Dynamic structured adaptive mesh refinement (SAMR) techniques along with the emergence of the computational Grid offer the potential for realistic scientific and engineering simulations of complex physical phenomena. However, the inherent dynamic nature of SAMR applications coupled with the heterogeneity and dynamism of the underlying Grid environment present significant research challenges. This paper presents proactive runtime partitioning strategies based on performance prediction functions that are experimentally formulated in terms of system parameters such as CPU load and available memory. These proactive partitioning strategies form a part of the GridARM autonomic framework which enables self-managing, self-adapting, and self-optimizing SAMR applications on the Grid. Experimental evaluation of the proactive schemes using the 3-D Richtmyer-Meshkov compressible fluid dynamics kernel for different system configurations and workloads demonstrates the improvement in overall runtime performance.