Date of Award

Spring 1987

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mathematics and Statistics


Computational and Applied Mathematics

Committee Director

Charlie H. Cooke

Committee Member

J. Mark Dorrepaal

Committee Member

Surendra N. Tiwari


A major problem which arises in computer simulation of the firing of a gun weapon is the development of numerical schemes which effectively account for the physics of projectile motion. The chief difficulty is that away from the projectile the calculation is ordinarily accomplished on a fixed numerical grid, whereas due to projectile movement some cells of the grid near the projectile undergo volume changes as the calculation proceeds. A local finite volume scheme is developed which accounts for the expansion or compression of cells fore-and-aft of the projectile. Through the process of numerical experiment, the effectiveness of the scheme is assessed, with quite good results.

The rapid discharge of propellant gas from a gun weapon produces a strong shock wave which propagates into the environment, while other interacting shocks form within the developing plume. For this reason, strong interest in the determination of shock capturing algorithms which can be used away from the projectile arises. In this respect, a theoretical weak derivative form (WDF) is derived for linear hyperbolic systems of conservation laws. The virtue of the WDF approach is that it indicates how to difference in the presence of a flow discontinuity, without differencing across the discontinuity. This differencing produces a robust shock capturing scheme whose extension to the nonlinear case is apparent.

The WDF shock capturing scheme so obtained is shown to be equivalent to a flux-splitting scheme studied by P. L. Roe, thus leading to a better understanding of the schemes of Godunov and Roe, as well as upwind differencing in general. Roe's scheme is investigated in detail. Three views of the scheme are obtained, one of which is new. Harten's second-order accurate extension of Roe's method is then used in simulating the flow around a typical weapon's configuration. These numerical results reinforce the belief that the local finite volume scheme effectively accounts for projectile motion.