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NASA NTRS2000

Computations of Boiling in Microgravity

The absence (or reduction) of gravity, can lead to major changes in boiling heat transfer. On Earth, convection has a major effect on the heat distribution ahead of an evaporation front, and buoyancy determines the motion of the growing bubbles. In microgravity, convection and buoyancy are absent or greatly reduced and the dynamics of the growing vapor bubbles can change in a fundamental way. In particular, the lack of redistribution of heat can lead to a large superheat and explosive growth of bubbles once they form. While considerable efforts have been devoted to examining boiling experimentally, including the effect of microgravity, theoretical and computational work have been limited. Here, the growth of boiling bubbles is studied by direct numerical simulations where the flow field is fully resolved and the effects of inertia, viscosity, surface deformation, heat conduction and convection, as well as the phase change, are fully accounted for. Boiling involves both fluid flow and heat transfer and thus requires the solution of the Navier-Stokes and the energy equations. The numerical method is based on writing one set of governing transport equations which is valid in both the liquid and vapor phases. This local, single-field formulation incorporates the effect of the interface in the governing equations as source terms acting only at the interface. These sources account for surface tension and latent heat in the equations for conservation of momentum and energy as well as mass transfer across the interface due to phase change. The single-field formulation naturally incorporates the correct mass, momentum and energy balances across the interface. Integration of the conservation equations across the interface directly yields the jump conditions derived in the local instant formulation for two-phase systems. In the numerical implementation, the conservation equations for the whole computational domain (both vapor and liquid) are solved using a stationary grid and the phase boundary is followed by a moving unstructured two-dimensional grid. While two-dimensional simulations have been used for preliminary studies and to examine the resolution requirement, the focus is on fully three-dimensional simulations. The numerical methodology, including the parallelization and grid refinement strategy is discussed, and preliminary results shown. For buoyancy driven flow, the heat transfer is in good agreement with experimental correlations. The changes when gravity is turned off and/or fluid shear is added are discussed, as well as the difference between simulations of a layer freely releasing bubbles versus simulations using only one wavelength initial perturbation. Figure 1 shows the early stages of the formation of a three-dimensional bubble from a thin vapor layer. The boundary conditions are periodic in the x and y direction, the bottom is a hot and the top allows a free outflow. The jagged edge of the surface close to the bottom of the computational domain is due to some of the surface elements being on the other side of the domain and some elements not plotted by our plotting routine. In the second figure, we show the temperature distribution through two perpendicular planes.

Tryggvason, G.↗

NASA NTRS2001

Entropy Splitting for High Order Numerical Simulation of Vortex Sound at Low Mach Numbers

A method of minimizing numerical errors, and improving nonlinear stability and accuracy associated with low Mach number computational aeroacoustics (CAA) is proposed. The method consists of two levels. From the governing equation level, we condition the Euler equations in two steps. The first step is to split the inviscid flux derivatives into a conservative and a non-conservative portion that satisfies a so called generalized energy estimate. This involves the symmetrization of the Euler equations via a transformation of variables that are functions of the physical entropy. Owing to the large disparity of acoustic and stagnation quantities in low Mach number aeroacoustics, the second step is to reformulate the split Euler equations in perturbation form with the new unknowns as the small changes of the conservative variables with respect to their large stagnation values. From the numerical scheme level, a stable sixth-order central interior scheme with a third-order boundary schemes that satisfies the discrete analogue of the integration-by-parts procedure used in the continuous energy estimate (summation-by-parts property) is employed.

Mueller, B.↗

NASA NTRS2001

The CE/SE Method: a CFD Framework for the Challenges of the New Millennium

The space-time conservation element and solution element (CE/SE) method, which was originated and is continuously being developed at NASA Glenn Research Center, is a high-resolution, genuinely multidimensional and unstructured-mesh compatible numerical method for solving conservation laws. Since its inception in 1991, the CE/SE method has been used to obtain highly accurate numerical solutions for 1D, 2D and 3D flow problems involving shocks, contact discontinuities, acoustic waves, vortices, shock/acoustic waves/vortices interactions, shock/boundary layers interactions and chemical reactions. Without the aid of preconditioning or other special techniques, it has been applied to both steady and unsteady flows with speeds ranging from Mach number = 0.00288 to 10. In addition, the method has unique features that allow for (i) the use of very simple non-reflecting boundary conditions, and (ii) a unified wall boundary treatment for viscous and inviscid flows. The CE/SE method was developed with the conviction that, with a solid foundation in physics, a robust, coherent and accurate numerical framework can be built without involving overly complex mathematics. As a result, the method was constructed using a set of design principles that facilitate simplicity, robustness and accuracy. The most important among them are: (i) enforcing both local and global flux conservation in space and time, with flux evaluation at an interface being an integral part of the solution procedure and requiring no interpolation or extrapolation; (ii) unifying space and time and treating them as a single entity; and (iii) requiring that a numerical scheme be built from a nondissipative core scheme such that the numerical dissipation can be effectively controlled and, as a result, will not overwhelm the physical dissipation. Part I of the workshop will be devoted to a discussion of these principles along with a description of how the ID, 2D and 3D CE/SE schemes are constructed. In Part II, various applications of the CE/SE method, particularly those involving chemical reactions and acoustics, will be presented. The workshop will be concluded with a sketch of the future research directions.

Chang, Sin-Chung↗

NASA NTRS2002

Application of Local Discretization Methods in the NASA Finite-Volume General Circulation Model

We present the basic ideas of the dynamics system of the finite-volume General Circulation Model developed at NASA Goddard Space Flight Center for climate simulations and other applications in meteorology. The dynamics of this model is designed with emphases on conservative and monotonic transport, where the property of Lagrangian conservation is used to maintain the physical consistency of the computational fluid for long-term simulations. As the model benefits from the noise-free solutions of monotonic finite-volume transport schemes, the property of Lagrangian conservation also partly compensates the accuracy of transport for the diffusion effects due to the treatment of monotonicity. By faithfully maintaining the fundamental laws of physics during the computation, this model is able to achieve sufficient accuracy for the global consistency of climate processes. Because the computing algorithms are based on local memory, this model has the advantage of efficiency in parallel computation with distributed memory. Further research is yet desirable to reduce the diffusion effects of monotonic transport for better accuracy, and to mitigate the limitation due to fast-moving gravity waves for better efficiency.

Yeh, Kao-San↗

NASA NTRS2002

Interchange Method in Compressible Magnetized Couette Flow: Magnetorotational and Magnetoconvective Instabilities

We obtain the general forms of the axisymmetric stability criteria in a magnetized compressible Couette flow using an energy variational principle, the so-called interchange or Chandrasekhar s met hod, which we applied successfully in the incompressible case. This formulation accounts for the simultaneous presence of gravity, rotation, a toroidal magnetic field, a weak axial magnetic field, entropy gradients, and density gradients in the initial equilibrium state. The power of the method lies in its simplicity which allows us to derive extremely compact and physically clear expressions for the relevant stability criteria despite the inclusion of so many physical effects. In the implementation of the method, all the applicable conservation laws are explicitly taken into account during the variations of a quantity with dimensions of energy which we call the free energy function. As in the incompressible case, the presence of an axial field invalidates the conservation laws of angular momentum and azimuthal magnetic flux and introduces instead isorotation and axial current conservation along field lines. Our results are therefore markedly different depending on whether an axial magnetic field is present, and generalize in two simple expressions all previously known, partial stability criteria for the appearance of magnetorotational instability. Furthermore, the coupling between magnetic tension and buoyancy and its influence to the dynamics of nonhomoentropic magnetized flows becomes quite clear from our results. In the limits of plane-parallel atmospheres and homoentropic flows, our formulation easily recovers the stability criteria for suppression of convective and Parker instabilities, as well as some related special cases studied over 40 years ago by Newcomb and Tserkovnikov via laborious variational techniques.

Christodoulou, Dimitris M.↗

NASA NTRS2003

Nonlinear Aeroacoustics Computations by the Space-Time CE/SE Method

The Space-Time Conservation Element and Solution Element Method, or CE/SE Method for short, is a recently developed numerical method for conservation laws. Despite its second order accuracy in space and time, it possesses low dispersion errors and low dissipation. The method is robust enough to cover a wide range of compressible flows: from weak linear acoustic waves to strong discontinuous waves (shocks). An outstanding feature of the CE/SE scheme is its truly multi-dimensional, simple but effective non-reflecting boundary condition (NRBC), which is particularly valuable for computational aeroacoustics (CAA). In nature, the method may be categorized as a finite volume method, where the conservation element (CE) is equivalent to a finite control volume (or cell) and the solution element (SE) can be understood as the cell interface. However, due to its careful treatment of the surface fluxes and geometry, it is different from the existing schemes. Currently, the CE/SE scheme has been developed to a matured stage that a 3-D unstructured CE/SE Navier-Stokes solver is already available. However, in the present review paper, as a general introduction to the CE/SE method, only the 2-D unstructured Euler CE/SE solver is chosen and sketched in section 2. Then applications of the 2-D and 3-D CE/SE schemes to linear, and in particular, nonlinear aeroacoustics are depicted in sections 3, 4, and 5 to demonstrate its robustness and capability.

Loh, Ching Y.↗

NASA NTRS2003

Single Stage to Orbit: Politics, Space Technology, and the Quest for Reusable Rocketry

While the glories and tragedies of the space shuttle make headlines and move the nation, the story of the shuttle forms an inseparable part of a lesser-known but no less important drama-the search for a re-useable single-stage-to-orbit rocket. Here an award-winning student of space science, Andrew J. Butrica, examines the long and tangled history of this ambitious concept, from it first glimmerings in the 1920s, when technicians dismissed it as unfeasible, to its highly expensive heyday in the midst of the Cold War, when conservative-backed government programs struggled to produce an operational flight vehicle. Butrica finds a blending of far-sighted engineering and heavy-handed politics. To the first and oldest idea-that of the reusable rocket-powered single-stage- to-orbit vehicle-planners who belonged to what President Eisenhower referred to as the military-industrial complex added experimental (" X "), "aircraft-like" capabilities and, eventually, a "faster, cheaper, smaller" managerial approach. Single Stage to Orbit traces the interplay of technology, corporate interest, and politics, a combination that well served the conservative space agenda and ultimately triumphed-not in the realization of inexpensive, reliable space transport-but in a vision of space militarization and commercialization that would appear settled United States policy in the early twenty-first century. "The 'holy grail' of the spaceship movement has been the development of a vehicle that could accomplish single stage to orbit (SSTO) flight. This study describes the evolution of this concept from the 192'0s to the present, revealing a conservative space agenda that has not yet been the subject of historical analysis. As such, it makes an important contribution to space history literature."-Roger D. Launius, The Smithsonian Institution.

Butrica, Andrew J.↗

NASA NTRS1999

Semiempirical Two-Dimensional Magnetohydrodynamic Model of the Solar Corona and Interplanetary Medium

We have developed a two-dimensional semiempirical MHD model of the solar corona and solar wind. The model uses empirically derived electron density profiles from white-light coronagraph data measured during the Skylub period and an empirically derived model of the magnetic field which is fitted to observed streamer topologies, which also come from the white-light coronagraph data The electron density model comes from that developed by Guhathakurta and coworkers. The electron density model is extended into interplanetary space by using electron densities derived from the Ulysses plasma instrument. The model also requires an estimate of the solar wind velocity as a function of heliographic latitude and radial component of the magnetic field at 1 AU, both of which can be provided by the Ulysses spacecraft. The model makes estimates as a function of radial distance and latitude of various fluid parameters of the plasma such as flow velocity V, effective temperature T(sub eff), and effective heat flux q(sub eff), which are derived from the equations of conservation of mass, momentum, and energy, respectively. The term effective indicates that wave contributions could be present. The model naturally provides the spiral pattern of the magnetic field far from the Sun and an estimate of the large-scale surface magnetic field at the Sun, which we estimate to be approx. 12 - 15 G. The magnetic field model shows that the large-scale surface magnetic field is dominated by an octupole term. The model is a steady state calculation which makes the assumption of azimuthal symmetry and solves the various conservation equations in the rotating frame of the Sun. The conservation equations are integrated along the magnetic field direction in the rotating frame of the Sun, thus providing a nearly self-consistent calculation of the fluid parameters. The model makes a minimum number of assumptions about the physics of the solar corona and solar wind and should provide a very accurate empirical description of the solar corona and solar wind Once estimates of mass density rho, flow velocity V, effective temperature T(sub eff), effective heat flux q(sub eff), and magnetic field B are computed from the model and waves are assumed unimportant, all other plasma parameters such as Mach number, Alfven speed, gyrofrequency, etc. can be derived as a function of radial distance and latitude from the Sun. The model can be used as a planning tool for such missions as Slar Probe and provide an empirical framework for theoretical models of the solar corona and solar wind The model will be used to construct a semiempirical MHD description of the steady state solar corona and solar wind using the SOHO Large Angle Spectrometric Coronagraph (LASCO) polarized brightness white-light coronagraph data, SOHO Extreme Ultraviolet Imaging Telescope data, and Ulysses plasma data.

Sittler, Edward C., Jr.↗

NASA NTRS2004

Three-Dimensional High-Order Spectral Volume Method for Solving Maxwell's Equations on Unstructured Grids

A three-dimensional, high-order, conservative, and efficient discontinuous spectral volume (SV) method for the solutions of Maxwell's equations on unstructured grids is presented. The concept of discontinuous 2nd high-order loca1 representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) method, but instead of using a Galerkin finite-element formulation, the SV method is based on a finite-volume approach to attain a simpler formulation. Conventional unstructured finite-volume methods require data reconstruction based on the least-squares formulation using neighboring cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every cell at each time step, or to store the inversion coefficients. In a high-order, three-dimensional computation, the former would involve impractically large CPU time, while for the latter the memory requirement becomes prohibitive. In the SV method, one starts with a relatively coarse grid of triangles or tetrahedra, called spectral volumes (SVs), and partition each SV into a number of structured subcells, called control volumes (CVs), that support a polynomial expansion of a desired degree of precision. The unknowns are cell averages over CVs. If all the SVs are partitioned in a geometrically similar manner, the reconstruction becomes universal as a weighted sum of unknowns, and only a few universal coefficients need to be stored for the surface integrals over CV faces. Since the solution is discontinuous across the SV boundaries, a Riemann solver is thus necessary to maintain conservation. In the paper, multi-parameter and symmetric SV partitions, up to quartic for triangle and cubic for tetrahedron, are first presented. The corresponding weight coefficients for CV face integrals in terms of CV cell averages for each partition are analytically determined. These discretization formulas are then applied to the integral form of the Maxwell equations. All numerical procedures for outer boundary, material interface, zonal interface, and interior SV face are unified with a single characteristic formulation. The load balancing in a massive parallel computing environment is therefore easier to achieve. A parameter is introduced in the Riemann solver to control the strength of the smoothing term. Important aspects of the data structure and its effects to communication and the optimum use of cache memory are discussed. Results will be presented for plane TE and TM waves incident on a perfectly conducting cylinder for up to fifth order of accuracy, and a plane wave incident on a perfectly conducting sphere for up to fourth order of accuracy. Comparisons are made with exact solutions for these cases.

Liu, Yen↗

NASA NTRS2005

Multi-Dimensional Spectral Difference Method for Unstructured Grids

A new, high-order, conservative, and efficient method for conservation laws on unstructured grids is developed. It combines the best features of structured and unstructured grid methods to attain computational efficiency and geometric flexibility; it utilizes the concept of discontinuous and high-order local representations to achieve conservation and high accuracy; and it is based on the finite-difference formulation for simplicity. Universal reconstructions are obtained by distributing unknowns in a geometrically similar manner for all unstructured cells. Placements of the unknown and flux points with various order of accuracy are given for the line, triangular and tetrahedral elements. The data structure of the new method permits an optimum use of cache memory, resulting in further computational efficiency on modern computers. A new pointer system is developed that reduces memory requirements and simplifies programming for any order of accuracy. Numerical solutions are presented and compared with the exact solutions for wave propagation problems in both two and three dimensions to demonstrate the capability of the method. Excellent agreement has been found. The method is simpler and more efficient than previous discontinuous Galerkin and spectral volume methods for unstructured grids.

Liu, Yen↗

NASA NTRS1998

Of mice and genes: evolution of vertebrate brain development

In this review the current understanding of genetic and molecular evolution of development, in particular the formation of the major axis of bilateral animals, is critically evaluated, and the early pattern formation in the hindbrain is related as much as possible to these processes. On the genetic level it is proposed that the exuberant multiplication of regulatory genes compared to that of structural genes relates to the increased flexibility of early vertebrate development. In comparisons to fruit flies, many conserved genes are found to be expressed very differently, while many others seem to reflect a comparable pattern and thus suggest a conservation of function. Even genes with a largely conserved pattern of expression may change the level at which they are expressed and the mechanisms by which they are regulated in their expression. Evolution and development of hindbrain motoneurons is reviewed, and it is concluded that both comparative data as well as more recent experimental data suggest a limited importance for the rhombomeres. Clearly, many cell fate-specifying processes work below the level of rhombomeres or in the absence of rhombomeres. It is suggested that more comparative developmental data are needed to establish firmly the relationship between homeobox genes and rhombomere specification in vertebrates other than a few model species.

NASA Discipline Developmental Biology↗

NASA NTRS1997

Structure of an anti-HIV-1 hammerhead ribozyme complex with a 17-mer DNA substrate analog of HIV-1 gag RNA and a mechanism for the cleavage reaction: 750 MHz NMR and computer experiments

The structure of an anti-HIV-1 ribozyme-DNA abortive substrate complex was investigated by 750 MHz NMR and computer modeling experiments. The ribozyme was a chimeric molecule with 30 residues-18 DNA nucleotides, and 12 RNA residues in the conserved core. The DNA substrate analog had 17 residues. The chimeric ribozyme and the DNA substrate formed a shortened ribozyme-abortive substrate complex of 47 nucleotides with two DNA stems (stems I and III) and a loop consisting of the conserved core residues. Circular dichroism spectra showed that the DNA stems assume A-family conformation at the NMR concentration and a temperature of 15 degrees C, contrary to the conventional wisdom that DNA duplexes in aqueous solution populate entirely in the B-form. It is proposed that the A-family RNA residues at the core expand the A-family initiated at the core into the DNA stems because of the large free energy requirement for the formation of A/B junctions. Assignments of the base H8/H6 protons and H1' of the 47 residues were made by a NOESY walk. In addition to the methyl groups of all T's, the imino resonances of stems I and III and AH2's were assigned from appropriate NOESY walks. The extracted NMR data along with available crystallographic data, were used to derive a structural model of the complex. Stems I and III of the final model displayed a remarkable similarity to the A form of DNA; in stem III, a GC base pair was found to be moving into the floor of the minor groove defined by flanking AT pairs; data suggest the formation of a buckled rhombic structure with the adjacent pair; in addition, the base pair at the interface of stem III and the loop region displayed deformed geometry. The loop with the catalytic core, and the immediate region of the stems displayed conformational multiplicity within the NMR time scale. A catalytic mechanism for ribozyme action based on the derived structure, and consistent with biochemical data in the literature, is proposed. The complex between the anti HIV-1 gag ribozyme and its abortive DNA substrate manifests in the detection of a continuous track of A.T base pairs; this suggests that the interaction between the ribozyme and its DNA substrate is stronger than the one observed in the case of the free ribozyme where the bases in stem I and stem III regions interact strongly with the ribozyme core region (Sarma, R. H., et al. FEBS Letters 375, 317-23, 1995). The complex formation provides certain guidelines in the design of suitable therapeutic ribozymes. If the residues in the ribozyme stem regions interact with the conserved core, it may either prevent or interfere with the formation of a catalytically active tertiary structure.

NASA Discipline Exobiology↗

NASA NTRS1995

Modeling of a possible conformational change associated with the catalytic mechanism in the hammerhead ribozyme

Here we describe a possible model of the cleavage mechanism in the hammerhead ribozyme. In this model, the 2' hydroxyl of C17 is moved into an appropriate orientation for an in-line attack on the G1.1 phosphate through a change in its sugar pucker from C3' endo to C2' endo. This conformational change in the active site is caused by a change in the uridine turn placing the N2 and N3 atoms of G5 of the conserved core in hydrogen bonding geometry with the N3 and N2 atoms on the conserved G16.2 residue. The observed conformational change in the uridine turn suggests an explanation for the conservation of G5. In the crystal structure of H.M. Pley et al., Nature 372, 68-74 (1994), G5 is situated 5.3A away from G16.2. However, the uridine turn is sufficiently flexible to allow this conformational change with relatively modest changes in the backbone torsion angles (average change of 14.2 degrees). Two magnesium ions were modeled into the active site with positions analogous to those described in the functionally similar Klenow fragment 3'-5' exonuclease (L.S. Beese and T.A. Steitz, EMBO J. 10, 25-33 (1991)), the Group I intron (T.A. Steitz and J.A. Steitz, P.N.A.S. U.S.A. 90, 6498-6502 (1993); R.F. Setlik et al., J. Biomol. Str. Dyn. 10, 945-972 (1993)) and other phosphotransferases. Comparison of this model with one in which the uridine turn conformation was not changed showed that although the changes in the C17 sugar pucker could be modeled, insufficient space existed for the magnesium ions in the active site.

Non-NASA Center↗

NASA NTRS2005

Space Based Ornithology: On the Wings of Migration and Biophysics

The study of bird migration on a global scale is one of the compelling and challenging problems of modern biology with major implications for human health and conservation biology. Migration and conservation efforts cross national boundaries and are subject to numerous international agreements and treaties. Space based technology offers new opportunities to shed understanding on the distribution and migration of organisms on the planet and their sensitivity to human disturbances and environmental changes. Migration is an incredibly diverse and complex behavior. A broad outline of space based research must address three fundamental questions: (1) where could birds be, i.e. what is their fundamental niche constrained by their biophysical limits? (2) where do we actually find birds, i.e. what is their realizable niche as modified by local or regional abiotic and biotic factors, and (3) how do they get there (and how do we know?), that is what are their migration patterns and associated mechanisms? Our working hypothesis is that individual organism biophysical models of energy and water balance, driven by satellite measurements of spatio-temporal gradients in climate and habitat, will help us to explain the variability in avian species richness and distribution. Dynamic state variable modeling provides one tool for studying bird migration across multiple scales and can be linked to mechanistic models describing the time and energy budget states of migrating birds. Such models yield an understanding of how a migratory flyway and its component habitats function as a whole and link stop-over ecology with biological conservation and management. Further these models provide an ecological forecasting tool for science and application users to address what are the possible consequences of loss of wetlands, flooding, drought or other natural disasters such as hurricanes on avian biodiversity and bird migration.

Smith, James A.↗

NASA NTRS2005

Numerical Modeling of Flow Distribution in Micro-Fluidics Systems

This paper describes an application of a general purpose computer program, GFSSP (Generalized Fluid System Simulation Program) for calculating flow distribution in a network of micro-channels. GFSSP employs a finite volume formulation of mass and momentum conservation equations in a network consisting of nodes and branches. Mass conservation equation is solved for pressures at the nodes while the momentum conservation equation is solved at the branches to calculate flowrate. The system of equations describing the fluid network is solved by a numerical method that is a combination of the Newton-Raphson and successive substitution methods. The numerical results have been compared with test data and detailed CFD (computational Fluid Dynamics) calculations. The agreement between test data and predictions is satisfactory. The discrepancies between the predictions and test data can be attributed to the frictional correlation which does not include the effect of surface tension or electro-kinetic effect.

Majumdar, Alok↗

NASA NTRS2006

Space-Based Ornithology: On the Wings of Migration and Biophysics

Understanding bird migration and avian biodiversity is one of the most compelling and challenging problems of modern biology with major implications for human health and conservation biology. Migration and conservation efforts cross national boundaries and are subject to numerous international agreements and treaties. Public interest is high with concerns about avian flu, Katrina and its impacts, and the recent sightings of the ivory-billed woodpecker. Space based technology gives us new opportunities to shed light on the distribution and movement of organisms on the planet and their sensitivity to human disturbances and environmental changes. Together with the USGS and other agencies, we are creating ecological forecasting tools for science and application users to address the consequences of loss of wetlands, flooding, drought or other natural disasters such as hurricanes on avian biodiversity and bird migration. In our work, we use individual organism biophysical models of energy and water balance and drive these models with satellite measurements of spatio-temporal gradients in climate and habitat. Dynamic state variable modeling provides an additional tool for studying bird migration across multiple scales and can be linked to our mechanistic models describing the time and energy budget states of migrating birds. Such models yield an understanding of how a migratory flyway and its component habitats function as a whole and link stop-over ecology with biological conservation and management. We also build upon the canopy done by the Environmental Laboratory over the past few years.

Smith, James A.↗

NASA NTRS2007

The alpha(3) Scheme - A Fourth-Order Neutrally Stable CESE Solver

The conservation element and solution element (CESE) development is driven by a belief that a solver should (i) enforce conservation laws in both space and time, and (ii) be built from a non-dissipative (i.e., neutrally stable) core scheme so that the numerical dissipation can be controlled effectively. To provide a solid foundation for a systematic CESE development of high order schemes, in this paper we describe a new 4th-order neutrally stable CESE solver of the advection equation Theta u/Theta + alpha Theta u/Theta x = 0. The space-time stencil of this two-level explicit scheme is formed by one point at the upper time level and three points at the lower time level. Because it is associated with three independent mesh variables u(sup n) (sub j), (u(sub x))(sup n) (sub j) , and (uxz)(sup n) (sub j) (the numerical analogues of u, Theta u/Theta x, and Theta(exp 2)u/Theta x(exp 2), respectively) and four equations per mesh point, the new scheme is referred to as the alpha(3) scheme. As in the case of other similar CESE neutrally stable solvers, the alpha(3) scheme enforces conservation laws in space-time locally and globally, and it has the basic, forward marching, and backward marching forms. These forms are equivalent and satisfy a space-time inversion (STI) invariant property which is shared by the advection equation. Based on the concept of STI invariance, a set of algebraic relations is developed and used to prove that the alpha(3) scheme must be neutrally stable when it is stable. Moreover it is proved rigorously that all three amplification factors of the alpha(3) scheme are of unit magnitude for all phase angles if |v| <= 1/2 (v = alpha delta t/delta x). This theoretical result is consistent with the numerical stability condition |v| <= 1/2. Through numerical experiments, it is established that the alpha(3) scheme generally is (i) 4th-order accurate for the mesh variables u(sup n) (sub j) and (ux)(sup n) (sub j); and 2nd-order accurate for (uxx)(sup n) (sub j). However, in some exceptional cases, the scheme can achieve perfect accuracy aside from round-off errors.

Chang, Sin-Chung↗

NASA NTRS2008

Modeling Bird Migration in Changing Habitats: Space-based Ornithology using Satellites and GIS

Understanding bird migration and avian biodiversity is one of the most compelling and challenging problems of modern biology with major implications for human health and conservation biology. Migration and conservation efforts cross national boundaries and are subject to numerous international agreements and treaties presenting challenges in both geographic space and time. Space based technology, coupled with geographic information systems, yields new opportunities to shed light on the distribution and movement of organisms on the planet and their sensitivity to human disturbances and environmental changes. At NASA, we are creating ecological forecasting tools for science and application users to address the consequences of loss of wetlands, flooding, drought or other natural disasters such as hurricanes on avian biodiversity and bird migration. In our work, we use individual organism biophysical models and drive these models with satellite observations and numerical weather predictions of the spatio-temporal gradients in climate and habitat. Geographic information system technology comprises one component of our overall simulation framework, especially for characterizing the changing habitats and conditions encountered by en-route migratory birds. Simulation provides a tool for studying bird migration across multiple scales and can be linked to mechanistic processes describing the time and energy budget states of migrating birds. Such models yield an understanding of how a migratory flyway and its component habitats function as a whole and link stop-over ecology with biological conservation and management. We present examples of our simulation of shorebirds, principally, pectoral sandpipers, along the central flyways of the United States and Canada from the Gulf of Mexico to Alaska.

Smith, James A.↗