ICERM, Providence, Rhode Island
Being central to gas dynamics, the Boltzmann equation describes gas flows at the microscopic level in regimes from free molecular to continuum. Its descriptive power makes it indispensable for predicting non-continuum phenomena in gases when experimental data is limited or not available. The Boltzmann equation is used in a wide range of applications, from external aerodynamics and thruster plume flows to vacuum facilities and microscale devices. Accurate solution of the Boltzmann equation for modeling gas flows arising in aerospace applications continues to be a challenge. Existing numerical capabilities fall short of capturing the complexities of engineering design. Reasons for this range from the absence of mathematical models that capture the physics properly to higher dimensionality of kinetic models and the resulting high cost of computations to the failure of mathematical theories to handle complex geometries of real life applications.
The goal of this workshop is to facilitate the development of high-fidelity computational capabilities for the solution of the Boltzmann equation in application to simulation of non-continuum flows. This will be accomplished by addressing the gaps in communication between mathematicians, engineers and researchers in various fields of research.
Topics of the workshop include but are not be limited to: different forms of the Boltzmann equation; reduced order models for the Boltzmann equation; mesh adaptation in velocity space; fast evaluation of the Boltzmann collision integral; simulations that account for real gas effects and chemical and electromagnetic interaction of particles; complex geometry simulations; coupling of continuum and non-continuum models; and quantification of numerical error and uncertainty of simulations.
To address the goal of the workshop, the presenters were asked to incorporate in their lectures at least one of the following three common topics:
Communication of issues related to high computational costs of simulations;
Communication of issues related to accuracy of models that is the accuracy in approximating the solutions to the Boltzmann equation and the accuracy in approximating physics of gas flows;
Communication of progress in the analysis of numerical errors.