Continuous and steady advances in computer technology have changed the way engineering design and
analyses are performed. These advances allow engineers to manage larger-scale problems and more complex systems, or to look in more detail at a specific process. Using advanced computer technology to perform engineering analysis, numerical modeling has emerged as an important field in engineering.

In general, the term numerical method describes solving a mathematical description of a physical process using a numerical rather than an analytical approach.

This may be done for a number of reasons, including:

1. An analytical means of solving the equations that describe the system may not exist
   
   
2. Although an analytical method is available, it may be necessary to repeat the calculation many times, and a numerical method can be used to accelerate the overall process.

A small-scale replica of an apparatus is considered a physical model because it describes the full-size apparatus on a smaller scale. This model can incorporate varying levels of detail depending on need and circumstances. A mathematical description of a physical system (referred to as a mathematical model) can also incorporate varying levels of detail. Similar to a physical model, the amount of detail is often determined by the accuracy required and the resources available to use the model. This creates a need to strike a balance between accuracy, complexity and efficiency.

There are two basic approaches to mathematical modeling.

1. Model the behavior of a system – Network flow models and heat exchanger heat transfer correlations are examples of a system model.
   
   
2. Model the fundamental physics of a system to determine the behavior – Computational fluid dynamics (CFD) and chemical reaction models fall into this category.

The term numerical modeling usually refers to the use of numerical methods on high powered computers to solve a complex system of mathematical models based on the fundamental physics of the system. In this respect, it describes the second approach previously identified.

Benefits of numerical modeling

There are numerous benefits to using a sophisticated tool such as a numerical model for engineering analysis. These tools can often provide information that can only be obtained through expensive experiments or may not be available any other way. Numerical modeling may often be used to obtain needed information quickly and at a reduced cost.

While it is important to understand the advantages of using numerical modeling, it is equally important to understand that it is only one means of obtaining the required information. Engineering has long relied on theory and experiments for design and analysis. Numerical modeling adds a third approach. Each approach offers different insights with different benefits.

• Increased understanding – the primary purpose of using numerical modeling is to increase understanding of a physical process. As such, it is often used in addition to or in conjunction with other available tools.
  
  
• Exploration of unfamiliar conditions – a CFD model of a new component can provide the missing information, or a CFD model of the entire system can be performed. The model allows the exploration and analysis of new equipment and systems.
  
  
• Design validation/examination of interactions – traditional methods of analysis and design are often focused on individual system components. Numerical modeling provides a vehicle to evaluate the interactions and validate the system design.
  
  
• Troubleshooting – engineering analysis often investigates the behavior of existing systems. This is particularly true when the behavior does not agree with expectations. Numerical modeling can play a vital role in determining the nature of the problem and suggesting solutions.
  
  
• Flexibility – numerical modeling is a flexible method of analysis. It can be used to look at a wide range of geometries or operating condition with varying levels of detail.

Stay tuned! More articles illustrating specific examples of how numerical modeling was used in power plant applications coming soon.