- Vijay Mahadevan, Argonne National Laboratory
- Paul Ullrich, University of California, Davis
Coupled multimodel simulations involve high degree of computationally complex workflows, and achieving consistently accurate solutions is strongly dependent on the choice of spatiotemporal numerical algorithms used to resolve the interacting scales in physical models. Rigorous spatial coupling between components in such systems involve field transformations, and communication of data across multiresolution grids, while preserving key attributes of interest such as global integrals and local features, which is usually referred to as the process of ""remapping"". Such remap procedures are critical in ensuring stability and accuracy of scientific codes simulating multiphysics problems that typically occur in many different scientific domains such as Fluid-Structure interaction, nuclear reactor analysis, magneto-hydrodynamics modeling, and Climate and Weather simulations to name a few.
Understanding and dynamically controlling the dominant sources of errors in these coupled system will be key to achieving predictable and verifiable results on current and future computing architectures. It is sufficiently well known that improper treatment of the coupled solution terms in multiphysics simulations can lead to large inaccuracies that can propagate and destroy the overall accuracy and stability of the numerical computation. And a critical factor contributing to the spatiotemporal accuracy in modeling such phenomena is due to the consistent solution mapping between different discretizations of the domain, which are often tuned to resolve spatial scales of interest in the various coupled model components.
Over the past several decades, many high-order, stable interpolators and remappers have been proposed for tackling nonlinear multimodel problems. Many of these methods utilize variations of standard interpolation techniques (nearest neighbor, bilinear/trilinear using lagrange functionals, and using high-order spline basis expansions), advanced interpolators with complex constraints (radial-basis, cubic-spline, generalized moving least-squares), and finite-element based patch-reconstruction or L2 minimization procedures. Other remapping methods for such problems utilize problem-specific approximations that may be discretization and resolution dependent.
In the current mini-symposia, we aim to bring together researchers and scientists from various scientific backgrounds to present stable remapping strategies to accurately resolve strongly dependent, homogeneous (volumetric, full-domain), and heterogeneous (surface, interface-exchange) coupling phenomena. This session will thus provide a glimpse of the current state-of-art remapping schemes that provide consistently accurate (preserving theoretical order of convergence for smooth solution fields), mass and energy conserving, monotone (preserving global solution bounds), and minimally dissipative (preserving local features). While all these features may not be possible in any single, general purpose remapping scheme, we expect discussions triggered from the talks in the session will enable interested researchers to improve and apply strategies to their own scientific domains.