Abstract: Simulation of dynamic physical systems is done using iterative solvers. However, this iterative process is a time consuming and compute intensive process and, for a given set of simulation parameters, the solution does not always converge to a physically meaningful solution, resulting in huge waste of man hours and computation resource. Embodiments herein provide a method and system for stabilizing a diverged numerical simulation and accelerating a converged numerical simulation by changing one or more control parameters. An automatic monitoring mechanism of residue history (to interpret convergence or divergence) and a subsequent control logic to auto-tune the under-relaxation factor would help in stabilizing a diverging simulation and reaching faster convergence by accelerating converging simulation.