Numerical Wave Propagation 211 Based on Wave Primitives

Compact higher order finite difference equations are applied to a sequence of problems in wave propagation and aeroacoustics. Systems of PDE's are reduced to a sequence of simple wave primitives using a local eigenvector decomposition. The wave primitives are first order PDE's in two independent variable and allow natural boundary conditions to be imposed for both single- and multidimensional problems. The method uses a "discrete dispersion relation" approach to obtain high order approximations to the wave primitives on a 3 spatial point / 2 time level computational molecule. The scheme is fourth order accurate for the class of system with constant coefficients, e.g., those that support exponential solutions. Weakly non-linear PDE's are solved in a similar manner using a variant of the "method of frozen coefficients." Experience with the new algorithm for linear, non-linear, and multi-dimensional test problems will be described.