Various magnetohydrodynamics (MHD) approximations have served scientists and engineers well for studying problems in astrophysics, space physics and engineering such as tokamaks, plasma propulsion, and plasma instability in engineering devices. Even so, the limitations in this approximation have now become evident. Especially when dealing with dilute plasmas, charge separation cannot be accommodated in MHD. To match the full range of observational data and experiments, it is imperative to provide the plasma physics community with a capability that goes beyond the MHD approximation. The work aims at developing high-order accurate, efficient and easy-to-use numerical methods for simulation-driven discoveries related to multiscale electromagnetohydrodynamic problems on complex geometry. Indeed, the methods developed will actually offer high-order accuracy and extremely robust performance for any conservation law beyond electromagnetics or elasticity applications. Therefore, several other fields of great importance in science and engineering, and indeed of great importance to the NSF mission, will be directly benefited by the methods developed here. Training a new generation of computational scientists capable of conducting interdisciplinary research is one of the central activities of the work. Courses relevant to the research such as numerical partial differential equations, advanced scientific computing, uncertainty quantification and machine learning have been introduced by the investigators and will be renovated by incorporating outcomes from the project into course materials.
The specific objectives of this project are to develop, analyze and evaluate data-enabled high-order accurate and robust computational modeling tools for simulating multiscale high energy density plasma flows containing both continuum and rarefied regimes in complex geometry. Both new high-order divergence-constraint-preserving central discontinuous Galerkin (DG) scheme on overlapping unstructured grid cells for simulating continuum plasma coupled with Maxwell's equations, and asymptotic preserving central DG scheme for solving Vlasov-Maxwell-Boltzmann (VMB) equations to model the dilute plasma flow will be developed. An innovative data-enabled stochastic concurrent coupling algorithm combining these schemes will be also devised for multiscale simulations. In this coupling algorithm, a novel data-enabled stochastic heterogeneous domain decomposition method to exchange statistical distribution at the interface of continuum and rarefied regimes will be developed. This will be the first attempt to stochastically couple continuum and kinetic plasma flow models. There is no current capability that integrates these unique advances, and the investigators will be the first group to deliver such a forward-looking capability to the plasma physics community. All numerical simulations will be validated by advanced data-enabled uncertainty quantification method developed in this project. A large-scale parallel code with these capabilities will be developed and released to the plasma physics community. It will not only enable the plasma physics community to carry out transformational simulations for new discoveries related to the multiscale electromagnetohydrodynamic physics for the first time but also lower the threshold for new computational scientists to use the new cutting-edge numerical methods for other applications such as nonlinear optics. Simulations will be used to explain new observations such as enhanced electron transport, which are difficult to study experimentally in a harsh plasma environment.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
