Iterative Scheme for Numerical Solution of Transonic Small Perturbation Equation

摘要

Computational aspects of Transonic Small Perturbation (TSP) equation are studied. The TSP equation is a consistent approximation of comparable Euler Equations with the sole restriction of small perturbation. A new algorithm for solving conservative discretization of TSP equation is presented. Unconditional stability of the scheme was shown and a number of computational experiments were carried out which demonstrate the ruggedness of the scheme. Despite the TSP equation, though not valid near the blunt leading edge, a large number of calculations in the literature have been made for flow past airfoils like NACA 0012 using TSP equation. Handling of boundary condition in the numerical calculation tends to be ad-hoc near the leading edge. It is shown that if the leading edge slope is integrable a satisfactory analysis can be carried out. Numerical calculations confirm the usefulness of the approach.