Abstract: The aim of this article is to study the linear growth of the density wave in galaxies by means of numerically resolving unsteady, two-dimensional hydrodynamic equations coupled with Poisson equation under the condition that the local asymptotic solution of linear density wave is given.as an initial value. The results show that the perturbed peak density of linear density wave grows to the same order as the basic state density during merely tens of million years,the spiral pattern emerging which has barred structure in its inner region. The angular velocity of the spiral pattern and the growth rate of perturbed density vary gradually with changes in spatial place and time. The approximate property of quasistationary spiral structure hypothesis is discussed in this paper.

Key words: porous media, wave propagation, visco-elastoplasticity, material stability, dispersivity, hydro-dynamic coupling