Initial Boundary Value Problems, Summation-By-Parts Operators and Weak Boundary Conditions with Multi-Physics Applications

Jan Nordstrom
Seminar

During the last decade, stable high order finite difference methods, as well as finite volume methods applied to initial-boundary-value-problems, have been developed. The stability is due to the use of so-called summation-by-parts operators (SBP), penalty techniques for implementing boundary and interface conditions, and the energy method for proving stability. In this talk, we discuss some aspects of this technique, including the relation to the initial-boundary-value-problem. By reusing the main ideas behind the recent development, new coupling precodures for multi-physics applications have been developed. We will present the theory by analyzing simple examples and apply to complex multi-physics problems such as fluid flow problems, elastic and electromagnetic wave propagation, fluid-structure interaction, and conjugate heat transfer.