The non-modal linear stability of miscible viscous fingering in a twodimensional homogeneous porous medium has been investigated. The linearizedperturbed equations for Darcy's law coupled with a convection-diffusionequation is discretized using finite difference method. The resultant initialvalue problem is solved by fourth order Runge-Kutta method, followed by asingular value decomposition of the propagator matrix. Particular attention isgiven to the transient behavior rather than the long-time behavior ofeigenmodes predicted by the traditional modal analysis. The transient behaviorsof the response to external excitations and the response to initial conditionsare studied by examining the $\epsilon-$pseudospectra structures and thelargest energy growth function. With the help of non-modal stability analysiswe demonstrate that at early times the displacement flow is dominated bydiffusion and the perturbations decay. At later times, when convectiondominates diffusion, perturbations grow. Furthermore, we show that the dominantperturbation that experiences the maximum amplification within the linearregime lead to the transient growth. These two important features werepreviously unattainable in the existing linear stability methods for miscibleviscous fingering. To explore the relevance of the optimal perturbationobtained from non-modal analysis, we performed direct numerical simulationsusing a highly accurate pseudo-spectral method. Further, a comparison of thepresent stability analysis with existing modal and initial value approach isalso presented. It is shown that the non-modal stability results are in betteragreement, than the other existing stability analyses, with those obtained fromdirect numerical simulations.
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