Initial Examples
This section provides introductory examples that tackle fundamental problems in computational mechanics. The examples explore key phenomena including linear elasticity, diffusion-reaction, and advection-diffusion. These examples provide a solid foundation for understanding more complex coupled problems in computational simulations.
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Linear elasticity
This example examines how materials deform under external loads, assuming that the material's response follows Hooke's Law. It provides insights into stress and strain distributions, and is foundational in understanding the mechanical behavior of solid structures.
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Diffusion-Reaction
This example focuses on the interaction between diffusion and chemical reactions, modeling how substances spread and react over time. It is essential for understanding processes like heat transfer, pollutant dispersion, and biological processes such as drug delivery.
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Advection-Diffusion
This example looks at the combined effects of advection (transport of a substance) and diffusion (spreading of a substance due to concentration gradients). It is widely used in environmental engineering, fluid dynamics, and heat transfer problems.
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