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All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

An Implicit, Conservative, Zonal-Boundary Scheme for Euler Equation Calculations

A "zonal," or "patched-grid," approach is one in which the flow region of interest is divided into subregions which are then discretized independently, using existing grid generators. The equations of motion are integrated in each subregion in conjunction with zonal-boundary schemes which allow proper information transfer across interfaces that separate subregions. The zonal approach greatly simplifies the treatment of complex geometries and also the addition of grid points to selected regions of the flow. In this study a conservative, zonal-boundary condition that could be used with explicit schemes has been extended so that it can be used with existing second-order accurate implicit integration schemes such as the Beam-Warming and Osher schemes. In the test case considered, the implicit schemes increased the rate of convergence considerably (by a factor of about 30 over that of the explicit scheme). Results demonstrating the time-accuracy of the zonal scheme and the feasibility of performing calculations on zones that move relative to each other are also presented.

Rai, Man Mohan↗
NASA NTRS1986

Applications of a Conservative Zonal Scheme to Transient and Geometrically Complex Problems

A conservative zoning technique, wherein the flow field for a finite-difference calculation is divided into several regions to simplify grid generation, is discussed and is applied in the solution of a two-dimensional problem of complex topology. Calculations are performed on two zonal, or patched, grid systems for the supersonic flow over a double-airfoil configuration. The solution is smooth and continuous across the zonal interfaces, and shock waves pass through the boundaries without distortion. In addition, the time accuracy of the zonal boundary method is verified by a two-zone cylinder calculation with a stationary inner and a rotating outer mesh. The feasibility of the zonal approach for use in the solution of geometrically complex and unsteady problems is thus demonstrated.

Hessenius, Kristin A.↗
NASA NTRS1999

Implicit Space-Time Conservation Element and Solution Element Schemes

Artificial numerical dissipation is in important issue in large Reynolds number computations. In such computations, the artificial dissipation inherent in traditional numerical schemes can overwhelm the physical dissipation and yield inaccurate results on meshes of practical size. In the present work, the space-time conservation element and solution element method is used to construct new and accurate implicit numerical schemes such that artificial numerical dissipation will not overwhelm physical dissipation. Specifically, these schemes have the property that numerical dissipation vanishes when the physical viscosity goes to zero. These new schemes therefore accurately model the physical dissipation even when it is extremely small. The new schemes presented are two highly accurate implicit solvers for a convection-diffusion equation. The two schemes become identical in the pure convection case, and in the pure diffusion case. The implicit schemes are applicable over the whole Reynolds number range, from purely diffusive equations to convection-dominated equations with very small viscosity. The stability and consistency of the schemes are analysed, and some numerical results are presented. It is shown that, in the inviscid case, the new schemes become explicit and their amplification factors are identical to those of the Leapfrog scheme. On the other hand, in the pure diffusion case, their principal amplification factor becomes the amplification factor of the Crank-Nicolson scheme.

Chang, Sin-Chung↗
NASA NTRS2000

Multigrid Relaxation of a Factorizable, Conservative Discretization of the Compressible Flow Equations

The second-order factorizable discretization of the compressible Euler equations developed by Sidilkover is extended to conservation form on general curvilinear body-fitted grids. The discrete equations are solved by symmetric collective Gauss-Seidel relaxation and FAS multigrid. Solutions for flow in a channel with Mach numbers ranging from 0.0001 to a supercritical Mach number are shown, demonstrating uniform convergence rates and no loss of accuracy in the incompressible limit. A solution for the flow around the leading edge of a semi-infinite parabolic body demonstrates that the scheme maintains rapid convergence for a flow containing a stagnation point.

Roberts, Thomas W.↗
NASA NTRS2000

Application of the Space-Time Conservation Element and Solution Element Method to One-Dimensional Convection-Diffusion Problems

In the space-time conservation element and solution element (CE/SE) method, the independent marching variables used comprise not only the mesh value of the physical dependent variables but also, in contrast to it typical numerical method, the Mesh values of the spatial derivatives of the physical variables The use of the extra marching variables results from the need to construct the two-level explicit and nondissipative schemes which are at the core of the CE/SE development. It also results from the need to minimize the stencil while maintaining accuracy. In this paper using the 1D(sub (alpha)-mu) scheme as an example, the effect of this added complication on consistency, accuracy and operation count is assessed. As part of this effort, an equivalent yet more efficient form of the alpha-mu scheme in which the independent marching variables are the local fluxes tied to each mesh point is introduced. Also, the intriguing relations that exist among the alpha-mu. Leapfrog, and DuFort-Frankel schemes are further explored. In addition, the redundance of the Leapfrog, DUFort-Frankel, and Lax scheme and the remedy for this redundance are discussed. This paper is concluded with the construction and evaluation of a CE/SE solver for the inviscid Burger equation.

Chang, Sin-Chung↗
NASA NTRS2000

Applications of the Space-Time Conservation Element and Solution Element (CE/SE) Method to Computational Aeroacoustic Benchmark Problems

The Internal Propagation problems, Fan Noise problem, and Turbomachinery Noise problems are solved using the space-time conservation element and solution element (CE/SE) method. The problems in internal propagation problems address the propagation of sound waves through a nozzle. Both the nonlinear and linear quasi 1D Euler equations are solved. Numerical solutions are presented and compared with the analytical solution. The fan noise problem concerns the effect of the sweep angle on the acoustic field generated by the interaction of a convected gust with a cascade of 3D flat plates. A parallel version of the 3D CE/SE Euler solver is developed and employed to obtain numerical solutions for a family of swept flat plates. Numerical solutions for sweep angles of 0, 5, 10, and 15 deg are presented. The turbomachinery problems describe the interaction of a 2D vortical gust with a cascade of flat-plate airfoils with/without a downstream moving grid. The 2D nonlinear Euler Equations are solved and the converged numerical solutions are presented and compared with the corresponding analytical solution. All the comparisons demonstrate that the CE/SE method is capable of solving aeroacoustic problems with/without shock waves in a simple and efficient manner. Furthermore, the simple non-reflecting boundary condition used in the CE/SE method which is not based on the characteristic theory works very well in 1D, 2D and 3D problems.

Wang, Xiao-Yen↗
NASA NTRS2001

Applications of the Method of Space-Time Conservation Element and the Solution Element to Unsteady Chemically Reactive Flows

This document reports the conclusion and findings of our research activities for this grant. The goal of the project is the development and application of the method of Space-Time Conservation Element and Solution Element, or the CE/SE method, to simulate chemically reacting flows. The product of this project will be a high-fidelity, time-accurate flow solver analyzing unsteady flow fields advanced propulsion concepts, including the low-emission turbojet engine combustion and flow fields of the Pulse Detonation Engines (PDE). Based on the documents and computer software of the CE/SE method that we have received from the CE/SE working group at NASA Lewis, we have focused our research effort on addressing outstanding technical issues related to the extension of the CE/SE method for unsteady, chemically reactive flows. In particular, we have made progresses in the following three aspects: (1) Derivation of the governing equations for reacting flows; (2) Numerical treatments of stiff source terms; and (3) Detailed simulations of ZND detonation waves.

Yu, Sheng-Tao↗
NASA NTRS2001

Ozone Loss From Quasi-Conservative Coordinate Mapping During the 1999-2000 SOLVE Campaign

During the winter of 1999-2000, the Sage III Ozone Loss and Validation Experiment (SOLVE) field experiment took place in Kiruna, Sweden. The purpose of SOLVE was to examine ozone depletion mechanisms in the Arctic stratosphere (from about 10 to 50 km altitude) during the winter and early spring, when a band of strong winds (the 'polar vortex') circle the pole. Measurements of stratospheric ozone were made by several different kinds of instruments in different meteorological situations. We analyzed these data using the 'quasi-conservative coordinate mapping' technique, in which the measurements are analyzed in terms of meteorological properties ('potential temperature' and 'potential vorticity') which tend not to change very much over a few days. This technique reduces or removes the changes that are associated with the polar vortex moving around. Over longer time periods, potential temperature and potential vorticity change as air cools and descends within the polar vortex. We account for these changes by calculating the trajectories of air parcels, and this enables us to extend the analysis over a ten-week period from January 10 to March 17, 2000. Using data from the NASA ER-2 aircraft, from the DIAL and AROTEL laser sounders on the NASA DC-8 aircraft, and balloon-borne ozonesondes, our analysis reveals changes in ozone which, because we have removed the effects of polar vortex motion and the descending air, indicate chemical destruction of ozone in early 2000. We find a peak decline rate of approximately 0.03 ppmv/day near 470 K of potential temperature (near 20 km) in mid-January which sinks in altitude to around 440 K (near 18 km) in mid-March.

Lait, L. R.↗
NASA NTRS1999

Practical Aspects of Stabilized FEM Discretizations of Nonlinear Conservation Law Systems with Convex Extension

This talk considers simplified finite element discretization techniques for first-order systems of conservation laws equipped with a convex (entropy) extension. Using newly developed techniques in entropy symmetrization theory, simplified forms of the Galerkin least-squares (GLS) and the discontinuous Galerkin (DG) finite element method have been developed and analyzed. The use of symmetrization variables yields numerical schemes which inherit global entropy stability properties of the POE system. Central to the development of the simplified GLS and DG methods is the Degenerative Scaling Theorem which characterizes right symmetrizes of an arbitrary first-order hyperbolic system in terms of scaled eigenvectors of the corresponding flux Jacobean matrices. A constructive proof is provided for the Eigenvalue Scaling Theorem with detailed consideration given to the Euler, Navier-Stokes, and magnetohydrodynamic (MHD) equations. Linear and nonlinear energy stability is proven for the simplified GLS and DG methods. Spatial convergence properties of the simplified GLS and DO methods are numerical evaluated via the computation of Ringleb flow on a sequence of successively refined triangulations. Finally, we consider a posteriori error estimates for the GLS and DG demoralization assuming error functionals related to the integrated lift and drag of a body. Sample calculations in 20 are shown to validate the theory and implementation.

Barth, Timothy↗
NASA NTRS2004

A-Posteriori Error Estimation for Hyperbolic Conservation Laws with Constraint

This lecture considers a-posteriori error estimates for the numerical solution of conservation laws with time invariant constraints such as those arising in magnetohydrodynamics (MHD) and gravitational physics. Using standard duality arguments, a-posteriori error estimates for the discontinuous Galerkin finite element method are then presented for MHD with solenoidal constraint. From these estimates, a procedure for adaptive discretization is outlined. A taxonomy of Green's functions for the linearized MHD operator is given which characterizes the domain of dependence for pointwise errors. The extension to other constrained systems such as the Einstein equations of gravitational physics are then considered. Finally, future directions and open problems are discussed.

Barth, Timothy↗
NASA NTRS2003

The expression and function of the achaete-scute genes in Tribolium castaneum reveals conservation and variation in neural pattern formation and cell fate specification

The study of achaete-scute (ac/sc) genes has recently become a paradigm to understand the evolution and development of the arthropod nervous system. We describe the identification and characterization of the ac/sc genes in the coleopteran insect species Tribolium castaneum. We have identified two Tribolium ac/sc genes - achaete-scute homolog (Tc-ASH) a proneural gene and asense (Tc-ase) a neural precursor gene that reside in a gene complex. Focusing on the embryonic central nervous system we find that Tc-ASH is expressed in all neural precursors and the proneural clusters from which they segregate. Through RNAi and misexpression studies we show that Tc-ASH is necessary for neural precursor formation in Tribolium and sufficient for neural precursor formation in Drosophila. Comparison of the function of the Drosophila and Tribolium proneural ac/sc genes suggests that in the Drosophila lineage these genes have maintained their ancestral function in neural precursor formation and have acquired a new role in the fate specification of individual neural precursors. Furthermore, we find that Tc-ase is expressed in all neural precursors suggesting an important and conserved role for asense genes in insect nervous system development. Our analysis of the Tribolium ac/sc genes indicates significant plasticity in gene number, expression and function, and implicates these modifications in the evolution of arthropod neural development.

Non-NASA Center↗
NASA NTRS2000

Evolutionary conservation of the presumptive neural plate markers AmphiSox1/2/3 and AmphiNeurogenin in the invertebrate chordate amphioxus

Amphioxus, as the closest living invertebrate relative of the vertebrates, can give insights into the evolutionary origin of the vertebrate body plan. Therefore, to investigate the evolution of genetic mechanisms for establishing and patterning the neuroectoderm, we cloned and determined the embryonic expression of two amphioxus transcription factors, AmphiSox1/2/3 and AmphiNeurogenin. These genes are the earliest known markers for presumptive neuroectoderm in amphioxus. By the early neurula stage, AmphiNeurogenin expression becomes restricted to two bilateral columns of segmentally arranged neural plate cells, which probably include precursors of motor neurons. This is the earliest indication of segmentation in the amphioxus nerve cord. Later, expression extends to dorsal cells in the nerve cord, which may include precursors of sensory neurons. By the midneurula, AmphiSox1/2/3 expression becomes limited to the dorsal part of the forming neural tube. These patterns resemble those of their vertebrate and Drosophila homologs. Taken together with the evolutionarily conserved expression of the dorsoventral patterning genes, BMP2/4 and chordin, in nonneural and neural ectoderm, respectively, of chordates and Drosophila, our results are consistent with the evolution of the chordate dorsal nerve cord and the insect ventral nerve cord from a longitudinal nerve cord in a common bilaterian ancestor. However, AmphiSox1/2/3 differs from its vertebrate homologs in not being expressed outside the CNS, suggesting that additional roles for this gene have evolved in connection with gene duplication in the vertebrate lineage. In contrast, expression in the midgut of AmphiNeurogenin together with the gene encoding the insulin-like peptide suggests that amphioxus may have homologs of vertebrate pancreatic islet cells, which express neurogenin3. In addition, AmphiNeurogenin, like its vertebrate and Drosophila homologs, is expressed in apparent precursors of epidermal chemosensory and possibly mechanosensory cells, suggesting a common origin for protostome and deuterostome epidermal sensory cells in the ancestral bilaterian. Copyright 2000 Academic Press.

NASA Discipline Evolutionary Biology↗
NASA NTRS2000

Functional conservation of atonal and Math1 in the CNS and PNS

To determine the extent to which atonal and its mouse homolog Math1 exhibit functional conservation, we inserted (beta)-galactosidase (lacZ) into the Math1 locus and analyzed its expression, evaluated consequences of loss of Math1 function, and expressed Math1 in atonal mutant flies. lacZ under the control of Math1 regulatory elements duplicated the previously known expression pattern of Math1 in the CNS (i.e., the neural tube, dorsal spinal cord, brainstem, and cerebellar external granule neurons) but also revealed new sites of expression: PNS mechanoreceptors (inner ear hair cells and Merkel cells) and articular chondrocytes. Expressing Math1 induced ectopic chordotonal organs (CHOs) in wild-type flies and partially rescued CHO loss in atonal mutant embryos. These data demonstrate that both the mouse and fly homologs encode lineage identity information and, more interestingly, that some of the cells dependent on this information serve similar mechanoreceptor functions.

NASA Discipline Developmental Biology↗
NASA NTRS2004

Non-coincident Inter-instrument Comparisons of Ozone Measurements Using Quasi-conservative Coordinates

Ozone measurements from ozonesondes, AROTAL, DIAL, and POAM III instruments during the SOLVE-2/VINTERSOL period are composited in a time-varying, flow-following quasi-conservative (PV-6) coordinate space; the resulting composites from each instrument are mapped onto the other instruments locations and times. The mapped data are then used to intercompare data from the different instruments. Overall, the four data sets are found to be in good agreement. AROTAL shows somewhat lower values below 16 km, and DIAL has a positive bias at the upper limits of its altitude range. These intercomparisons are consistent with those obtained from more conventional near-coincident profiles, where available. Although the PV-theta mapping technique entails larger uncertainties of individual profile differences compared to direct near-coincident comparisons, the ability to include much larger numbers of comparisons can make this technique advantageous.

Lait, L. R.↗
NASA NTRS2004

On the Total Variation of High-Order Semi-Discrete Central Schemes for Conservation Laws

We discuss a new fifth-order, semi-discrete, central-upwind scheme for solving one-dimensional systems of conservation laws. This scheme combines a fifth-order WENO reconstruction, a semi-discrete central-upwind numerical flux, and a strong stability preserving Runge-Kutta method. We test our method with various examples, and give particular attention to the evolution of the total variation of the approximations.

Bryson, Steve↗
NASA NTRS2000

Reduced-Noise Gas Flow Design Guide Developed as a Noise-Control Design Tool for Meeting Glenn's Hearing Conservation and Community Noise Goals

A Reduced-Noise Gas Flow Design Guide has been developed for the NASA Glenn Research Center at Lewis Field by Nelson Acoustical Engineering of Elgin, Texas. Gas flow systems are a significant contributor to t he noise exposure landscape at Glenn. Because of the power of many of these systems, hearing conservation and community noise are importan t issues. The purpose of the Guide is to allow Glenn engineers and de signers to address noise emission and control at the design stage by using readily available system parameters. Although the Guide was deve loped with Glenn equipment and systems in mind, it is expected to hav e wide application in industry.

Cooper, Beth A.↗
NASA NTRS2003

The Expression and Function of the Achaete-Scute Genes in Tribolium castaneum Reveals Conservation and Variation in Neural Pattern Formation and Cell Fate Specification

SUMMARY The study of achaete-scute (ac/sc) genes has recently become a paradigm to understand the evolution and development of the arthropod nervous system. We describe the identification and characterization of the ache genes in the coleopteran insect species Tribolium castaneum. We have identified two Tribolium ache genes - achaete-scute homolog (Tc-ASH) a proneural gene and asense (Tc-ase) a neural precursor gene that reside in a gene complex. Focusing on the embryonic central nervous system we fmd that Tc-ASH is expressed in all neural precursors and the proneural clusters from which they segregate. Through RNAi and misexpression studies we show that Tc-ASH is necessary for neural precursor formation in Triboliurn and sufficient for neural precursor formation in Drosophila. Comparison of the function of the Drosophila and Triboliurn proneural ac/sc genes suggests that in the Drosophila lineage these genes have maintained their ancestral function in neural precursor formation and have acquired a new role in the fate specification of individual neural precursors. Furthermore, we find that Tc-use is expressed in all neural precursors suggesting an important and conserved role for asense genes in insect nervous system development. Our analysis of the Triboliurn ache genes indicates significant plasticity in gene number, expression and function, and implicates these modifications in the evolution of arthropod neural development.

Wheeler, Scott R.↗