The interaction between the mechanisms of ablation and boundary layer transition is one of the phenomena that leads to difficulties in heat-flux prediction during atmospheric entries. The objective of this work is to develop a computational tool based on a highorder discontinuous Galerkin method (DGM), that simulates and models the flow and wall phenomena in a unified approach. As a first step, a one-dimensional code has been developed for the in-depth thermal response of ablative materials. This paper demonstrates the capability of DGM for discretizing the highly-nonlinear problem equations, discusses specificities of the method to ensure stability and illustrates the subsequent validation. A sharp interface method is proposed to face the challenges of recession front modeling.Nomenclature E a Activation energy, J · mol −1 e Specific energy, J · kg −1 h Specific enthalpy, J · kg −1