The text gives a practice-oriented introduction in modern numerical methods as they typically are applied in mechanical, chemical, or civil engineering. Problems from heat transfer, structural mechanics, and fluid mechanics constitute a thematical focus of the text.

For the basic understanding of the topic aspects of numerical mathematics, natural sciences, computer science, and the corresponding engineering area are simultaneously important. Usually, the necessary information is distributed in different textbooks from the individual disciplines. In the present text the subject matter is presented in a comprehensive multidisciplinary way, where aspects from the different fields are treated insofar as it is necessary for general understanding. Overarching aspects and important questions related to accuracy, efficiency, and cost effectiveness are discussed.

The topics are presented in an introductory manner, such that besides basic mathematical standard knowledge in analysis and linear algebra no further prerequisites are necessary.

The book is suitable either for self-study or as an accompanying textbook for corresponding lectures. It can be useful for students of engineering disciplines as well as for computational engineers in industrial practice.

Contenu

Introduction.- Modeling of Continuum Mechanical Problems.- Discretization of Problem Domain.- Finite-Volume Methods.- Finite-Element Methods.- Other Discretization Methods.- Time Discretization.- Solution of Algebraic Systems of Equations.- Properties of Numerical Methods.- Finite-Element Methods in Structural Mechanics.- Finite-Volume Methods for Incompressible Flows.- Lattice-Boltzmann Methods for Flow Simulation.- Computation of Turbulent Flows.- Acceleration of Computations.