Part II. Numerical Simulation

Transcription

1 Part II Numerical Simulation

2 Overview Computer simulation is the rapidly evolving third way in science that complements classical experiments and theoretical models in the study of natural, man-made, and abstract systems and processes. Today, computer simulations are used to provide valuable insights in virtually all fields of science and engineering. A particular type of computer simulations that is widely used in engineering and the natural sciences is what we here refer to as numerical simulation, i.e., the use of computers to solve differential equations describing particular phenomena in natural and man-made processes. Numerical simulation is also the branch of applied mathematics and computer science that is concerned with the correctness, robustness, and efficiency of simulation algorithms and their computer implementation. Through the history of SINTEF Applied Mathematics, our activity on numerical simulation has had two branches, one in Oslo and one in Trondheim. Whereas the activity in Oslo has sprung from a scientific tradition within applied mathematics, our Trondheim activity is more rooted in engineering disciplines and traditions. In Oslo, the earliest activities within numerical simulation among people who were later to become part of SINTEF Applied Mathematics, started in the late 1960s and were concerned with wave analysis. In the beginning, the primary interest was in creating holographic computer displays, but later the research focused more on water waves. Among the highlights of this activity during the last three decades we mention the construction in 1985 of a prototype ocean-wave power plant at Toftestallen in Øygarden, outside Bergen, using the novel and innovative tapered channel principle, and the development in of the UNDA computer simulator for calculations of fully nonlinear and dispersive waves around marine structures based on a novel spline-collocation method for potential flow. The development of UNDA was funded by a consortium of Norwegian oil companies (Norsk Hydro, Statoil, Norske Conoco, Saga Petroleum, and Norske Shell) and is a good example of fundamentally new mathematical and numerical algorithms being invented to answer current industry needs. After the turn of the century, our activities within wave modelling started to focus more on using nonlinear wave models (higher-order modified nonlinear Schrödinger equations) as described in the paper by Trulsen. The aim of this activity was to describe various aspects of nonlinear ocean waves such as deterministic wave forecasting and statistical analysis of extreme waves (sometimes called freak or rogue waves) based on deterministic wave simulation. Potential benefits include better understanding of their occurrence, properties and statistics, including the possibility for predicting hazardous wave conditions that might affect marine operations. Due to the lack of a sufficient level of industry funding, the activity on wave modelling has been relocated from SINTEF to the University of Oslo. For more information on past and current activity, see

3 188 Part II: Numerical Simulation In Trondheim, an important milestone in the prehistory of SINTEF Applied Mathematics was the initiation of the national supercomputing project in late 1986 and the subsequent installation of the first Norwegian supercomputer, a Cray X-MP/24. Since then, our researchers have been concerned with high-performance computing, in the beginning on specialised hardware like the Cray X-MP and its predecessors, and later on cluster solutions based on commodity hardware. In early 2003, researchers in Oslo spotted an emerging and exotic field called GPGPU (general-purpose computing using graphics hardware), in which researchers around the world were trying to exploit the unrivalled ability of modern graphics hardware to process floating-point data in scientific computing. Soon we were convinced that this was going to be important in the future, and we therefore initiated a strategic project within this field with funding from the Research Council of Norway. To investigate the capabilities of graphics cards, we choose to study the implementation of high-resolution schemes for hyperbolic conservation laws, which are particularly well suited for the parallel computing paradigm of data-based stream processing. The paper by Hagen et al. gives a thorough introduction to the idea and the results we obtained, which are in fact amazing. By moving computations from the CPU to the GPU, we typically observe a speedup of at least one order of magnitude. Given the current trend with multi-core computers and emerging multi-gpu solutions, we believe that harnessing the combined computing power of instruction-driven CPUs and data-stream processors like GPUs will be the predominant way of scientific and technical computing in the future. The Department of Numerical Simulation, the predecessor of the current simulation group in Oslo, was formed in the mid 1990s. Before the turn of the century, its researchers worked mainly on mathematical and numerical analysis of flow models in particular models for flow in porous media as part of two large strategic research programs. The main theme in these projects was the development of object-oriented numerical software tools, a new and groundbreaking idea in the early 1990s, which in SINTEF s case led to the development of Diffpack ( in collaboration with the University of Oslo. This work has been documented in a previous book by SINTEF Applied Mathematics, Numerical Methods and Software Tools in Industrial Mathematics, Birkhäuser, 1997, and in the popular textbook Computational Partial Differential Equations - Numerical Methods and Diffpack Programming by Hans Petter Langtangen on Springer Verlag. These early strategic research programs had a strong focus on educating doctoral and master students and laid the foundations of what are now flourishing research groups at Simula Research Laboratory ( The simulation group in Oslo still has a focus on educating students, as is clearly reflected in the paper by Aarnes, Gimse, and Lie. The paper gives an introduction to flow modelling in petroleum reservoirs, where the emphasis has been put on presenting simple, yet efficient Matlab codes that can later be a starting point for (advanced) students in their studies and research. The

4 Overview 189 material has been used by several of our master and doctoral students and will hopefully prove to be useful to others as well. Given Norway s role as a major international exporter of oil, it is natural that research related to the recovery of petroleum resources from the North Sea has been an important activity at SINTEF Applied Mathematics throughout the past fifteen years. The focus of our geometric modelling group has been on geological modelling and in particular on surface reconstruction of horizons and faults from large sets of geological data for customers like Roxar and former Technoguide (now Schlumberger Petrel). The simulation group, on the other hand, focuses more on discretisation of models for fluid flow and development of solvers with very high efficiency. On the industry side, the group has had a long-term alliance with the FrontSim-group within Schlumberger, dating back to the former company Technical Software Consultants, with whom we have developed streamline methods for three-phase and compositional flow. Similarly, in industry projects for Statoil, our researchers have studied flow in pore networks, models for nuclear magnetic resonance in core samples, and aspects of upscaling small-scale geological models. In 2004, our activities took a new direction, when we were awarded a strategic institute program on multiscale methods for reservoir simulation from the Research Council of Norway; see for a description of the project. Here, this activity is represented through the paper by Aarnes, Kippe, Lie, and Rustad, which describes problems in modelling and simulation related to the large discrepancies in physical scales in geological models. A thorough discussion of various upscaling methods is given, leading up to our current research on multiscale simulation methods. From being purely academic research ten years ago, multiscale techniques are now starting to migrate into industry. Our group has made several important contributions to this end; for instance, the extension of the methodology to the complex grid types used by the petroleum industry. Starting from our basic research on multiscale methodologies in the strategic GeoScale project, we have during the last year built up a portfolio of industry projects aiming at the development of highly efficient solvers for direct flow simulation of industry-standard geomodels of highly heterogeneous and fractured porous media. At the time of writing (October 2006), the focus of our research is on extending the multiscale methodology to complex grids with nonmatching faces used, for instance, to model faults. Another application of our multiscale methodologies is within history matching (i.e., adjustment of the geological reservoir description to reflect observed production history), where these methods can be used to enable fast matching of models with multimillion cells. In the final paper in the second part of the book, Utnes gives an introduction to stratified geophysical flow over variable topography. Simulating fine-scale processes like e.g., extreme wind and turbulence in mountain areas, is a main challenge within weather prediction. Researchers in our simulation group in Trondheim have since around 1990 worked on predicting local flow in

5 190 Part II: Numerical Simulation mountainous terrain in an effort to increase aviation safety. This work has been motivated by the belief that turbulence-windshear has been the major cause of at least 11 fatal accidents in Norwegian aviation during the last 25 years. High-resolution non-hydrostatic models enable a much better description of the vertical motion in geophysical flows in steep terrain and in small-scale dynamic weather systems, e.g., as seen around a number of Norwegian airports. SINTEF has developed a high-resolution non-hydrostatic finite-element code denoted SIMRA. This code is today used in daily operation by the Norwegian Meteorological Institute in a nested system for local wind prediction at a number of airports in Norway in an effort to increase aviation safety by avoiding the most hazardous flying conditions; the paper reports an example of use for the Trondheim Airport at Værnes. Knut Andreas Lie Chief Scientist Editor, Numerical Simulation