1. Modeling a phenomenon

The first step is to create a model of the phenomenon under study. In most cases, the model is defined by means of a mathematical representation of one type or another. The model includes descriptions of various aspects of the phenomenon, such as interactions between its components and the structure of the object under study.

The methods used in modeling differ widely, depending on the application and the field of study. The modeling task may also include subordinate tasks that need to be solved independently.

Most often, a model is based on knowledge and data derived from theoretical or empirical research. For instance, the input data may consist of measured data about the properties of chemical compounds. The information needed can be found, for example, in chemical databases. This information can serve as the foundation of a model that strives to describe the measured data.

Measurement data are reviewed in step 6, when the results given by the model need to be verified by means of experiments.

2. Development of a solution method

If there is no ready-made solution method for the problem, the method must be planned. Planning can be facilitated, for instance, by using operations in numerical linear algebra or algorithms developed in computer science.

The task to be executed may be, for example, comparison of one’s own data with data contained in various databases. Execution of this task requires search algorithms that enable meaningful comparison and combination of data from various sources.

Modeling tasks in engineering sciences represent another type of example. They often involve multiphysical phenomena. For instance, the model may contain electromagnetism combined with interactions between flows and structures. Solving a problem of this type may require the development of new methods.

3. Implementation of the solution method

If there is a reliable and efficient solution method that has been implemented either as a program that can be run or as a program code in the source language, this should be used. If the solution method has not been programmed or if it is not possible to use the ready program code, the method must be implemented by means of programming.

4. Studying the phenomenon on the computer

Steps 1 to 3 have yielded a program that makes it possible to study the phenomenon on the computer. At this stage it may be noticed that the model is inappropriate, the solution method is unreliable or inefficient, or that the program does not operate correctly. In the event of errors, it may be advisable to consult the program developer or experts in numerical methods, or to compare the results with those published elsewhere.

If the computer does not have enough capacity, there may be reason to modify the model so that it is easier to solve or to devise a more powerful algorithm for executing the task. Parallel computing may also be helpful in executing extensive tasks.

5. Presentation of results

The results obtained by means of a computer can be presented using various techniques, which are often based on statistical methods or graphical representation.

The model and its underlying data can be compared with each other by means of computer-based visualization. The values calculated during computer simulation can also be presented as an animation. This makes it possible to study the behavior of the phenomenon as a function of time.

6. Interpretation and assessment of results

Once the results given by the model have been received, they must be compared with the measurement results and results published earlier so that their correctness can be verified. At this stage it may be discovered that the model and the solution method need improvement in order for the results to meet the requirements set.