Computational Science and High Performance Computing IV The 4th Russ
This volume contains 27 contributions to the Forth Russian-German Advanced Research Workshop on Computational Science and High Performance Computing presented in October 2009 in Freiburg, Germany. The workshop was organized jointly by the High Performance
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bstract. In this work we present simulations of different types of geophysical problems using the D UNE and D UNE -F EM software framework. We consider twophase flow in porous media, a Stokes-Darcy coupled problem, and atmospheric flow problems. The basis of our schemes is the Discontinuous Galerkin discretizations.
1 Introduction The main aspect of the D UNE and D UNE -F EM project is the development of an interface library for solving partial differential equations, especially non-linear systems of evolution equations. These systems are used in many different fields of applications from astrophysics to industrial problems to model the evolution of physical quantities U, e.g., density, momentum, and energy of a fluid. A very general form of these equations is
∂t U + ∇ · (F(U) − A(U)∇U) = S(U) + T [U].
(1)
This is an advection-diffusion-reaction equation including a non-local operator T ; this last term is used to model for example self-gravitation or radiation in astrophysics. Our goal is to develop a general framework for solving this type of equations based on modern software design techniques. Hereby, efficiency and the reuse of code is a major aspect in the design process. Furthermore, the interface should allow for a straight forward modification of both the model and the underlying scheme, so that the development and testing of new numerical schemes becomes an easy task. Also, due to the complexity of the applications mentioned above, parallelization combined with local grid adaptation is a central ingredient for the Slavko Brdar · Andreas Dedner · Robert Klöfkorn · Mirko Kränkel · Dietmar Kröner Section of Applied Mathematics, University of Freiburg i. Br., Hermann-Herder-Straße 10, Freiburg i. Br., 79104, Germany e-mail: dedner,slavko,robertk,kraenkel, [email protected] E. Krause et al. (Eds.): Computational Sci., & High Performance Computing IV, NNFM 115, pp. 93–106. c Springer-Verlag Berlin Heidelberg 2011 springerlink.com
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implementation of efficient numerical schemes. To be able to concentrate on the underlying applications and on the design of new numerical schemes, aspects like load-balancing in a distributed computational environment should not be a concern of the researcher working on the project; the underlying software library should handle all these aspects in a transparent manner.
2 The D UNE Interface Library – Recent Development All the design restrictions mentioned in the introduction require the use of modern software design techniques. These strategies have already been successfully applied during the development of the D UNE grid interface [2, 3, 4]. The grid interface library allows the generic access to the grid structure which forms the basis of most numerical schemes for solving partial differential equations. Lately, version 2.0 of D UNE (consisting of the the D UNE core modules: D UNE -C OMMON, D UNE -G RID, D UNE -I STL) has been released showing that the development on the grid interface and the iterative solver template library has reac
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