In this case small grid cells arise only near the boundary, and it is desirable to use a time step appropriate for the regular interior cells. Numerical results in two dimensions show that this can be achieved.

Leveque, Randall J.↗

NASA NTRS2004

Topography Modeling in Atmospheric Flows Using the Immersed Boundary Method

Numerical simulation of flow over complex geometry needs accurate and efficient computational methods. Different techniques are available to handle complex geometry. The unstructured grid and multi-block body-fitted grid techniques have been widely adopted for complex geometry in engineering applications. In atmospheric applications, terrain fitted single grid techniques have found common use. Although these are very effective techniques, their implementation, coupling with the flow algorithm, and efficient parallelization of the complete method are more involved than a Cartesian grid method. The grid generation can be tedious and one needs to pay special attention in numerics to handle skewed cells for conservation purposes. Researchers have long sought for alternative methods to ease the effort involved in simulating flow over complex geometry.

Ackerman, A. S.↗

NASA NTRS1991

A locally refined rectangular grid finite element method - Application to computational fluid dynamics and computational physics

The present FEM technique addresses both linear and nonlinear boundary value problems encountered in computational physics by handling general three-dimensional regions, boundary conditions, and material properties. The box finite elements used are defined by a Cartesian grid independent of the boundary definition, and local refinements proceed by dividing a given box element into eight subelements. Discretization employs trilinear approximations on the box elements; special element stiffness matrices are included for boxes cut by any boundary surface. Illustrative results are presented for representative aerodynamics problems involving up to 400,000 elements.

Young, David P.↗

NASA NTRS1997

On Efficient Parallel Implementation of Moving Body Overset Grid Methods

An investigation into the parallel performance of moving-body overset grid methods will be presented. Parallel versions of the OVERFLOW flow solver, DCF3D domain connectivity software, and SIXDO six-degree-of-freedom routine are coupled with an automatic load balance routine and tested for 3D Navier-Stokes calculations on the IBM SP2. The primary source of parallel inefficiency in moving and problems are the domain connectivity costs with DCF 3D. Although this algorithm constitutes a relatively low fraction of the total solution cost (e.g. 10-20%) in calculations on serial machines, the consequently cause a significant degradation in the overall parallel performance. The paper will highlight some approaches for improving the scalability of DCF3D. The paper will present results of a proposed new load balancing scheme that seeks more equal distribution of the inter-grid boundary points in order to more evenly load balance the donor search costs associated with DCF3D. Some preliminary results will also be given from a new solution-adaption algorithm coupled with OVERFLOW which incorporates overset cartesian grids with various levels of refinement. The measured parallel performance from a descending delta-wing configuration and a generic store-separation from a wing/pylon case will be presented.

Wissink, Andrew M.↗

NASA NTRS1980

An investigation into grid patching techniques

In the past decade significant advances were made using flow field methods in the calculation of external transonic flows over aerodynamic configurations. It is now possible to calculate inviscid transonic flow over three dimensional configurations by solving the potential equation. However, with the exception of the transonic small disturbance methods which have the advantage of a simple cartesian grid, the configurations over which it is possible to calculate such flows are relatively simple. The major reason for this is the difficulty of producing compatibility between grid generation and flow equation solutions. The main programs in use, use essentially analytic transformations for prescribed configurations and, as such, are not easy to extend. While there is work in progress to extend this type of system to a limited extent, the long term effort is directed towards a more general approach. This approach should not be restricted to producing grid systems in isolation but rather a consideration of the overall problem of flow field solution.

Forsey, C. R.↗

NASA NTRS2004

CFD Approaches for Simulation of Wing-Body Stage Separation

A collection of computational fluid dynamics tools and techniques are being developed and tested for application to stage separation and abort simulation for next-generation launch vehicles. In this work, an overset grid Navier-Stokes flow solver has been enhanced and demonstrated on a matrix of proximity cases and on a dynamic separation simulation of a belly-to-belly wing-body configuration. Steady cases show excellent agreement between Navier-Stokes results, Cartesian grid Euler solutions, and wind tunnel data at Mach 3. Good agreement has been obtained between Navier-Stokes, Euler, and wind tunnel results at Mach 6. An analysis of a dynamic separation at Mach 3 demonstrates that unsteady aerodynamic effects are not important for this scenario. Results provide an illustration of the relative applicability of Euler and Navier-Stokes methods to these types of problems.

Buning, Pieter G.↗

NASA NTRS2004

Overview of Transonic to Hypersonic Stage Separation Tool Development for Multi-Stage-to-Orbit Concepts

An overview of research efforts at NASA in support of the stage separation and ascent aerothermodynamics research program is presented. The objective of this work is to develop a synergistic suite of experimental, computational, and engineering tools and methods to apply to vehicle separation across the transonic to hypersonic speed regimes. Proximity testing of a generic bimese wing-body configuration is on-going in the transonic (Mach numbers 0.6, 1.05, and 1.1), supersonic (Mach numbers 2.3, 3.0, and 4.5) and hypersonic (Mach numbers 6 and 10) speed regimes in four wind tunnel facilities at the NASA Langley Research Center. An overset grid, Navier-Stokes flow solver has been enhanced and demonstrated on a matrix of proximity cases and on a dynamic separation simulation of the bimese configuration. Steady-state predictions with this solver were in excellent agreement with wind tunnel data at Mach 3 as were predictions via a Cartesian-grid Euler solver. Experimental and computational data have been used to evaluate multi-body enhancements to the widely-used Aerodynamic Preliminary Analysis System, an engineering methodology, and to develop a new software package, SepSim, for the simulation and visualization of vehicle motions in a stage separation scenario. Web-based software will be used for archiving information generated from this research program into a database accessible to the user community. Thus, a framework has been established to study stage separation problems using coordinated experimental, computational, and engineering tools.

Murphy, Kelly J.↗

NASA NTRS1995

Navier-Stokes Aerodynamic Simulation of the V-22 Osprey on the Intel Paragon MPP

The paper will describe the Development of a general three-dimensional multiple grid zone Navier-Stokes flowfield simulation program (ENS3D-MPP) designed for efficient execution on the Intel Paragon Massively Parallel Processor (MPP) supercomputer, and the subsequent application of this method to the prediction of the viscous flowfield about the V-22 Osprey tiltrotor vehicle. The flowfield simulation code solves the thin Layer or full Navier-Stoke's equation - for viscous flow modeling, or the Euler equations for inviscid flow modeling on a structured multi-zone mesh. In the present paper only viscous simulations will be shown. The governing difference equations are solved using a time marching implicit approximate factorization method with either TVD upwind or central differencing used for the convective terms and central differencing used for the viscous diffusion terms. Steady state or Lime accurate solutions can be calculated. The present paper will focus on steady state applications, although time accurate solution analysis is the ultimate goal of this effort. Laminar viscosity is calculated using Sutherland's law and the Baldwin-Lomax two layer algebraic turbulence model is used to compute the eddy viscosity. The Simulation method uses an arbitrary block, curvilinear grid topology. An automatic grid adaption scheme is incorporated which concentrates grid points in high density gradient regions. A variety of user-specified boundary conditions are available. This paper will present the application of the scalable and superscalable versions to the steady state viscous flow analysis of the V-22 Osprey using a multiple zone global mesh. The mesh consists of a series of sheared cartesian grid blocks with polar grids embedded within to better simulate the wing tip mounted nacelle. MPP solutions will be shown in comparison to equivalent Cray C-90 results and also in comparison to experimental data. Discussions on meshing considerations, wall clock execution time, load balancing, and scalability will be provided.

Vadyak, Joseph↗