Modelling based on Conservation Principles

This chapter presents conservation principles as a foundational approach for modeling physical and engineering systems. It begins with the introduction of basic concepts, including density as the measure of a conserved quantity, flux as its transport across boundaries, and sources and sinks as mechanisms of addition or removal. These elements are formalized through the universal conservation law, providing a general framework for system analysis. The chapter then focuses on one-dimensional conservation laws, emphasizing nonlinear phenomena that lead to complex solution structures. Key topics include the Riemann problem, the formation of contact discontinuities, rarefaction waves, and shock solutions, illustrating how mathematical methods capture the dynamics of transport and wave propagation. Exercises are provided to reinforce theoretical concepts and enhance practical skills, enabling students to apply conservation principles effectively across diverse applications in science and engineering.