http://oa.upm.es/927/1/Acta_Astronautica(1007-1039).pdf

The asymptotic structure of counterflow diffusion flames for large activation energies

The use of a general-purpose code, COLSYS, is described. The code is capable of solving mixed-order systems of boundary-value problems in ordinary differential equations. The method of spline collocation at Gaussian points is implemented using a B-spline basis. Approximate solutions are computed on a sequence of automatically selected meshes until a user-specified set of tolerances is satisfied. A damped Newton's method is used for the nonlinear iteration. The code has been found to be particularly effective for difficult problems. It is intended that a user be able to use COLSYS easily after reading its algorithm description. The use of the code is then illustrated by examples demonstrating its effectiveness and capabilities.

Collocation Software for Boundary-Value ODEs

Counterflow diffusion flames

We discuss algorithmic matters of a computer code for solving linear two-point boundary-value problems. The method of solution uses superposition coupled with an orthonormalization procedure and a variable-step Runge–Kutta–Fehlberg integration scheme. Each time the linearly independent solutions start to lose their numerical independence, the vectors are reorthonormalized before integration proceeds. The underlying principle of the algorithm is then to piece together the intermediate (orthogonalized) solutions, defined on the various subintervals, to obtain the desired solution.

Computational Solution of Linear Two-Point Boundary Value Problems via Orthonormalization

Dispersion-managed solitons in fibre systems and lasers

Solution of nonlinear two-point boundary-value problems is often an extremely difficult task. Quite apart from questions of reality and uniqueness, there is no established numerical technique for this problem. At present, shooting techniques are the easiest method of attacking these problems. When these fail, the more difficult method of finite differences can often be used to obtain a solution. This paper gives examples and discusses the finite difference method for nonlinear two-point boundary-value problems.

Numerical solution of nonlinear two-point boundary problems by finite difference methods

: The development of diffusion flame is analyzed for the stagnation mixing layer created by a jet of fuel injected into the oncoming stream of oxidant at the stagnation region of blunt body. From the analysis, the conditions which distinguish the simple and multiple transitions, from each other, between frozen and equilibrium chemical states were clarified. Though the actual numerical results were obtained for the stagnation mixing layer geometry, the basic findings of the analysis should hold for other diffusion flames also. (Author)

Nonequilibrium anomalies in the development of diffusion flames.

: The paper presents the formulation of the problem, the numerical method leading to solution, and the physical significance of the results obtained for the fluid flow of a viscous merged layer with nonequilibrium chemical reactions The solution is limited to the stagnation region of a blunt body The chemical reactions considered are the dissociation and the recombination of air It is first shown that the reduced Navier-Stokes equation and the corresponding energy and species conservation equations, wherein certain curvature effects have been neglected, are sufficiently accurate for the flow regime in which Re > or approx 20, where Re is the Reynolds number behind the bow shock It is also shown that only in this regime are the nonequilibrium chemical reactions important From the solutions it was found, as was expected, that a strong coupling exists between the chemical reactions and the rarefaction of the shock layer One of the unexpected results is that, for a given flight condition, increase of the surface catalycity causes the shock layer to become thinner Since the increase in surface catalycity reduces the degree of dissociation within the merged shock layer, it had been expected that it would increase the shock layer thickness instead of decreasing it The physical interpretation of the phenomenon and its possible implications are discussed (Author)

James F. Holt

Papers

Numerical solution of nonlinear two-point boundary problems by finite difference methods

Nonequilibrium anomalies in the development of diffusion flames.

Merged stagnation shock layer of nonequilibrium dissociating gas.