A Numerical Algorithm for the Multidimensional, Multiphase, Viscous Equations of Interior Ballistics,
ARMY BALLISTIC RESEARCH LAB ABERDEEN PROVING GROUND MD
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A numerical method based on a linearized ADIAlternating Direction Implicit scheme is described in the context of the solution procedure for the nonlinear partial differential equations associated with an average two-phase gas-solid, two-dimensional, fully viscous model of interior ballistics. This method was chosen because the linearization of the time-differenced equations within the temporal truncation error permits a non-iterative solution procedure for this implicit scheme, and the splitting of difference equations along the coordinate directions provides a block tridiagonal structure of the solution matrices. The implementation of the algorithm possesses several novel features the algorithm is derived in the context of a moving coordinate system the non-conservational form of the governing equations avoids both mass sources which can be generated by grid motion and singular solutions matrices which can arise in regions on one-phase flow in a two-phase calculation and finally, the Jacobian type matrices which arise from the linearization process are determined by numerical differentiation instead of the usual analytic calculations. This numerical scheme is encoded in the DELTA computer code. Verification of the DELTA algorithm is obtained by comparing simulations to an analytic solution of an isentropic core flow and to the two-dimensional results of an experiment.