Choosing the ideal algorithms and solutions for a scientific application is difficult because of the heterogeneity and dynamism of the application execution phases at runtime. In this paper we present an autonomic programming framework that is capable of self-configuring and self-composing the application solution methods in order to exploit the heterogeneity and the dynamism of the application execution states. We focus our approach on partial differential equation (PDE) problems involving multiple computational phases that are defined in terms of their spatial and temporal characteristics. We have implemented a physics aware runtime manager (PARM) that periodically monitors and analyzes the spatial and temporal characteristics of the application to identify its current execution phase (state). Then PARM will determine an appropriate numerical schemes and algorithms that will most efficiently exploit the current state. Our preliminary results show a significant speedup can be achieved by using PARM