Bound-Preserving Space and Time Discretizations for Convection-Dominated Problems

The development of high-performance simulation tools for real-life problems involving fluid flows and related transport phenomena frequently requires the use of numerical methods that are high-order accurate in space and time and preserve important physical properties of certain quantities of interest (such as nonnegativity of the water height in shallow water equation models). In recent years, the state of the art in the development of such schemes was significantly advanced by a breakthrough in theoretical analysis which has provided illuminating insights into the properties of existing methods and new design criteria for the development of improved solution strategies. However, many theoretical aspects of physics-aware discretization techniques still require further exploration or have not been put into practice so far. The purpose of this workshop is to bridge the gap between the mathematical theory and engineering practice.