Applications of intrinsic coordinates for simulation of thin shocks in relaxing media

Abstract

The augmented Burgers equation that describes nonlinear propagation in a relaxing fluid can be expressed using intrinsic coordinates [Hammerton and Crighton, JFM 252, 585 (1993)]. A multivalued pressure waveform in physical coordinates can be represented as single-valued with intrinsic coordinates. Shocks can then be inserted into the multivalued pressure waveform using the equal area rule from weak shock theory to obtain a single-valued waveform solution, thus avoiding the high computational cost associated with discretizing thin shocks with conventional algorithms. By first solving the evolution equation in intrinsic coordinates, and then using the solution as the input to a conventional algorithm based on the augmented Burgers equation, a two-stage approach can be developed that achieves both high accuracy and significantly reduced computational cost when compared to solving the Burgers equation with conventional numerical algorithms alone. Approaches based on intrinsic coordinates are applied to realistic problems in relaxing media, which include air and seawater, to allow for comparisons of computational efficiency and accuracy. [WAW is supported by the ARL:UT Chester M. McKinney Graduate Fellowship in Acoustics.]