Computational Fluid Dynamics (CFD) simulation involves the solution of a sparse system of linear equations. Faster convergence to a physically meaningful CFD simulation result of steady-state physics depends largely on the choice of optimum value of the under-relaxation factor (URF) and continuous manual monitoring of simulation residues. In this paper, we present an algorithm for classifying simulation convergence (or divergence) based on the residues using a spiking neural network (SNN) and a control logic. This algorithm maintains optimum URF throughout the simulation process and ensure accelerated convergence of the simulation. The algorithm is also able to stabilize and bring back a diverging simulation to the converging range automatically without manual intervention. To the best of our knowledge, SNN is used for the first time to solve such complex classification problem and it achieves an accuracy of 92.4% to detect the divergent cases. When tested on two steady-state incompressible CFD problems, our solution is able to stabilize every diverging simulation and accelerate the simulation time by at least 10% compared to a constant value of URF.