Project A5 (finished)

Project A5 - Higher Order Finite Volume Particle Methods using the ADER Approach

Principal investigator: Armin Iske

Background and Motivation

In contemporary applications of scientific computing, models based on conservation laws are considered. These physical laws are usually described by a system of time-dependent hyperbolic partial differential equations. Although there already exists a large variety of different high-performance numerical methods to solve these equations, novel approaches are still under investigation. One example is the Finite Volume Particle Method (FVPM), which may be regarded as a meshfree method, i.e., its formulation does not necessarily require to a mesh. Therefore, the conservative FVPM is highly flexible and, moreover, potentially useful for the numerical simulation of multiscale phenomena, for high-dimensional problems, for problems with complicated geometries, moving boundaries, or rapid variations of the solution. .

Aims and Objectives

The aim of this project is to design and to analyze a FVPM of arbitrary high order. To this end, we combine a kernel-based high order spatial reconstruction scheme with the ADER approach for the flux evaluation. The resulting highly accurate FVPM will be a prototype for a class of highly flexible meshfree methods, giving an alternative tool to efficiently solve hyperbolic problems in future applications.

PhD student: Libor Kadrnka

Libor Kadrnka successfully defended his PhD on 28 January 2015.