## Numerical Modeling

CONTENTS:

Overview

Simulations and Modeling

Numerical Modeling and Space Exploration

SciberNet's Simulations

Related SciberNet Work

Overview

What is the weather going to be like 25 years from now? Is the passenger in a newly designed car going to survive a crash at 50 mph? There are many scientific and engineering questions in modern society that are so complex that they cannot be answered by solving a few simple equations. With the increase in computational speed of workstations and super computers over the past several decades, numerical modeling has become a mainstream approach to understanding complex systems in almost any conceivable technical or research field.

The nature of the questions at hand may vary from problems regarding prediction, to optimization, or even those of strategy. Evidently, the detailed methods and techniques that are employed vary as well. However, there are a number of underlying procedures that are common to modeling and simulation approaches.

Many problems, including those dealing with predictions, are related to the evolution of complex systems over time. These systems consist of various elements that interact with each other. In the example of the weather, these elements are for example the cloud cover, the Sun's light, and the oceans' water temperature. In the case of a car crash study, some of the elements are the various structural parts of the car and their material properties.

Simulations and Modeling

The beauty of simulations is that typically, each of its elements can be described in fairly simple terms --- it is the number of elements that makes the problem hard. But that is what computers are here for!

Of course, life is not always that easy. When some of the elements or their interaction cannot be described in simple terms, or they are not known that well, they must be modeled. The difference is that instead of an exact description of (part of) the system, one deals with an approximation. Since the results of such models can be compared to tests or observations, models can be refined over time and their parameters (unknown quantities) may eventually become determined. In the case of our weather example, it may be difficult to describe exactly how human-produced dust darkens snow cover (and thus changes the Earth's radiation balance), but one can go out there and measure how dark the snow got.

All models involve a certain number of assumptions and approximations. This is why modeling is an art: it is the insight and intuition with regard to the quality of the underlying assumptions that enables a successful modeler to achieve great results with limited (computational and human) resources. As far as the terminology is concerned, most people realize that a certain amount of modeling is always part of performing simulations, and little distinction is made between the two in practicality.

Numerical Modeling and Space Exploration

Interestingly, even such an "exotic" area as Space Exploration just mimics the rest of the world when it comes down to the use of simulations. Sure, the tools may at times be a little more avant-garde than in fields that have only recently entered the world of quantifiable analysis. But the bottom line is, simulations are quite universal. For example, the aerodynamics of launch vehicles is simulated in quite similar ways to those of air planes, race cars, or family sedans. Like many other hi-tech instruments, the operation of satellite instruments is often simulated on computers in the final design stages, because there is no lab on Earth that can reproduce the environment of space. And the near-Earth space environment is numerically modeled in parts or as a whole, in an effort to understand and predict what has recently been christened "Space Weather" --- not unlike our more familiar atmospheric weather.

SciberNet's Simulations

One of the topic areas SciberNet is contributing to is our understanding of the near-Earth space environment. Although the Earth's atmosphere becomes thinner with altitude, it never quite vanishes and eventually merges with the interplanetary medium (which is also not quite "empty space"). The gas becomes very dilute, hot, and electrically conducting --- a state that is known as plasma. And the interplanetary space is filled with particles streaming out from the Sun (the solar wind). The interaction of the incoming solar wind with the outer reaches of Earth's atmosphere produces a rather violent chain of events with significant consequences to us on Earth.

What are some of these effects? Certain particles (like protons and electrons) are accelerated to high energies and will damage satellite equipment in orbit. Also, the outer atmosphere may expand. As a consequence, the increased drag on satellites makes them descend prematurely and burn up in the atmosphere. In principal, all types of satellites can be affected: communication satellites, weather forecast satellites, and satellites used in the Global Positioning System. As mentioned above, a plasma can conduct currents. Some of the generated currents are so large that they lead to failures in communication lines and power lines at high latitude, e.g., in Canada and in Scandinavia.

SciberNet develops and uses what are called particle simulation codes. In these computer programs, the plasma is not simply described as a gas, but rather as an interacting ensemble of charged particles (e.g., protons and electrons). The motion of these particles is followed in the ambient electric and magnetic fields, and currents are calculated as well as any changes of the surrounding fields. These simulations tell us how the particles get accelerated, how the plasma is heated, and how waves (similar to low frequency radio waves) are generated. Waves produced in the simulations are actually observed with satellites in orbit and at ground stations. By using the particle approach, the simulations do not make many assumptions about the properties of the plasma. This makes the results more generally valid than a gas (or "fluid") description, which is known to be less accurate. The outcome of particle simulations can be compared to in situ satellite observations in great detail, since many satellites carry field and particle instrumentation.

Related SciberNet Work

Simulations typically generate large amounts of information (e.g., many hundreds of Mbyte for a single "run"). SciberNet is actively involved in producing practical solutions for large database management and visualization of data.

Modern simulation codes are often run on super computers and/or parallel machines, which requires the use of special programming techniques and languages. Further, simulation codes and their output are now more and more managed through GUIs (Graphical User Interfaces). SciberNet personnel has longstanding experience in these areas.

SciberNet also employs the latest techniques to diagnose the information generated from simulations, from wavelet analysis to neural nets. Beyond the work listed above, SciberNet personnel also has experience in the simulation of laboratory plasmas, radio wave propagation, complex dynamical systems, and astrophysical phenomena.