A NUMERICAL STUDY OF NONLINEAR PROPAGATION OF DISTURBANCES IN 2-DIMENSIONS

In the spirit of the method of characteristics, we present in this pap er a generalized Taylor-Galerkin finite element model to simulate the nonlinear propagation of finite-amplitude disturbances. In a nonlinear Euler system, the multi-dimensional formulation is constructed throug h the conservation variables. Noticeable is that the scheme is found t o exhibit high-phase-accuracy, together with minimal numerical damping . This scheme, therefore, is best-suited to simulation of disturbances in an acoustic field. To begin with, we validate the characteristic m odel by simulating two transport problems amenable to analytic solutio ns. Motivated by the apparent success, we apply the proposed third-ord er accurate upwind model to investigate a truly nonlinear acoustic fie ld. The present analysis is intended to elucidate to what extent the n ondissipative, nondispersive and isotropic characteristics pertaining to three wave modes of the acoustic system are still valid.