Engineering topics
Publications and source records attributed to Horn, M. K..
New interpolation method used with existing Runge-Kutta algorithms. Algorithm evaluates solution at intermediate point within integration step. Only few additional computations required to produce intermediate solution data. Runge-Kutta method provides accurate solution with larger time steps than allowable in other methods.
A set of scaled Runge-Kutta algorithms for the third- through fifth-orders are developed to determine the solution at any point within the integration step at a relatively small increase in computing time. Each scaled algorithm is designed to be used with an existing Runge-Kutta formula, using the derivative evaluations of the defining algorithm along with an additional derivative evaluation (or two). Third-order, scaled algorithms are embedded within the existing formulas at no additional derivative expense. Such algorithms can easily be adopted to generate interpolating polynomials (or dependent variable stops) efficiently.
Low order Runge-Kutta algorithms are developed which determine the solution of a system of ordinary differential equations at any point within a given integration step, as well as at the end of each step. The scaled Runge-Kutta methods are designed to be used with existing Runge-Kutta formulas, using the derivative evaluations of these defining algorithms as the core of the system. For a slight increase in computing time, the solution may be generated within the integration step, improving the efficiency of the Runge-Kutta algorithms, since the step length need no longer be severely reduced to coincide with the desired output point. Scaled Runge-Kutta algorithms are presented for orders 3 through 5, along with accuracy comparisons between the defining algorithms and their scaled versions for a test problem.
The basic structure of a program to generate the truncation error coefficients for Runge-Kutta (RK) methods is reformulated to reduce storage requirements significantly and to accommodate variable dimensioning. This FORTRAN program, SUBROUTINE RKEQ, determines truncation error coefficients for RK algorithms for orders 1 through 10 and extends the order of coefficients through 12 with the 11th- and 12th-order terms determined following the patterns used to establish the lower order coefficients. Both subroutines (the original and RKEQ) are also written to treat RK m-fold methods which utilize m known derivatives of f to increase the order of the algorithm. Setting m = 0 gives the classical RK algorithm.
The effect was studied of nose geometry on the transition criteria for the windward boundary layer, on the extent of separation, on the heat transfer perturbation due to the canopy, and on the surface pressure and the heat transfer in the separated region. The data for each of these problems is analyzed. A literature review that concentrates on separation and the leeward flow-field is presented.