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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS2000

DRAGON Grid: A Three-Dimensional Hybrid Grid Generation Code Developed

Because grid generation can consume 70 percent of the total analysis time for a typical three-dimensional viscous flow simulation for a practical engineering device, payoffs from research and development could reduce costs and increase throughputs considerably. In this study, researchers at the NASA Glenn Research Center at Lewis Field developed a new hybrid grid approach with the advantages of flexibility, high-quality grids suitable for an accurate resolution of viscous regions, and a low memory requirement. These advantages will, in turn, reduce analysis time and increase accuracy. They result from an innovative combination of structured and unstructured grids to represent the geometry and the computation domain. The present approach makes use of the respective strengths of both the structured and unstructured grid methods, while minimizing their weaknesses. First, the Chimera grid generates high-quality, mostly orthogonal meshes around individual components. This process is flexible and can be done easily. Normally, these individual grids are required overlap each other so that the solution on one grid can communicate with another. However, when this communication is carried out via a nonconservative interpolation procedure, a spurious solution can result. Current research is aimed at entirely eliminating this undesired interpolation by directly replacing arbitrary grid overlapping with a nonstructured grid called a DRAGON grid, which uses the same set of conservation laws over the entire region, thus ensuring conservation everywhere. The DRAGON grid is shown for a typical film-cooled turbine vane with 33 holes and 3 plenum compartments. There are structured grids around each geometrical entity and unstructured grids connecting them. In fiscal year 1999, Glenn researchers developed and tested the three-dimensional DRAGON grid-generation tools. A flow solver suitable for the DRAGON grid has been developed, and a series of validation tests are underway.

Liou, Meng-Sing↗
NASA NTRS1999

Space-Time Conservation Element and Solution Element Method Being Developed

The engineering research and design requirements of today pose great computer-simulation challenges to engineers and scientists who are called on to analyze phenomena in continuum mechanics. The future will bring even more daunting challenges, when increasingly complex phenomena must be analyzed with increased accuracy. Traditionally used numerical simulation methods have evolved to their present state by repeated incremental extensions to broaden their scope. They are reaching the limits of their applicability and will need to be radically revised, at the very least, to meet future simulation challenges. At the NASA Lewis Research Center, researchers have been developing a new numerical framework for solving conservation laws in continuum mechanics, namely, the Space-Time Conservation Element and Solution Element Method, or the CE/SE method. This method has been built from fundamentals and is not a modification of any previously existing method. It has been designed with generality, simplicity, robustness, and accuracy as cornerstones. The CE/SE method has thus far been applied in the fields of computational fluid dynamics, computational aeroacoustics, and computational electromagnetics. Computer programs based on the CE/SE method have been developed for calculating flows in one, two, and three spatial dimensions. Results have been obtained for numerous problems and phenomena, including various shock-tube problems, ZND detonation waves, an implosion and explosion problem, shocks over a forward-facing step, a blast wave discharging from a nozzle, various acoustic waves, and shock/acoustic-wave interactions. The method can clearly resolve shock/acoustic-wave interactions, wherein the difference of the magnitude between the acoustic wave and shock could be up to six orders. In two-dimensional flows, the reflected shock is as crisp as the leading shock. CE/SE schemes are currently being used for advanced applications to jet and fan noise prediction and to chemically reacting flows.

Chang, Sin-Chung↗
NASA NTRSDate not supplied

A Moving Discontinuous Galerkin Method with Interface Condition Enforcement for Reacting Hypersonic Flows

The necessity of enforcing conservation in computational elements or cells (element conservation) for discontinuous solutions is well understood and respected for solving conservation laws in computational fluid dynamics (CFD). In contrast, interface conservation, where the conservation across cell interfaces is enforced, is long ignored, and yet is also ruled and required by the underlying physics just like element conservation. Violation of the interface conservation across discontinuities is the root cause why an exact discontinuous solution can never be achieved in shock capturing methods. The interface conservation is examined and explored in this talk. Moving discontinuous Galerkin (MDG) finite element method with interface conservation enforcement (MDG-ICE) [1],[2] are then presented for solving compressible flow problems with discontinuities based on the observation that the interface conservation can only be satisfied, only when mesh interfaces are aligned with discontinuities. In the MDG-ICE formulation, both conservative quantities and grid geometry are considered as independent variables. A space-time DG formulation is used to solve the multi-material compressible Euler equations in the standard discontinuous solution space and the discrete grid geometry is solved using a variational formulation in a continuous space. A self-adaptive Levenberg-Marquardt method is utilized to solve the resulting over-determined system of nonlinear equations arising from the MDG-ICE formulation. A number of numerical experiments for a variety of flow problems are conducted to assess the accuracy and performance of the MDG-ICE method. Numerical results obtained indicate that the MDG-ICE method is able to deliver the designed order of both h- and p-convergence even for discontinuous solutions, and detect all types of interfaces, via interface condition enforcement and satisfy, via grid movement, the compressible Euler equations and the associated interface condition.

Discontinuous Galekin↗
NASA NTRS1992

Computing interface motion in compressible gas dynamics

An analysis is conducted of the coupling of Osher and Sethian's (1988) 'Hamilton-Jacobi' level set formulation of the equations of motion for propagating interfaces to a system of conservation laws for compressible gas dynamics, giving attention to both the conservative and nonconservative differencing of the level set function. The capabilities of the method are illustrated in view of the results of numerical convergence studies of the compressible Rayleigh-Taylor and Kelvin-Helmholtz instabilities for air-air and air-helium boundaries.

Mulder, W.↗
NASA NTRS1989

Constructing space difference schemes which satisfy a cell entropy inequality

A numerical methodology for solving convection problems is presented, using finite difference schemes which satisfy the second law of thermodynamics on a cell-by-cell basis in addition to the usual conservation laws. It is shown that satisfaction of a cell entropy inequality is sufficient, in some cases, to guarantee nonlinear stability. Some details are given for several one-dimensional problems, including the quasi-one-dimensional Euler equations applied to flow in a nozzle.

Merriam, Marshal L.↗
NASA NTRS1990

Flowfield computation of entry vehicles

The equations governing the multidimensional flow of a reacting mixture of thermally perfect gasses were derived. The modeling procedures for the various terms of the conservation laws are discussed. A numerical algorithm, based on the finite-volume approach, to solve these conservation equations was developed. The advantages and disadvantages of the present numerical scheme are discussed from the point of view of accuracy, computer time, and memory requirements. A simple one-dimensional model problem was solved to prove the feasibility and accuracy of the algorithm. A computer code implementing the above algorithm was developed and is presently being applied to simple geometries and conditions. Once the code is completely debugged and validated, it will be used to compute the complete unsteady flow field around the Aeroassist Flight Experiment (AFE) body.

Prabhu, Dinesh K.↗
NASA NTRS1986

On symmetric and upwind TVD schemes

The performance of the upwind and symmetric total variation diminishing (TVD) schemes in viscous and inviscid airfoil steady-state calculations is considered, and the extension of the implicit second-order-accurate TVD scheme for hyperbolic systems of conservative laws in curvilinear coordinates is discussed. For two-dimensional steady-state applications, schemes are implemented in a conservative noniterative alternating direction implicit form, and results illustrate that the algorithm produces a fairly good solution for an RAE2822 airfoil calculation. The study demonstrates that the symmetric TVD scheme is as accurate as the upwind TVD scheme, while requiring less computational effort than it.

Yee, H. C.↗
NASA NTRS1995

Non-Noetherian symmetries for oscillators in classical mechanics and in field theory

Infinitely many new conservation laws both for free fields as well as for test fields evolving on a given gravitational background are presented. The conserved currents are constructed using the field theoretical counterpart of a recently discovered non-Noetherian symmetry which gives rise to a new way of solving the classical small oscillations problem. Several examples are discussed.

Hojman, Sergio A.↗
NASA NTRS2014

Conservation of Mass and Preservation of Positivity with Ensemble-Type Kalman Filter Algorithms

This paper considers the incorporation of constraints to enforce physically based conservation laws in the ensemble Kalman filter. In particular, constraints are used to ensure that the ensemble members and the ensemble mean conserve mass and remain nonnegative through measurement updates. In certain situations filtering algorithms such as the ensemble Kalman filter (EnKF) and ensemble transform Kalman filter (ETKF) yield updated ensembles that conserve mass but are negative, even though the actual states must be nonnegative. In such situations if negative values are set to zero, or a log transform is introduced, the total mass will not be conserved. In this study, mass and positivity are both preserved by formulating the filter update as a set of quadratic programming problems that incorporate non-negativity constraints. Simple numerical experiments indicate that this approach can have a significant positive impact on the posterior ensemble distribution, giving results that are more physically plausible both for individual ensemble members and for the ensemble mean. In two examples, an update that includes a non-negativity constraint is able to properly describe the transport of a sharp feature (e.g., a triangle or cone). A number of implementation questions still need to be addressed, particularly the need to develop a computationally efficient quadratic programming update for large ensemble.

EnKF↗
NASA NTRS1989

Nonlinear filters for efficient shock computation

A new type of methods for the numerical approximation of hyperbolic conservation laws with discontinuous solution is introduced. The methods are based on standard finite difference schemes. The difference solution is processed with a nonlinear conservation form filter at every time level to eliminate spurious oscillations near shocks. It is proved that the filter can control the total variation of the solution and also produce sharp discrete shocks. The method is simpler and faster than many other high resolution schemes for shock calculations. Numerical examples in one and two space dimensions are presented.

Engquist, Bjorn↗
NASA NTRS1989

Two-phase potential flow

Some features of two recent approaches of two-phase potential flow are presented. The first approach is based on a set of progressive examples that can be analyzed using common techniques, such as conservation laws, and taken together appear to lead in the direction of a general theory. The second approach is based on variational methods, a classical approach to conservative mechanical systems that has a respectable history of application to single phase flows. This latter approach, exemplified by several recent papers by Geurst, appears generally to be consistent with the former approach, at least in those cases for which it is possible to obtain comparable results. Each approach has a justifiable theoretical base and is self-consistent. Moreover, both approaches appear to give the right prediction for several well-defined situations.

Wallis, Graham B.↗
NASA NTRS2000

Detection of Extraterrestrial Ecology (Exoecology)

Researchers in the Astrobiology Technology Branch at Ames Research Center have begun investigating alternate concepts for the detection of extraterrestrial life. We suggest searching for extraterrestrial ecology, exoecology, as well as for extraterrestrial biology, exobiology. Ecology describes the interactions of living things with their environment. All ecosystems are highly constrained by their environment and are constrained by well-known system design principles. Ecology could exist wherever there is an energy source and living I things have discovered some means to capture, store, and use the available energy. Terrestrial ecosystems use as energy sources, light, organic molecules, and in thermal vents and elsewhere, simple inorganic molecules. Ecosystem behavior is controlled by matter and energy conservation laws and can be described by linear and nonlinear dynamic systems theory. Typically in an ecosystem different molecules are not in chemical equilibrium and scarce material is conserved, stored, or recycled. Temporal cycles and spatial variations are often observed. These and other -eneral principles of exoecology can help guide the search for extraterrestrial life. The chemical structure observed in terrestrial biology may be highly contingent on evolutionary accidents. Oxygen was not always abundant on Earth. Primitive sulfur bacteria use hydrogen sulfide and sulfur to perform photosynthesis instead of water and oxygen. Astrobiologists have assumed, for the sake of narrowing and focusing our life detection strategies, that extraterrestrial life will have detailed chemical similarities with terrestrial life. Such assumptions appear very reasonable and they allow us to design specific and highly sensitive life detection experiments. But the fewer assumptions we make, the less chance we have of being entirely wrong The best strategy for the detection of extraterrestrial life could be a mixed strategy. We should use detailed assumptions based on terrestrial biology to guide some but not all future searches for alien life. The systems principles of exoecology seem much more fundamental and inescapable than the terrestrial biology analogies of exobiology. We should search for exoecology as well as exobiology.

Jones, Harry↗
NASA NTRS2018

High-Order Stabilized Finite Elements on Dynamic Meshes

The development of dynamic mesh capability for turbulent flow simulations using the Streamlined Upwind Petrov-Galerkin (SUPG) discretization is described. The current work extends previous research to include high-order spatial accuracy, including the satisfaction of the discrete geometric conservation law (GCL) on curved elements. Two closely-related schemes are described and the ability of these schemes to satisfy the GCL, while also maintaining temporal accuracy and conservation is assessed. Studies indicate that although one scheme discretizes the time derivative in conservative form, both schemes exhibit temporal conservation errors that decrease according to the expected design order of accuracy. The source of the temporal conservation errors is examined, and it is demonstrated that many finite-volume and finite-element schemes can also be expected to have difficulty strictly satisfying conservation in time. The effects on conservation are examined and, while present in the simulations, are seen to be negligible for the problems considered.

Anderson, W. Kyle↗
NASA NTRS2001

On the Conservation and Convergence to Weak Solutions of Global Schemes

In this paper we discuss the issue of conservation and convergence to weak solutions of several global schemes, including the commonly used compact schemes and spectral collocation schemes, for solving hyperbolic conservation laws. It is shown that such schemes, if convergent boundedly almost everywhere, will converge to weak solutions. The results are extensions of the classical Lax-Wendroff theorem concerning conservative schemes.

Carpenter, Mark H.↗
NASA NTRS1995

The direction of heat flow in an expanding current free stellar atmosphere

The energy budgets of the corona are substantially influenced by losses attributed to thermal conduction losses down the transition region, towards the chromosphere. Although Fourier law for such a plasma regime is now universally criticized as inappropriate, the direction of this heat flow seems to be certain. The purpose of this paper is to point out, based on conservation laws, the direction in which the heat must flow in this regime, provided it is known that there is a time independent expansion devoid of parallel currents. It will be argued that the direction of the heat flux is from the base of the transition region up into the corona, rather than the opposite. Under the circumstances mentioned above, the direction of the heat flow should be opposite to the gradient of the electron pressure gradient. Although the transition region is modeled as isobaric, this is only approximately true. Such a likely scenario makes the heat flow almost certainly to flow from the lower temperature base of the TR up into the incipient corona if a steady state current free expansion is to be maintained.

Scudder, J. D.↗
NASA NTRS2002

The Delta(dot) B = O Constraint vs. Minimization of Numerical Errors in MHD Simulations

The MHD equations are a system of non-strictly hyperbolic conservation laws. The non-convexity of the inviscid flux vector resulted in corresponding Jacobian matrices with undesirable properties. On the other hand, the MHD equations can be derived from basic principles in either conservative or non-conservative form. The non-conservative system has a better conditioned eigensystem. The Delta(dot)B = 0 constraint of the A4HD equations is only an initial condition constraint. One does not need the Delta(dot)B condition to close the MHD system. We formulate our new low dissipative high order scheme together with the Cargo & Gallice (1997) form of the MHD approximate Riemann solver in curvilinear grids for both versions of the MHD equations. A novel feature of our new method is that the well-conditioned eigen-decomposition of the non-conservative MHD equations is used to solve the conservative equations. This new feature of the method provides well-conditioned eigenvectors for the conservative formulation, so that correct wave speeds for discontinuities are assured. The justification for using the non-conservative eigen-decomposition to solve the conservative equations is that our scheme has a better control of the numerical error associated with the Delta(dot)B condition. Consequently, computing both forms of the equations with the same eigen-decomposition is almost equivalent. It will be shown that this approach, using the non-conservative eigensystem when solving the conservative equations, also works well in the context of standard shock-capturing schemes.

Yee, H. C.↗
NASA NTRS1993

A new flux conserving Newton's method scheme for the two-dimensional, steady Navier-Stokes equations

A new numerical method is developed for the solution of the two-dimensional, steady Navier-Stokes equations. The method that is presented differs in significant ways from the established numerical methods for solving the Navier-Stokes equations. The major differences are described. First, the focus of the present method is on satisfying flux conservation in an integral formulation, rather than on simulating conservation laws in their differential form. Second, the present approach provides a unified treatment of the dependent variables and their unknown derivatives. All are treated as unknowns together to be solved for through simulating local and global flux conservation. Third, fluxes are balanced at cell interfaces without the use of interpolation or flux limiters. Fourth, flux conservation is achieved through the use of discrete regions known as conservation elements and solution elements. These elements are not the same as the standard control volumes used in the finite volume method. Fifth, the discrete approximation obtained on each solution element is a functional solution of both the integral and differential form of the Navier-Stokes equations. Finally, the method that is presented is a highly localized approach in which the coupling to nearby cells is only in one direction for each spatial coordinate, and involves only the immediately adjacent cells. A general third-order formulation for the steady, compressible Navier-Stokes equations is presented, and then a Newton's method scheme is developed for the solution of incompressible, low Reynolds number channel flow. It is shown that the Jacobian matrix is nearly block diagonal if the nonlinear system of discrete equations is arranged approximately and a proper pivoting strategy is used. Numerical results are presented for Reynolds numbers of 100, 1000, and 2000. Finally, it is shown that the present scheme can resolve the developing channel flow boundary layer using as few as six to ten cells per channel width, depending on the Reynolds number.

Scott, James R.↗
NASA NTRS2002

The Delta x B = 0 Constraint Versus Minimization of Numerical Errors in MHD Simulations

The MHD equations are a system of non-strictly hyperbolic conservation laws. The non-convexity of the inviscid flux vector resulted in corresponding Jacobian matrices with undesirable properties. It has previously been shown by Powell et al. (1995) that an 'almost' equivalent MHD system in non-conservative form can be derived. This non-conservative system has a better conditioned eigensystem. Aside from Powell et al., the MHD equations can be derived from basic principles in either conservative or non-conservative form. The Delta x B = 0 constraint of the MHD equations is only an initial condition constraint, it is very different from the incompressible Navier-Stokes equations in which the divergence condition is needed to close the system (i.e., to have the same number of equations and the same number of unknown). In the MHD formulations, if Delta x B = 0 initially, all one needs is to construct appropriate numerical schemes that preserve this constraint at later time evolutions. In other words, one does not need the Delta x B condition to close the MHD system. We formulate our new scheme together with the Cargo & Gallice (1997) form of the MHD approximate Riemann solver in curvilinear grids for both versions of the MHD equations. A novel feature of our new method is that the well-conditioned eigen-decomposition of the non-conservative MHD equations is used to solve the conservative equations. This new feature of the method provides well-conditioned eigenvectors for the conservative formulation, so that correct wave speeds for discontinuities are assured. The justification for using the non-conservative eigen-decomposition to solve the conservative equations is that our scheme has a better control of the numerical error associated with the divergence of the magnetic condition. Consequently, computing both forms of the equations with the same eigen-decomposition is almost equivalent. It will be shown that this approach, using the non-conservative eigensystem when solving the conservative equations, also works well in the context of standard shock-capturing schemes.

Yee, H. C.↗