A numerical model is a type of modeling that uses a computer to solve a mathematical description of a physical process. It can be more efficient than an analytical approach and is often used to explore a complex system’s behavior or examine a specific function.
Numerical models are used in a variety of fields, including engineering. They can be a powerful tool in solving complex problems and evaluating the performance of equipment and systems.
What is Numerical Modelling?
Numerical modeling is the use of computer technology to solve engineering problems. It involves describing a physical process in terms of mathematical equations and then solving them using numerical methods on high-powered computers.
It is an integral part of the analysis and design process for many types of systems. It can provide information that cannot be obtained through expensive experiments or may not be available any other way.
Using a numerical model allows engineers to explore unfamiliar conditions or troubleshoot problems with existing systems. It can also assess the interaction between system components and evaluate design choices.
In addition, numerical modelling can consider reservoir heterogeneity, mass transfer effects between phases, fluid properties, relative permeability characteristics, and other aspects of the flow in a rock formation that would not be possible with an analytical approach. It can also incorporate rigorously the effects of multiphase flow, capillary, and gravity forces, spatial variations in rock properties, and other factors that influence the behavior of reservoirs.
What are the Basic Concepts of Numerical Modelling?
Engineers can explore and investigate a physical system’s behavior using mathematical models. These techniques have become increasingly important in engineering as computer technology has advanced.
The basic concept of numerical modeling is that it solves a mathematical description of a physical process using a more computationally intensive method than an analytical approach. Rather than repeating the calculation many times, this approach allows for faster results and more precise predictions.
A numerical solution to a model equation is represented by a table or graph (e.g., eqn 2) and is more intuitive than an analytical solution that requires complex integrals.
Numerical models also simplify real-world problems by removing some less critical variables. This simplification is a good idea as it allows the model to describe complex systems and their behavior better.
What are the Methods of Numerical Modelling?
Many different methods of numerical modeling are used in engineering. They are typically based on applying discretization and numerical approximation to a system of equations that describe a physical process or problem.
In particular, the finite element method is a well-known technique in engineering. It involves dividing the model domain into several non-overlapping triangles (elements) and then calculating the values of the nodes in these triangles.
The result is a mathematical model that shows the system’s behavior over time. This type of analysis is commonly used to predict the performance of an item or device under various operating conditions. For example, slope stability is crucial while managing various mining operations or civil engineering projects.
Another advantage of numerical models is that they can be built with fewer simplifying assumptions than analytical models. This means that multiphase behavior (including effects of relative permeability and mass transfer between phases), forces/ mechanisms responsible for the flow, and the change in rock properties and fluid properties with pressure can be incorporated rigorously.
What are the Applications of Numerical Modelling?
In engineering, numerical modeling is used to solve large-scale problems and complex systems or to look at a specific process in more detail. It is often used in the development of new equipment or systems.
In geology, numerical methods simulate the movement of tectonic plates or the Earth’s mantle. It can also be used to study rock mechanics or the thermal history of rocks.
The primary step in a numerical model is to capture the geological scenario quantitatively, using heat equations and equations to describe the flow of fluids. Then, governing equations are converted to discrete equations and solved by algorithms on a computer.
Several methods exist, including the finite element method (FEM), finite difference method (FDM), and meshless methods. Each method has its unique characteristics, which can be exploited to make the problem easier to solve and to reduce computational costs.