High order scalable solvers
Abstract
Overview: Mutliscale problems arise in all of nature. These problems universally fall under the category of grand challenge problems. Two examples of direct relevant to the Navy are the modeling of catastrophic weather events, such as accurately predicting the formation of a hurricane, and the modeling of dense plasmas, such as those generated in railguns and in dense plasma focuses. These problems are especially challenging because of the vast number of temporal and spatial scales that are coupled.In this proposal, we outline the first steps in producing a state-of-the-art numerical solver for multiscale problems of interest to the Navy. The work develops the idea of Differential Transforms (DT) for creating arbitrary order accuracy numerical simulations for a large class of problems, including shallow water equations on a sphere as well as MHD simulations for simulating flow past the earth to study the magnetosphere. The work also lays out a systematic approach for including geometry through the incorporation of mappedgrids and the Inverse Lax Wendroff (ILW) procedure as an embedded boundary method on logically Cartesian grids. The ILW requires a mix of high order spatial and temporal derivatives that are constructed out of the original Partial Differential Equation. By using DTs, we propose to automate the construction ofthis boundary data needed for the solution. Further, leveraging modern programming paradigms based on Sandia~s Kokkos, we will generate an MPI hardware independent scalable code that can be easily adapted to new architectures as they rapidly advance.This work will give us the underpinnings to start to go after modeling of a DPF as well as modeling of hurricane formation. The new framework with these problems will be the subject of our next proposal.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 20, 2019
- Source ID
- N000141912476
Entities
People
- Andrew Christlieb
Organizations
- Michigan State University
- Office of Naval Research
- United States Navy