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Multiphysics: Advances and Applications

Aim & scope

Multiphysics is defined as a coupled modelling approach that demands simultaneous addressing of hitherto separate physical disciplines and combines them to generate relational mathematical models. These models are then validated through controlled experiments to enhance the understanding of natural behaviour.

All problems arising from natural phenomena are of a Multiphysics nature, yet most of the engineered solutions available today do not reflect this complexity. Therefore, while all research is interrelated, it is no longer conceivable to neglect this fundamental issue within the scientific and industrial communities.

Multiphysics-Advances-and-Applications cover

Most industrial solutions are simplified to extremes to reduce the complexities of design, a fundamental aspect of engineering. However, this simplification also affects the quality and cost of products, which have become central concerns for both researchers and engineers in simulations.

Over the last couple of centuries, everyday problems have been solved via simplified mathematical models. With the advent of more powerful computers, more complicated models have been developed, albeit still ignoring the real-time interactions between different disciplines. As models became more complex, primarily due to numerical methods such as finite elements, the physical complexities were increasingly overlooked, prioritizing "boundary conditions" of a differential equation over their real impact on solution quality. The question arises: do these boundary conditions truly exist in nature? What are the boundaries of a physical object, and what happens if these boundary conditions are extended?

Even in a more realistic perception of boundary limits, the issue of physical complexity is often ignored, often confused with complicated models. Nearly all differential equations contain "constant" terms or model parameters, which represent the effects or interactions of other important physical phenomena, reduced to simple, static effects.

There is a vast field to cover, and Multiphysics modelling is believed to be a particularly potent tool in addressing the complex features of physical interaction. The treatment of sources of dispersion lies in the interaction of fields, which can only be accounted for through a true Multiphysics treatment of physical problems. Progress in the treatment of coupled field problems heavily depends on the success of solution methodologies in providing robust and reliable solution algorithms.

Multiphysics analysis has been developed in recent years to better represent the behaviour of complex processes by simultaneously modelling multiple systems. This development is driven by the industrial need to further understand real physical phenomena to develop and design safer, more efficient, and environmentally friendly products.

Previously, such analyses and investigations were impossible due to a lack of powerful computing systems. However, advances in computer hardware have enabled more sophisticated investigations with increased computation speeds. Accompanied by new software packages that leverage the improved architecture of new-generation microprocessors, there have been dramatic improvements in coupling many mathematical simulation techniques. Many research establishments are comparing the results of such studies with experimental tests to improve modelling accuracy and validate processes for future certification.

Today, many science and engineering communities are customising their research toward Multiphysics analytical and simulation methods to save costs and reduce time to market, utilizing rapid prototyping. This is particularly evident in advanced technologies for innovative product design. Examples include a new generation of nuclear reactors, precise design of airbags, and crashworthiness of aerostructures. However, despite the use of different modelling techniques, the real coupling of various phenomena remains a significant challenge, particularly in industrial applications.

The trend of Multiphysics simulations in academia and industry mainly focuses on appropriate techniques for coupling aspects and their credibility, which can be verified and validated. Many still use Lagrangian or Eulerian methods to simplify simulations with assumptions and boundary conditions but approaches like Arbitrary Lagrangian-Eulerian (ALE), including penalty methods, require robust validations. Therefore, it is essential to establish a clear direction for publications to provide appropriate reading materials accompanied by the latest techniques.

The enhancement of Multiphysics analyses depends mainly on two aspects: a better understanding of physics and physical representations of interactions, and advancements in computing facilities to solve complex and large mathematical equations. Progress in both fields is of paramount importance. More research and development are needed to ensure the accuracy of new tools for Multiphysics simulations and the effectiveness of more significant and more stable parallel computing facilities.

Despite the importance of Multiphysics modelling and analyses in providing accurate solutions for new products and problem-solving in industrial applications, compared to conventional one-way coupling, the cost of such analyses remains a significant factor. Therefore, recognizing the cost-effectiveness and identifying the necessary time and space to dedicate to modelling complexity in engineering and science applications is essential.

In recent years, many studies have focused on various issues to address the importance of Multiphysics analysis; however, some modelling and simulations have been presented as a Multiphysics approach when a multidisciplinary approach may suffice. Multiphysics simulation is expected to continue to be a key technology in the future of engineering design and simulation. As the complexity of engineered systems continues to increase, so too will the need for more accurate and comprehensive analysis of physical systems. Multiphysics simulation can provide a more accurate representation of the physical system's behaviour and performance, enabling engineers to optimize the design of systems that are more energy-efficient, have better performance, and are more reliable.

The integration of Multiphysics simulation with artificial intelligence (AI), machine learning (ML), and computer-aided engineering (CAE) is expected to lead to significant advancements in engineering design and simulation. This integration will enable scientists and engineers to design and analyse more complex and sophisticated systems, resulting in better products and more efficient resource utilization. The future scope for the integration of these technologies in engineering design and simulation is promising. Recent focus has been on virtual engineering and how modelling and simulations in Multiphysics can contribute to the introduction of a digital twin in the world of production and maintenance. However, this may take a few more years to mature, at which point the Elsevier Multiphysics Series will be well-positioned to offer volumes in such an area.

‘Multiphysics: Advances and Applications’ combines academic and industrial expertise in a range of books that bridge the gap between researchers and engineers, focusing on applications central to the work of both. Each volume is written with a thorough understanding of its place in the academic literature but with a focus on the application of modelling techniques in practice. This collection of books serves as an authoritative resource for academics from various backgrounds who want to ensure that their studies are relevant beyond the lab, while also providing practitioners with detailed guides to the latest advances in their field.


The series will cover the basic understanding and theoretical overview leading to practical and industrial applications as well as the new advances in research. The books are intended for Academics, Researchers, Industrialists, Students, etc.

Series Editor

Mojtaba Moatamedi


Mojtaba Moatamedi


The International Society of Multiphysics

Read more about Mojtaba Moatamedi