Flux-based finite-volume formulations and adaptive time-stepping strategies for modeling of reentry thermal protection systems

This article describes effective thermal modeling and analysis formulations of reusable thermal protection systems (TPS) used in reentry space vehicles employing flux-based finite-volume representations in conjunction with adaptive time-stepping strategies for accurately tracking the nonlinear transient thermal response of such configurations. The flux-based finite-volume representations are developed following the spirit of a Lax-Wendroff /finite-volume-type formulation. In conjunction with a trapezoidal γT family of algorithms and adaptive automated time-stepping strategies that permit a good global error control, the representations offer an improved physical interpretation and mathematical representation of the thermal models with several computationally convenient and attractive features. The adaptive time stepping provides use of an optimal number of time steps in a single analysis and is effective in conjunction with the present physically improved flux-based finite-volume representations for the thermal analysis of large TPS models and the associated structural configurations.