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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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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Conjugate quasilinear Dirichlet and Neumann problems and a posteriori error bounds

Quasilinear Dirichlet and Neumann problems on a rectangle D with boundary D prime are considered. Using these concepts, conjugate problems, that is, a pair of one Dirichlet and one Neumann problem, the minima of the energies of which add to zero, are introduced. From the concept of conjugate problems, two-sided bounds for the energy of the exact solution of any given Dirichlet or Neumann problem are constructed. These two-sided bounds for the energy at the exact solution are in turn used to obtain a posteriori error bounds for the norm of the difference of the approximate and exact solutions of the problem. These bounds do not involve the unknown exact solution and are easily constructed numerically.

Lavery, J. E.↗
NASA NTRS1988

Solution of the Neumann pressure problem in general orthogonal coordinates using the multigrid technique

The multigrid (MG) technique has been advanced for use with Neumann boundary-value problems in clustered curvilinear orthogonal coordinates. This comprises an important step in the analysis of incompressible flow using the velocity-pressure formulation of the Navier-Stokes equations. The finite-difference representation of the problem and the formulation of the restriction and coarse-grid correction operators are examined in detail. Maintaining consistency between these and the integral constraint associated with the Neumann problem is found to be critical for the success of the MG technique. The influence of the smoothing operator is examined by employing Gauss-Seidel, alternating-direction implicit, and strongly implicit techniques. The MG procedure enhances the efficiency of fine-grid solutions of the Neumann problem by a factor of 3 to 14, depending on the type of smoothing operator employed and the values of the problem parameters.

Ghia, U.↗
NASA NTRS1996

Convergence of a Substructuring Method with LaGrange Multipliers

We analyze the convergence of a substructuring iterative method with Lagrange multipliers, proposed recently by Farhat and Roux. The method decomposes finite element discretization of an elliptic boundary value problem into Neumann problems on the subdomains and a coarse problem for the subdomain nullspace components. For linear conforming elements and preconditioning by the Dirichlet problems on the subdomains, we prove the asymptotic bound on the condition number C(1 + log(H/h))(sup gamma), gamma = 2 or 3, where h is the characteristic element size and H is the subdomain size.

Mandel, Jan↗
NASA NTRS1983

Multi-grid solution of Neumann pressure problem for viscous flows using primitive variables

The multi-grid (MG) technique has been advanced for use with the Neumann boundary-value problem in clustered curvilinear orthogonal coordinates. This comprises an important step in the analysis of viscous flows using the velocity-pressure formulation of the Navier-Stokes equations. With successive over-relaxation (SOR) as the smoothing operator and with suitably formulated restriction and coarse-grid-correction operators, a 4-grid procedure enhances the efficiency of fine-grid solutions of the Neumann problem by a factor of 3 to 5, depending on the problem parameters. Thy influence of the smoothing operator is also examined by employing the alternating-direction implicit and the strongly implicit techniques instead of SOR.

Ghia, U.↗
DOE OSTI2025

On nonlocal problems with Neumann boundary conditions: scaling and convergence for nonlocal operators and solutions

Formulations of Neumann-type boundary conditions for boundary value problems in the nonlocal framework are beset with difficulties, some related to the choice of a proper scaling. Here we identify a space-dependent scaling for a nonlocal Neumann operator, for which we prove linear in δ (δ being the radius for the support for the kernel) convergence of the Neumann operator and $\mathcal{O}$(δ 2 ) convergence of solutions to their classical counterparts. The pointwise-like convergence of the nonlocal normal operator is cast as a new type of two-scale operator-point convergence, which we call condensated convergence . The results hold for general integrable kernels, a setting which is favored in numerical simulations. We support this analysis with numerical convergence studies using a piecewise linear discontinuous Galerkin discretization and show an $\mathcal{O}$(δ 2 ) rate of convergence of solutions, also exhibiting an $\mathcal{O}$(h 2 ) convergence, where h is the mesh size.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1986

Improving the convergence rate to steady state of parabolic ADI methods

The present, residuals' L(2)-norms analysis of the rate of convergence to steady state for parabolic ADI solvers allows the prediction of the number of iterations required for convergence, as a function of the Courant number alpha. A modification of current ADI codes is presented which significantly improves the convergence rate and is insensitive to the Courant number over a large range of alpha. This corrected algorithm is tested for the cases of Dirichlet problems for uniform grids of many mesh sizes, mixed Dirichlet-Neumann problems, and problems defined on stretched grids and/or problems with variable coefficients.

Abarbanel, Saul S.↗
NASA NTRS1979

A new approach to the solution of large, full matrix equations: A two-dimensional potential flow feasibility study

An approach to the solution of matrix problems resulting from integral equations of mathematical physics is presented. Based on the inherent smoothness in such equations, the problem is reformulated using a set of orthogonal basis vectors, leading to an equivalent coefficient problem which can be of lower order without significantly impairing the accuracy of the solution. This approach was evaluated using a two-dimensional Neumann problem describing the inviscid, incompressible flow over an airfoil. Two different kinds of mode functions were investigated, namely eigenfunction series and Fourier series. The method using Fourier series was found preferable. It uses all of the coefficients from a Fast Fourier Transform algorithm in an approximate method which exploits the known structure of the transformed coefficient matrix and very promising results for the flow over a realistic airfoil are obtained. On the basis of the results presented here, an order of magnitude reduction in this computer time can be expected for such problems as compared with the time for a direct matrix solution.

James, R. M.↗
NASA NTRS1980

Grid generation using classical techniques

A brief historical review of conformal mapping and its applications to problems in fluid mechanics and electromagnetism is presented. The use of conformal mapping as a grid generator is described. The philosophy of the 'closed form' approach and its application to a Neumann problem is discussed. Karman-Trefftz mappings and grids for ablated, three dimensional bodies are also discussed.

Moretti, G.↗
NASA NTRS1978

A well posed boundary value problem in transonic gas dynamics

A boundary value problem for the Tricomi equation was studied in connection with transonic gas dynamics. The transformed equation delta u plus 1/3Y u sub Y equals 0 in canonical coordinates was considered in the complex domain of two independent complex variables. A boundary value problem was then set by prescribing the real part of the solution on the boundary of the real unit circle. The Dirichlet problem in the upper unit semicircle with vanishing values of the solution at Y = 0 was solved explicitly in terms of the hypergeometric function for the more general Euler-Poisson-Darboux equation. An explicit representation of the solution was also given for a mixed Dirichlet and Neumann problem for the same equation and domain.

Sanz, J. M.↗
NASA NTRS1981

New approach to the solution of large, full matrix equations

A new approach to the solution of matrix equations resulting from integral equations is presented and applied to the solution of two-dimensional Neumann problems describing the inviscid, incompressible flow past an airfoil. The problem is reformulated in terms of a preselected set of mode functions giving an equivalent matrix equation to be solved for the mode-function expansion coefficients. Because of the inherent smoothness of the original problem, the coefficient problem can be solved approximately without significantly affecting the accuracy of the final solution. Very promising two-dimensional results are obtained and the extension of the method to three-dimensional problems is investigated. On the basis of these results it is shown that the computing time for the matrix solution for a large three-dimensional panel method calculation could be reduced by an order of magnitude compared with that required for a direct solution.

Clark, R. W.↗
NASA NTRS1982

Computer prediction of three-dimensional potential flow fields in which aircraft propellers operate

A computer program was developed to calculate the three dimensional, steady, incompressible, inviscid, irrotational flow field at the propeller plane (propeller removed) located upstream of an arbitrary airframe geometry. The program uses a horseshoe vortex of known strength to model the wing. All other airframe surfaces are modeled by a network source panels of unknown strength which is exposed to a uniform free stream and the wing-induced velocity field. By satisfying boundary conditions on each panel (the Neumann problem), relaxed boundary conditions being used on certain panels to simulate inlet inflow, the source strengths are determined. From the known source and wing vortex strengths, the resulting velocity fields on the airframe surface and at the propeller plane are obtained. All program equations are derived in detail, and a brief description of the program structure is presented. A user's manual which fully documents the program is cited. Computer predictions of the flow on the surface of a sphere and at a propeller plane upstream of the sphere are compared with the exact mathematical solutions. Agreement is good, and correct program operation is verified.

Jumper, S. J.↗
NASA NTRS1987

Gravity and conduction driven melting in a sphere

In the Stefan and Neumann problems fundamentally characterizing melting, unmolten portions of a solid undergoing phase changes within spherical containers are assumed to remain stationary. An approach to these issues that is related to the theories of lubrication and film condensation is presently employed in conjunction with an approximate, closed-form solution of melting within spheres. It is shown that a group of dimensionless parameters containing Prandtl, Archimides and Stefan numbers can describe the melting process. Also given are the results of fundamental heat transfer experiments performed on the melting of a phase-change medium in a spherical shell.

Bahrami, P. A.↗
DOE OSTI2025

Development, Verification, and Validation of an OpenFOAM-Based Solver for Modeling Inertial Fusion Energy Chambers

Our work seeks to introduce a computational tool tailored to the physics of inertial fusion energy chambers, in particular, those concepts based on thick liquid walls. In this approach, the structural materials are protected by several neutron mean-free-paths of renewable liquid and thus will be able to survive much longer than un-shielded walls, with virtually all structures lasting for the life of the plant and enabling the use of commercially available and qualified materials. The OpenFOAM-based solver named rhoCentralFoam has been used as a starting point. rhoCentralFoam belongs to the standard OpenFOAM solver toolset. It is a high-speed, explicit compressible flow solver with shock-capturing capability. While the main features have been retained, the solver had to be restructured to make use of tabular data for equations of states, a necessary addition to model the complex thermo-physical properties of ionized gasses. This entailed the need to change the independent state variables used by the solver, resulting in a new thermodynamic library and slightly different solution algorithm. Moreover, a radiation heat transfer model based on the P-1 approximation was added to the solver. The solver is verified against an analytical solution from the Sedov-Taylor-Neumann test problem to showcase the ability of the hydrodynamic solvers to handle strong shocks, whereas the P-1 model was verified using a simple one-dimensional problem with an analytical solution. Additionally, a validation case involving shock-wave propagation through jet array is presented, and the results are compared with experimental data from the open literature. Lastly, in order to showcase the utility of the solver for practical cases, we applied the refined solver to two representative scenarios: gas venting within the HYLIFE-II chamber and the compression of the gas following the partial ablation of the liquid wall.

Chamber dynamics↗