A new finite element based Lax-Wendroff/Taylor-Galerkin methodology for computational dynamics

The present paper proposes the development of a new and effective methodology of computation for general computational dynamics. Fundamental concepts and characteristic features of the proposed Lax-Wendroff/Taylor-Galerkin algorithm are described and developed in technical detail. The methodology is based on first expressing the finite difference approximations of the transient time-derivative terms in conservation form in terms of a Taylor-series expansion including higher-order time derivatives, which are then evaluated from the governing dynamic equations also expressed in conservation form. The resulting expressions are discretized in space emploting classical Galerkin schemes and quite naturally we advocate the use of finite elements as the principal computational tool for general computational dynamic modeling/analysis. Therein, the concept of average velocity-based formulations is invoked for updating the necessary conservation variables. The stability characteristics and accuracy properties of the proposed formulations are also examined. Comparative sample test cases of numerical model test problems validate the proposed concepts for applicability to general linear/nonlinear computational dynamic problems.