On a Taylor Weak Statement for Finite Element Computations in Gas Dynamics

The Taylor Weak Statement has been developed as a potential unified approach for approximate computation of fluid flows. It is verified to contain a variety of numerical dissipative methods developed for advection problems by specific identification of its expansion parameters. Generalized Fourier modal analysis has been completed in one space dimension for both semi-and fully-discrete approximations, from which the flux limiter method is herein developed and evaluated for finite element computations. Its application to 1- and 2-dimensional scalar models is investigated for continuous and discontinuous initial value problems, and its use for the Euler equation system of gas dynamics in 1- and 2-dimensional cases is demonstrated.