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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

Implementation of Preconditioned Dual-Time Procedures in OVERFLOW

Preconditioning methods have become the method of choice for the solution of flowfields involving the simultaneous presence of low Mach and transonic regions. It is well known that these methods are important for insuring accurate numerical discretization as well as convergence efficiency over various operating conditions such as low Mach number, low Reynolds number and high Strouhal numbers. For unsteady problems, the preconditioning is introduced within a dual-time framework wherein the physical time-derivatives are used to march the unsteady equations and the preconditioned time-derivatives are used for purposes of numerical discretization and iterative solution. In this paper, we describe the implementation of the preconditioned dual-time methodology in the OVERFLOW code. To demonstrate the performance of the method, we employ both simple and practical unsteady flowfields, including vortex propagation in a low Mach number flow, flowfield of an impulsively started plate (Stokes' first problem) arid a cylindrical jet in a low Mach number crossflow with ground effect. All the results demonstrate that the preconditioning algorithm is responsible for improvements to both numerical accuracy and convergence efficiency and, thereby, enables low Mach number unsteady computations to be performed at a fraction of the cost of traditional time-marching methods.

Pandya, Shishir A.↗
NASA NTRS2010

L Band Brightness Temperature from Forest: Comparison of Approximate Techniques

In this paper, three approximate physical microwave radiometry models have been used to calculate brightness temperatures from a forest canopy at L-band. These models are (1) tau-omega model (zero order scattering approximation to radiative transfer equations), (2) successive order of scattering model up to first order (first order scattering approximation to the radiative transfer equations), and (3) Peak technique utilizing the active solution obtained from the Distorted Born Approximation (DBA). These models are physically-based and treat vegetation as a layer of discrete scatterers over a rough surface. Vegetation components within the canopy are represented by canonical shapes such as dielectric discs and cylinders. The tau-omega model is based on a zero-order solution to the radiative transfer (RT) equations. The model ignores scattering except for the effect of the scatterers in the attenuation of the emission through the vegetation. Application of the tau-omega model to data acquired during airborne and ground-based campaigns over the years has solidified scientific understanding of microwave interactions with different landscapes. In particular, shrubland, grasslands, agricultural crops, and light to moderate vegetation have been investigated. Its applicability to areas with a significant tree fraction is unknown. The first order scattering model is based on an iterative solution of the RT equation up to the first order. The first order solution is obtained by substituting the zeroth-order solution into the scattering source term and then solving the resulting radiative transfer equations. This formulation adds a new scattering term to the tau-omega model. It represents emission by particles in the layer and emission by the ground that is scattered once by particles in the layer. The resulting model represents an improvement over the standard zero-order solution (the tau-omega model) since it accounts for the scattered vegetation and ground radiation that can have a pronounced effect on the observed brightness temperature. The third model is based on the Peake formulation in conjunction with the DBA. The procedure for calculation of forest emission is accomplished by first calculating the bistatic scattering cross section for each type of scatterer, then by using the DBA to calculate specular albedo of the ground and the diffused albedo of the layer. Once the albedos are determined, Peake s principle relating active and passive problems can be used to determine the effective emissivity of the forest layer.

Kurum, Mehmet↗
NASA NTRS1986

New integration techniques for chemical kinetic rate equations. I - Efficiency comparison

A comparison of the efficiency of several recently developed numerical techniques for solving chemical kinetic rate equations is presented. The solution procedures examined include two general-purpose codes, EPISODE and LSODE, developed as multipurpose differential equation solvers, and three specialzed codes, CHEMEQ, CREK1D, and GCKP84, developed specifically for chemical kinetics. The efficiency comparison is made by applying these codes to two practical combustion kinetics problems. Both problems describe adiabatic, constant-pressure, gas-phase chemical reactions and include all three combustion regimes: induction, heat release, and equilibration. The comparison shows that LSODE is the fastest routine currently available for solving chemical kinetic rate equations. An important finding is that an iterative solution of the algebraic enthalpy conservation equation for temperature can be significantly faster than evaluation of the temperature by integration of its time derivative. Significant increases in computational speed are realized by updating the reaction rate constants only when the temperature change exceeds an amount Delta-T that is problem dependent. An approximate expression for the automatic evaluation of Delta-T is presented and is shown to result in increased computational speed.

Radhakrishnan, K.↗
NASA NTRS1994

Methodology for sensitivity analysis, approximate analysis, and design optimization in CFD for multidisciplinary applications

The straightforward automatic-differentiation and the hand-differentiated incremental iterative methods are interwoven to produce a hybrid scheme that captures some of the strengths of each strategy. With this compromise, discrete aerodynamic sensitivity derivatives are calculated with the efficient incremental iterative solution algorithm of the original flow code. Moreover, the principal advantage of automatic differentiation is retained (i.e., all complicated source code for the derivative calculations is constructed quickly with accuracy). The basic equations for second-order sensitivity derivatives are presented; four methods are compared. Each scheme requires that large systems are solved first for the first-order derivatives and, in all but one method, for the first-order adjoint variables. Of these latter three schemes, two require no solutions of large systems thereafter. For the other two for which additional systems are solved, the equations and solution procedures are analogous to those for the first order derivatives. From a practical viewpoint, implementation of the second-order methods is feasible only with software tools such as automatic differentiation, because of the extreme complexity and large number of terms. First- and second-order sensitivities are calculated accurately for two airfoil problems, including a turbulent flow example; both geometric-shape and flow-condition design variables are considered. Several methods are tested; results are compared on the basis of accuracy, computational time, and computer memory. For first-order derivatives, the hybrid incremental iterative scheme obtained with automatic differentiation is competitive with the best hand-differentiated method; for six independent variables, it is at least two to four times faster than central finite differences and requires only 60 percent more memory than the original code; the performance is expected to improve further in the future.

Taylor, Arthur C., III↗
NASA NTRS1996

MSC/NASTRAN DMAP Alter Used for Closed-Form Static Analysis With Inertia Relief and Displacement-Dependent Loads

Solving for the displacements of free-free coupled systems acted upon by static loads is a common task in the aerospace industry. Often, these problems are solved by static analysis with inertia relief. This technique allows for a free-free static analysis by balancing the applied loads with the inertia loads generated by the applied loads. For some engineering applications, the displacements of the free-free coupled system induce additional static loads. Hence, the applied loads are equal to the original loads plus the displacement-dependent loads. A launch vehicle being acted upon by an aerodynamic loading can have such applied loads. The final displacements of such systems are commonly determined with iterative solution techniques. Unfortunately, these techniques can be time consuming and labor intensive. Because the coupled system equations for free-free systems with displacement-dependent loads can be written in closed form, it is advantageous to solve for the displacements in this manner. Implementing closed-form equations in static analysis with inertia relief is analogous to implementing transfer functions in dynamic analysis. An MSC/NASTRAN (MacNeal-Schwendler Corporation/NASA Structural Analysis) DMAP (Direct Matrix Abstraction Program) Alter was used to include displacement-dependent loads in static analysis with inertia relief. It efficiently solved a common aerospace problem that typically has been solved with an iterative technique.

Source record↗
NASA NTRS1995

Parallel CFD Algorithms for Aerodynamical Flow Solvers on Unstructured Meshes

The Advisory Group for Aerospace Research and Development (AGARD) has requested my participation in the lecture series entitled Parallel Computing in Computational Fluid Dynamics to be held at the von Karman Institute in Brussels, Belgium on May 15-19, 1995. In addition, a request has been made from the US Coordinator for AGARD at the Pentagon for NASA Ames to hold a repetition of the lecture series on October 16-20, 1995. I have been asked to be a local coordinator for the Ames event. All AGARD lecture series events have attendance limited to NATO allied countries. A brief of the lecture series is provided in the attached enclosure. Specifically, I have been asked to give two lectures of approximately 75 minutes each on the subject of parallel solution techniques for the fluid flow equations on unstructured meshes. The title of my lectures is "Parallel CFD Algorithms for Aerodynamical Flow Solvers on Unstructured Meshes" (Parts I-II). The contents of these lectures will be largely review in nature and will draw upon previously published work in this area. Topics of my lectures will include: (1) Mesh partitioning algorithms. Recursive techniques based on coordinate bisection, Cuthill-McKee level structures, and spectral bisection. (2) Newton's method for large scale CFD problems. Size and complexity estimates for Newton's method, modifications for insuring global convergence. (3) Techniques for constructing the Jacobian matrix. Analytic and numerical techniques for Jacobian matrix-vector products, constructing the transposed matrix, extensions to optimization and homotopy theories. (4) Iterative solution algorithms. Practical experience with GIVIRES and BICG-STAB matrix solvers. (5) Parallel matrix preconditioning. Incomplete Lower-Upper (ILU) factorization, domain-decomposed ILU, approximate Schur complement strategies.

Barth, Timothy J.↗
NASA NTRS1983

A fully vectorized numerical solution of the incompressible Navier-Stokes equations

A vectorizable algorithm is presented for the implicit finite difference solution of the incompressible Navier-Stokes equations in general curvilinear coordinates. The unsteady Reynolds averaged Navier-Stokes equations solved are in two dimension and non-conservative primitive variable form. A two-layer algebraic eddy viscosity turbulence model is used to incorporate the effects of turbulence. Two momentum equations and a Poisson pressure equation, which is obtained by taking the divergence of the momentum equations and satisfying the continuity equation, are solved simultaneously at each time step. An elliptic grid generation approach is used to generate a boundary conforming coordinate system about an airfoil. The governing equations are expressed in terms of the curvilinear coordinates and are solved on a uniform rectangular computational domain. A checkerboard SOR, which can effectively utilize the computer architectural concept of vector processing, is used for iterative solution of the governing equations.

Patel, N.↗
NASA NTRS1977

Combustion response modeling for composite solid propellants

A computerized mathematical model of the combustion response function of composite solid propellants was developed with particular attention to the contributions of the solid phase heterogeneity. The one-dimensional model treats the solid phase as alternating layers of ammonium perchlorate and binder, with an exothermic melt layer at the surface. Solution of the Fourier heat equation in the solid provides temperature and heat flux distributions with space and time. The problem is solved by conserving the heat flux at the surface from that produced by a suitable model of the gas phase. An approximation of the BDP flame model is utilized to represent the gas phase. By the use of several reasonable assumptions, it is found that a significant portion of the problem can be solved in closed form. A method is presented by which the model can be applied to tetramodal particle size distributions. A computerized steady-state version of the model was completed, which served to validate the various approximations and lay a foundation for the combustion response modeling. The combustion response modeling was completed in a form which does not require an iterative solution, and some preliminary results were acquired.

Source record↗
NASA NTRS1969

Water-glycol system volume calculation

Two methods calculate the volume of a thermodynamic system. Integral method uses an iterative solution to determine volume based on constants of liquid mass and gas mass. Differential method approximates volume by its initial values plus first-order differential changes in volume as functions of temperature and pressure.

Liley, B.↗
NASA NTRS1967

Study of a global search algorithm for optimal control.

Adaptive random search algorithm utilizing boundary cost-function hypersurfaces measurement to implement Pontryagin maximum principle, discussing hybrid computer use, iterative solution and convergence properties

Brocker, D. H.↗