Simulation-based engineering

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Engineers, mathematicians, and scientists were always interested in numerical solutions of real-world problems. The ultimate objective within nearly all engineering projects is to reach a functional design without violating any of the performance, cost, time, and safety constraints while optimizing the design with respect to one of these metrics. A good mathematical model is at the heart of each powerful engineering simulation being a key component in the design process. In this chapter, we review role of simulation in the engineering process, the historical developments of different approaches, in particular simulation of machinery and continuum problems which refers basically to the numerical solution of a set of differential equations with different initial/boundary conditions. Then, an overview of well-known methods to conduct continuum based simulations within solid mechanics, fluid mechanics and electromagnetic is given. These methods include FEM, FDM, FVM, BEM, and meshless methods. Also, a summary of multi-scale and multi-physics-based approaches are given with various examples. With constantly increasing demands of the modern age challenging the engineering development process, the future of simulations in the field hold great promise possibly with the inclusion of topics from other emerging fields. As technology matures and the quest for multi-functional systems with much higher performance increases, the complexity of problems that demand numerical methods also increases. As a result, large-scale effective computing continues to evolve allowing for efficient and practical performance evaluation and novel designs, hence the enhancement of our thorough understanding of the physics within highly complex systems.