Discretization Techniques for Transient, Dynamic and Cyclic Problems in Geotechnical Engineering: First Order Hyperbolic Partial Differential Equations

摘要

In the Chapter devoted to mathematical modelling of transient, cyclic and dynamic problems we have studied two alternative ways to describe these problems, (i) as a system of first order, or (ii) as second order partial differential equations. We will devote this Chapter to Discretization techniques which can be applied for the former. The Chapter is structured as follows: First of all, we will present a fundamental difficulty found in standard Boubnov Galerkin Finite Element methods, which do not work here. Then, we will introduce the Finite Differences Method where we will consider their stability, numerical diffusion and dispersion. In this way, we will gain insight into the problem found in standard FEM. In particular, we will describe the Lax Wendroff scheme, which is the basis of the Taylor Galerkin method in FE described in last Section of the Chapter.