Finite difference schemes for the solution of the nosetip shape change equations - Crowell, P. G.; United States. Air Force. Systems Command; Space and Missile Systems Organization (U.S.); Aerospace Corporation (Los Angeles, California : Space and Missile Systems Organization, Los Angeles Air Force Station, Air Force Systems Command, United States Air Force, 1975)
A number of finite difference schemes have been used to solve the nosetip shape change equation for the same surface recession model. The physical description of the surface recession rate (i.e, S) has been made as realistic as possible and includes most of the effects known to influence the shape change process. In particular, two different assumptions concerning the boundary layer edge entropy have been used to obtain both 'smooth' and 'rough' S distributions. Both explicit and implicit first and second order accurate schemes were considered. Naturally dissipative schemes and implicit schemes with the addition of a viscous damping term are examined. Stability limits are obtained from a linearized stability analysis and examined numerically. A number of computationally difficult cases, involving high recession rates and large surface curvature, have been used to evaluate the various difference schemes. The results indicate that the 'standard' forward time-central space explicit scheme is inherently unstable and should not be used for the shape change equation. The sensitivity of the S model to small changes in surface shape is shown to exhibit a strong influence on the accuracy of the difference schemes. The implicit schemes are shown to be superior, particularly for 'rough' S distributions, and are recommended for use in nosetip shape change codes.
"30 September 1975."
Report prepared by Laboratory Operations, Aerospace Corporation, El Segundo, California, under contract No.
Mode of access: Internet.
Keywords: Ablation (Aerothermodynamics); Finite differences; Space vehicles -- Atmospheric entry