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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

Numerical solution of the Navier-Stokes equations for arbitrary 2-dimensional multi-element airfoils

Numerical solutions of the Navier-Stokes equations, with an algebraic turbulence model, for time-dependent two dimensional flow about multi-element airfoils were developed. Fundamental to these solutions was the use of numerically-generated boundary-conforming curvilinear coordinate systems to allow bodies of arbitrary shape to be treated. A general two dimensional grid generation code for multiple-body configuration was written as a part of this project and made available through the COSMIC code library.

Thompson, J. F.↗
NASA NTRS1990

Numerical solution of the boundary-layer equations for a general aviation fuselage

Numerical solutions of the three-dimensional, compressible laminar boundary-layer equations for a general aviation fuselage are presented. The numerical procedure is second-order accurate and independent of the cross-flow velocity direction. Numerical results are presented for a Mach number and unit Reynolds number of 0.3 and 7 x 10 to the 6th/m, respectively, for angles of attack of 0 and 3 deg. Comparisons are made between results obtained using a general nonorthogonal curvilinear body oriented coordinate system and a streamline coordinate system. Axisymmetric analogue results are also compared with the three-dimensional solutions.

Wie, Yong-Sun↗
NASA NTRS1978

Numerical solution of a class of integral equations arising in two-dimensional aerodynamics

We consider the numerical solution of a class of integral equations arising in the determination of the compressible flow about a thin airfoil in a ventilated wind tunnel. The integral equations are of the first kind with kernels having a Cauchy singularity. Using appropriately chosen Hilbert spaces, it is shown that the kernel gives rise to a mapping which is the sum of a unitary operator and a compact operator. This allows the problem to be studied in terms of an equivalent integral equation of the second kind. A convergent numerical algorithm for its solution is derived by using Galerkin's method. It is shown that this algorithm is numerically equivalent to Bland's collocation method, which is then used as the method of computation. Extensive numerical calculations are presented establishing the validity of the theory.

Fromme, J.↗
NASA NTRS1976

Higher-order numerical solutions using cubic splines

A cubic spline collocation procedure was developed for the numerical solution of partial differential equations. This spline procedure is reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy of a nonuniform mesh. Solutions using both spline procedures, as well as three-point finite difference methods, are presented for several model problems.

Rubin, S. G.↗
NASA NTRS1976

Oscillations and stability of numerical solutions of the heat conduction equation

The mathematical model and results of numerical solutions are given for the one dimensional problem when the linear equations are written in a rectangular coordinate system. All the computations are easily realizable for two and three dimensional problems when the equations are written in any coordinate system. Explicit and implicit schemes are shown in tabular form for stability and oscillations criteria; the initial temperature distribution is considered uniform.

Kozdoba, L. A.↗
NASA NTRS1982

Finite analytic numerical solution of heat transfer and flow past a square channel cavity

A numerical solution of flow and heat transfer characteristics is obtained by the finite analytic method for a two dimensional laminar channel flow over a two-dimensional square cavity. The finite analytic method utilizes the local analytic solution in a small element of the problem region to form the algebraic equation relating an interior nodal value with its surrounding nodal values. Stable and rapidly converged solutions were obtained for Reynolds numbers ranging to 1000 and Prandtl number to 10. Streamfunction, vorticity and temperature profiles are solved. Local and mean Nusselt number are given. It is found that the separation streamlines between the cavity and channel flow are concave into the cavity at low Reynolds number and convex at high Reynolds number (Re greater than 100) and for square cavity the mean Nusselt number may be approximately correlated with Peclet number as Nu(m) = 0.365 Pe exp 0.2.

Chen, C.-J.↗
NASA NTRS1990

Numerical solution of the time-dependent kinetic equation for electrons in magnetized plasma

A numerical solution is developed for the time-dependent kinetic equation describing the evolution of arbitrary distributions of electrons injected into a magnetized plasma. Included in the equation are pitch-angle scattering and energy loss because of Coulomb collisions and magnetic mirroring. The numerical code can be easily modified to include other scattering or radiation terms. The numerical results are shown to agree well with known analytic solutions for various simplified configurations such as homogeneous injection in a homogeneous plasma, electron beams moving with small pitch angle with respect to the magnetic field, and injection into a magnetic trap.

Hamilton, Russell J.↗
NASA NTRS2014

Comptonization in Ultra-Strong Magnetic Fields: Numerical Solution to the Radiative Transfer Problem

We consider the radiative transfer problem in a plane-parallel slab of thermal electrons in the presence of an ultra-strong magnetic field (B approximately greater than B(sub c) approx. = 4.4 x 10(exp 13) G). Under these conditions, the magnetic field behaves like a birefringent medium for the propagating photons, and the electromagnetic radiation is split into two polarization modes, ordinary and extraordinary, that have different cross-sections. When the optical depth of the slab is large, the ordinary-mode photons are strongly Comptonized and the photon field is dominated by an isotropic component. Aims. The radiative transfer problem in strong magnetic fields presents many mathematical issues and analytical or numerical solutions can be obtained only under some given approximations. We investigate this problem both from the analytical and numerical point of view, provide a test of the previous analytical estimates, and extend these results with numerical techniques. Methods. We consider here the case of low temperature black-body photons propagating in a sub-relativistic temperature plasma, which allows us to deal with a semi-Fokker-Planck approximation of the radiative transfer equation. The problem can then be treated with the variable separation method, and we use a numerical technique to find solutions to the eigenvalue problem in the case of a singular kernel of the space operator. The singularity of the space kernel is the result of the strong angular dependence of the electron cross-section in the presence of a strong magnetic field. Results. We provide the numerical solution obtained for eigenvalues and eigenfunctions of the space operator, and the emerging Comptonization spectrum of the ordinary-mode photons for any eigenvalue of the space equation and for energies significantly lesser than the cyclotron energy, which is on the order of MeV for the intensity of the magnetic field here considered. Conclusions. We derived the specific intensity of the ordinary photons, under the approximation of large angle and large optical depth. These assumptions allow the equation to be treated using a diffusion-like approximation.

acceleration of particles↗
NASA NTRS1993

Numerical solution of wave equations for the stability of the inner cometo-sheath

Numerical solution of the MHD wave equations for stability of the cometary sheath determined by the balance between the inward Lorentz body force and the outward ion-neutral drag force is obtained by using a two-point boundary value method. The eigenvalues and the eigenfunctions are obtained numerically by treating the cometary inner sheath as a layer of finite thickness, bounded by the contact surface, i.e., the diamagnetic cavity boundary. The magnetic field structure discovered in the ionosphere of Comets Halley and Giacobini-Zinner is found to be unstable. The effects of finite plasma pressure, dissociative recombination, and mass loading due to photoionization are found to be stabilizing but are unable to quench the instability completely. It is also found that the higher the neutral production rate the lesser is the growth rate for the instability.

Srivastava, Krishna M.↗