ASA 126th Meeting Denver 1993 October 4-8

5aPA3. A multidimensional numerical algorithm to simulate the propagation of a shock wave through caustics.

Andrew A. Piacsek

Graduate Program in Acoust., Penn State Univ., P.O. Box 30, State College, PA 16804

One strategy in the effort to explain features of observed sonic boom profiles that deviate from the classical N shape is to simulate, one a computer, the propagation of shock waves in an inhomogeneous medium. A time-marching finite-difference code is being developed by the author which employs a multidimensional explicit flux corrected transport scheme, based on work by Zalesak [J. Comp. Phys. 31, 335--362 (1979)] and McDonald (NPE source code and private communication). Certain essential features of the program have been examined by comparing the results of some simplified cases to published results of other numerical schemes and, where they are known, to analytical solutions. Specifically, results will be shown regarding the code's ability to simulate the 2-D linear propagation of a curved shock wave front in a homogeneous medium, and 1-D nonlinear propagation of pulses with dissipation and molecular relaxation. Also presented will be some results of 2-D nonlinear propagation, in which an N wave with a curved wave front passes through a caustic. [Work supported by NASA and the William E. Leonhard endowment to the Pennsylvania State University.]