A boundary method for calculating the growth of an instability in a system of two fluids



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A boundary method is presented to solve numerically the problem of gravitational instability for large perturbations in a system of two visco-elastic materials. It is assumed that the inertial terms in the Navier-Stokes[raised 1] equations could be neglected because of the large viscosities. The resulting linear equations were solved by finite sine and cosine transforms. The infinite series solutions were truncated, an initial interface was assumed, the constants of integrations were found from the boundary conditions, and, hence, the velocity fields were determined. The interface was then advanced to a new position. Thus, the new shape of the interface was traced for any time. When the initial perturbation was small the results were nearly those obtainable by the linear theory. Numerical results are presented for large and small perturbations. The method seems to offer a new tool for attacking a certain class of moving-boundary problems.