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At least 1,207 records · Page 67

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NASA NTRS1984

The large-time behavior of the scalar, genuinely nonlinear Lax-Friedrichs scheme

The Lax-Friedrichs scheme, approximating the scalar, genuinely nonlinear conservation law u sub t + f sub x (u) = O where f(u) is, say, strictly double dot f dot a sub asterisk O is studied. The divided differences of the numerical solution at time t do not exceed 2 (t dot a sub asterisk) to the -1. This one-sided Lipschitz boundedness is in complete agreement with the corresponding estimate one has in the differential case; in particular, it is independent of the initial amplitude in sharp contrast to linear problems. It guarantees the entropy compactness of the scheme in this case, as well as providing a quantitative insight into the large-time behavior of the numerical computation.

Tadmor, E.↗

NASA NTRS1985

High Marangoni number convection in a square cavity

Steady thermocapillary flows in a square cavity are computed using a finite difference procedure. Accurate numerical solutions are obtained for as high a Reynolds number as possible, in order to characterize the nature of strongly convective flows of this general class. Only the case of capillary number going to zero is considered, so that the free surface is assumed flat at the leading order. Surface deflections are computed by domain perturbation. Boundary layer formation at different values of the Prandtl number is observed at large values of the Marangoni number and Re. The numerical results are used to infer the relevant scalings of a consistent boundary layer picture of the flow, valid asymptotically as Re goes to infinity.

Zebib, A.↗

NASA NTRS1975

Advances in Application of Fast Semidirect Computational Methods in Transonic Flow

This paper is intended as a review and summary of the advances made in a recently developed approach for rapid numerical solution of the equations of inviscid transonic aerodynamics. The investigation has been limited to two-dimensional, steady, inviscid flow over airfoils in a subsonic free stream, with emphasis on development of a rapid computational technique, rather than on generality of application. The approach uses finite-difference algorithms called "fast direct elliptic solvers" within an iteration scheme. "Direct" means that the entire computation field is solved at once, rather than in successive traverses over the field as in a point- or line-relaxation method. Such an iterative method is referred to as "semidirect." The iterative convergence can be faster than in other relaxation methods because changes are felt simultaneously at all points in each succeeding iteration. Direct elliptic solvers and semidirect methods have restrictions, but these are gradually being removed. Direct solvers were first developed for solving Poisson's equation on a rectangle without interior boundaries. A method to treat first-order systems, a direct Cauchy-Riemann solver has also been developed. Numerical treatment of part of a system of nonlinear equations by a Poisson solver has been reported. Also Poisson solvers in semidirect methods were used for nonseparable elliptic equations. The semidirect method was extended to the solution of a problem of mixed type, where the improved Murman-Cole transonic small-disturbance difference equations were solved. A slightly supercritical flow over a biconvex airfoil was treated successfully, but the iterations did not converge for more strongly supercritical conditions In another work the addition of terms ot both sides of the difference equations stabilized the iteration for supercritical conditions with large supersonic zones. For this, the Cauchy-Riemann solver was revised to incl,ude the needed terms. Most recently, the evaluation of parameters for rapid convergence and comparisons, with Murman's line-relaxation method was described. The method was extended to full second order accuracy in a fully conservative formulation in another work.

Martin, E. Dale↗

NASA NTRS1987

Acoustic gravity waves: A computational approach

This paper discusses numerical solutions of a hyperbolic initial boundary value problem that arises from acoustic wave propagation in the atmosphere. Field equations are derived from the atmospheric fluid flow governed by the Euler equations. The resulting original problem is nonlinear. A first order linearized version of the problem is used for computational purposes. The main difficulty in the problem as with any open boundary problem is in obtaining stable boundary conditions. Approximate boundary conditions are derived and shown to be stable. Numerical results are presented to verify the effectiveness of these boundary conditions.

Hariharan, S. I.↗

NASA NTRS1988

Acoustic gravity waves - A computational approach

Hariharan, S. I.↗

NASA NTRS1980

A perturbation solution for transverse pressure-sensitive combustion instability in an annulus

A method for analysis of combustion instability in rocket motors based on a combination of the Galerkin method and the two-variable (or multiple-scales) perturbation method is developed. The method is illustrated by applying it to the problem of pressure-sensitive combustion instability in a liquid-fuel annular combustion chamber. To the order of approximation inherent in the method it is found that the complete linear stability analysis and most of the nonlinear stability analysis can be carried out in closed form. The results thus obtained are used to clarify several aspects of the interpretation of numerical solutions obtained by previous investigators.

Googerdy, A.↗

NASA NTRS2000

A Posteriori Error Estimation for Finite Volume and Finite Element Approximations Using Broken Space Approximation

We consider a posteriori error estimates for finite volume and finite element methods on arbitrary meshes subject to prescribed error functionals. Error estimates of this type are useful in a number of computational settings: (1) quantitative prediction of the numerical solution error, (2) adaptive meshing, and (3) load balancing of work on parallel computing architectures. Our analysis recasts the class of Godunov finite volumes schemes as a particular form of discontinuous Galerkin method utilizing broken space approximation obtained via reconstruction of cell-averaged data. In this general framework, weighted residual error bounds are readily obtained using duality arguments and Galerkin orthogonality. Additional consideration is given to issues such as nonlinearity, efficiency, and the relationship to other existing methods. Numerical examples are given throughout the talk to demonstrate the sharpness of the estimates and efficiency of the techniques. Additional information is contained in the original.

Barth, Timothy J.↗

NASA NTRS1992

An engineering aerodynamic heating method for hypersonic flow

A capability to calculate surface heating rates has been incorporated in an approximate three-dimensional inviscid technique. Surface streamlines are calculated from the inviscid solution, and the axisymmetric analog is then used along with a set of approximate convective-heating equations to compute the surface heat transfer. The method is applied to blunted axisymmetric and three-dimensional ellipsoidal cones at angle of attack for the laminar flow of a perfect gas. The method is also applicable to turbulent and equilibrium-air conditions. The present technique predicts surface heating rates that compare favorably with experimental (ground-test and flight) data and numerical solutions of the Navier-Stokes (NS) and viscous shock-layer (VSL) equations. The new technique represents a significant improvement over current engineering aerothermal methods with only a modest increase in computational effort.

Riley, Christopher J.↗

NASA NTRS1992

An Engineering Aerodynamic Heating Method for Hypersonic Flow

Riley, Christopher J.↗

NASA NTRS1987

A Taylor weak-statement algorithm for hyperbolic conservation laws

Finite element analysis, applied to computational fluid dynamics (CFD) problem classes, presents a formal procedure for establishing the ingredients of a discrete approximation numerical solution algorithm. A classical Galerkin weak-statement formulation, formed on a Taylor series extension of the conservation law system, is developed herein that embeds a set of parameters eligible for constraint according to specification of suitable norms. The derived family of Taylor weak statements is shown to contain, as special cases, over one dozen independently derived CFD algorithms published over the past several decades for the high speed flow problem class. A theoretical analysis is completed that facilitates direct qualitative comparisons. Numerical results for definitive linear and nonlinear test problems permit direct quantitative performance comparisons.

Baker, A. J.↗

NASA NTRS1987

Application of the CSCM method to the design of wedge cavities

This paper describes the application of the conservative supra characteristic method (CSCM) to predict the flow around two-dimensional slot injection cooled cavities in hypersonic flow. Seven different numerical solutions are presented that model three different experimental designs. The calculations manifest outer flow conditions including the effects of nozzle/lip geometry, angle of attack, nozzle inlet conditions, boundary and shear layer growth and turbulance on the surrounding flow. The calculations were performed for analysis prior to wind tunnel testing for sensitivity studies early in the design process. Qualitative and quantitative understanding of the flows for each of the cavity designs and design recommendations are provided. The present paper demonstrates the ability of numerical schemes, such as the CSCM method, to play a significant role in the design process.

Venkatapathy, Ethiraj↗

NASA NTRS1986

Flash spectroscopic studies of the kinetics of the halorhodopsin photocycle

The photoreactions of halorhodopsin are complicated by the fact that the parent pigment and its photoproducts interact with chloride. Thus, in any photoreaction scheme at least four species have to be accounted for: HR565 and HR578 Cl-, as well as HR640 and HR520 Cl-. A photocycle scheme proposed earlier places the two main photointermediates of halorhodopsin, HR520 Cl- and HR640, into a single photocycle, with a chloride-dependent equilibrium between them [Oesterhelt, D., Hegemann, P., & Tittor, J. (1985) EMBO J. 4, 2351-2356]. This scheme, with the additional feature of direct photoproduction of HR640 from HR565, was tested in this work by using numerical solutions of the appropriate differential equations to simulate flash-induced absorption changes at 500 nm (production of HR520 Cl-) and at 660 nm (production of HR640). The time scale of the simulation was ms following the flash. Comparison of the simulated curves with experimental traces yielded a unique set of three rate constants. The proposed photocycle scheme and these rate constants predict well the shapes and amplitudes of flash traces at various chloride concentrations. It appears from the photocycle scheme, and the numerical values of rate constants, that chloride is bound with high affinity to the parent halorhodopsin molecule, but with much lower affinity to its main photointermediate. This may be the consequence of the fact that in the parent halorhodopsin in the retinal configuration is all-trans, but in the two photointermediates it is 13-cis.

Non-NASA Center↗

DOE OSTI2021

Entropy stable modal discontinuous Galerkin schemes and wall boundary conditions for the compressible Navier-Stokes equations

Entropy stable schemes ensure that physically meaningful numerical solutions also satisfy a semi-discrete entropy inequality under appropriate boundary conditions. Here in this work, we describe a discretization of viscous terms in the compressible Navier-Stokes equations which enables a simple and explicit imposition of entropy stable no-slip and reflective (symmetry) wall boundary conditions for discontinuous Galerkin (DG) discretizations. Specifically, we derive methods for imposing adiabatic no-slip and reflective (symmetry) boundary conditions for modal entropy stable DG formulations which preserve a semi-discrete entropy inequality. Numerical results confirm the robustness and accuracy of the proposed approaches.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1980

Similarity solutions of a strong shock wave propagation in a mixture of a gas and dusty particles

The similarity solutions of a strong shock wave propagation in a mixture of a gas and small solid particles have been investigated. Similarity solution exists only when the shock is very strong and the surrounding medium is of a constant density and at rest and with negligible counterpressure. The non-dimensional fundamental equations are derived and studied. The results depend on three non-dimensional parameters; i.e. (1) the ratio of the specific heats of the gas, (2) the mass concentration of the solid particles in the mixture and (3) the ratio of the density of the solid to that of initial density of the gas. Numerical solutions for various values of these parameters are presented and discussed. The speeds of the shock wave front and its location with various energy releases are given.

Pai, S. I.↗

NASA NTRS2002

Gust Acoustics Computation with a Space-Time CE/SE Parallel 3D Solver

The benchmark Problem 2 in Category 3 of the Third Computational Aero-Acoustics (CAA) Workshop is solved using the space-time conservation element and solution element (CE/SE) method. This problem concerns the unsteady response of an isolated finite-span swept flat-plate airfoil bounded by two parallel walls to an incident gust. The acoustic field generated by the interaction of the gust with the flat-plate airfoil is computed by solving the 3D (three-dimensional) Euler equations in the time domain using a parallel version of a 3D CE/SE solver. The effect of the gust orientation on the far-field directivity is studied. Numerical solutions are presented and compared with analytical solutions, showing a reasonable agreement.

Wang, X. Y.↗

DOE OSTI2022

Conservative DG method for the micro-macro decomposition of the Vlasov–Poisson–Lenard–Bernstein model

The micro-macro (mM) decomposition approach is considered for the numerical solution of the Vlasov– Poisson–Lenard–Bernstein (VPLB) system, which is relevant for plasma physics applications. In the mM approach, the kinetic distribution function is decomposed as $f$ = $\mathscr{E}$[$ρ_f$] + g , where $\mathscr{E}$ is a local equilibrium distribution, depending on the macroscopic moments $ρ_f$ = $∫_{\mathbb{R}}$ $efdv$ = $\langle$$ef$$\rangle$$_{\mathbb{R}}$, where e = (1, $v$, $\frac{1}{2}$ $v^2$) T , and $g$, the microscopic distribution, is defined such that $\langle$$eg$$\rangle$$_{\mathbb{R}}$ = 0. We aim to design numerical methods for the mM decomposition of the VPLB system, which consists of coupled equations for $ρ_f$ and $g$. To this end, we use the discontinuous Galerkin (DG) method for phase-space discretization, and implicit-explicit (IMEX) time integration, where the phase-space advection terms are integrated explicitly and the collision operator is integrated implicitly. We give special consideration to ensure that the resulting mM method maintains the $\langle$$eg$$\rangle$$_{\mathbb{R}}$ = 0 constraint, which may be necessary for obtaining (i) satisfactory results in the collision dominated regime with coarse velocity resolution, and (ii) unambiguous conservation properties. The constraint-preserving property is achieved through a consistent discretization of the equations governing the micro and macro components. Here, we present numerical results that demonstrate the performance of the mM method. The mM method is also compared against a corresponding DG-IMEX method solving directly for $f$.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Bio‐Imaging quorum sensing signal molecules in a soil‐mimic gel

Rhizosphere, the narrow region surrounding plant roots directly influenced by root exudates and the root associated microbiome, plays an important role in plant productivity and the rhizosphere is well known for stimulating microbial metabolic activities. How microbial communities interact to form stable, metabolically interconnected functional communities is an area of intense interest. The question remains on how microbially produced secreted molecules that function as intercellular communication signals shape the structure and function of microbial communities. Our goal is to detect and quantify signal molecules produced by microbes or plants in the root‐soil environment, spatially and temporarily. As a proof‐of‐concept, we are imaging diffusible extracellular microbial metabolites involved in a bacteria‐bacteria communication process called quorum‐sensing. Quorum‐sensing relies on the accumulation of high concentrations of signal molecules in the environment to control bacterial gene expression, influencing rhizosphere colonization and plant health. Local concentration of quorum sensing molecules are determined using aptamer based sensors. Aptamers that can specifically bind the desired signal molecules are selected through SELEX and immobilized on the surface of nano‐porous membranes. Binding of the signal molecules and aptamer covered surface results in changes in surface charge distribution and steric hinderance and thus modifying the transmembrane ionic transport. Changes in transmembrane impedance can be measured through electrochemical impedance spectroscopy methods to monitor local concentrations of signal molecules. Sensor responses were determined for different concentrations of signal molecules and results showed detection of C4‐HSL in a soil‐mimic solution with K D of 10 nM. We demonstrate that the quorum‐sensing signal molecule C4‐homoserine lactone and (C4‐HSL) can rapidly diffuse in a soil‐mimic gel, providing evidence for our use of a soil‐mimic for further aptasensor development and validation. The sensors were then inserted into soil mimic gel for monitoring C4‐HSL diffusion and the resulted impedance changes were used to determine the C4‐HSL concentration at different positions in the gel. Measurements of local C4‐HSL concentrations variation and numerical solution of diffusion equation were used to create 4D images of C4‐HSL molecule diffusion in the soil‐mimic gel.

Jiang, Nianyu↗

NASA NTRS1974

A study of the solar wind angular momentum including proton thermal anisotropy

The solution to the steady state magnetohydrodynamic equations governing the supersonic expansion of the solar corona into interplanetary space is obtained for various assumptions regarding the form in which proton thermal energy is carried away from the sun. The one-fluid, inviscid, formulation of the MHD equations is considered assuming that thermal energy is carried away by conduction from a heat source located at the base of the corona. Angular motion of the solar wind led to the existence of three critical points through which the numerical solutions must pass to extend from the sun's surface to large heliocentric distances. The results show that the amount of magnetic field energy converted into kinetic energy in the solar wind is only a small fraction of the total expansion energy flux and has little effect upon the final radial expansion velocity.

Acuna, M. H.↗