Bound-Preserving Space and Time Discretizations for Convection-Dominated Problems (21w5065)


Manuel Quezada de Luna (King Abdullah University of Science and Technology)

(Universidad Nacional Autonoma de Mexico)

(Lawrence Livermore National laboratory)

Dmitri Kuzmin (TU Dortmund University)


The Casa Matemática Oaxaca (CMO) will host the "Bound-Preserving Space and Time Discretizations for Convection-Dominated Problems" workshop in Oaxaca, from August 22 to August 27, 2021.

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.

The key topics will include i) spatial discretizations satisfying discrete maximum principles, ii) strong stability preserving and positivity-preserving time stepping schemes, iii) theoretical analysis and practical applications of such discretization techniques. The participants of this workshop possess complementary expertise in the fields of numerical analysis, algorithm design, and high-performance computing. Putting all this knowledge together will create synergy effects that will have a profound impact on the analysis-based development of property-preserving schemes for general-purpose CFD software and customized PDE models.

The Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station in Banff is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT). The research station in Oaxaca is funded by CONACYT