Numerical modeling and simulation are vastly used for engineering applications, and as complement to theoretical and experimental developments boosting progress in scientific knowledge. Due to their versatility, numerical methods are successively and increasingly replacing physical tests in industrial design processes. They are also an important item in the toolbox of scientific researchers, both in fundamental and applied disciplines. There are …

Numerical modeling and simulation are vastly used for engineering applications, and as complement to theoretical and experimental developments boosting progress in scientific knowledge. Due to their versatility, numerical methods are successively and increasingly replacing physical tests in industrial design processes. They are also an important item in the toolbox of scientific researchers, both in fundamental and applied disciplines. There are two competing trends in the development of numerical methods. While the models become more elaborate, e.g. by considering more detailed and/or coupled physical phenomena on one or several time- and length-scales, there is a strong drive towards obtaining fast predictions with applications to, e.g., real-time decision tools. Other applications requiring fast numerical simulations while controlling accuracy are large-scale optimization problems and statistical analysis, where a large number of simulations are required to evaluate the parameter space.