Search for: All records

Abstract Unconditionally stable time stepping schemes are useful and often practically necessary for advancing parabolic operators in multi-scale systems. However, serious accuracy problems may emerge when taking time steps that far exceed the explicit stability limits. In our previous work, we compared the accuracy and performance of advancing parabolic operators in a thermodynamic MHD model using an implicit method and an explicit super time-stepping (STS) method. We found that while the STS method outperformed the implicit one with overall good results, it was not able to damp oscillatory behavior in the solution efficiently, hindering its practical use. In this follow-up work, we evaluate an easy-to-implement method for selecting a practical time step limit (PTL) for unconditionally stable schemes. This time step is used to ‘cycle’ the operator-split thermal conduction and viscosity parabolic operators. We test the new time step with both an implicit and STS scheme for accuracy, performance, and scaling. We find that, for our test cases here, the PTL dramatically improves the STS solution, matching or improving the solution of the original implicit scheme, while retaining most of its performance and scaling advantages. The PTL shows promise to allow more accurate use of unconditionally stable schemes for parabolic operators and reliable use of STS methods. 

Abstract To address Objective II of the National Space Weather Strategy and Action Plan “Develop and Disseminate Accurate and Timely Space Weather Characterization and Forecasts” and US Congress PROSWIFT Act 116–181, our team is developing a new set of open-source software that would ensure substantial improvements of Space Weather (SWx) predictions. On the one hand, our focus is on the development of data-driven solar wind models. On the other hand, each individual component of our software is designed to have accuracy higher than any existing SWx prediction tools with a dramatically improved performance. This is done by the application of new computational technologies and enhanced data sources. The development of such software paves way for improved SWx predictions accompanied with an appropriate uncertainty quantification. This makes it possible to forecast hazardous SWx effects on the space-borne and ground-based technological systems, and on human health. Our models include (1) a new, open-source solar magnetic flux model (OFT), which evolves information to the back side of the Sun and its poles, and updates the model flux with new observations using data assimilation methods; (2) a new potential field solver (POT3D) associated with the Wang–Sheeley–Arge coronal model, and (3) a new adaptive, 4-th order of accuracy solver (HelioCubed) for the Reynolds-averaged MHD equations implemented on mapped multiblock grids (cubed spheres). We describe the software and results obtained with it, including the application of machine learning to modeling coronal mass ejections, which makes it possible to improve SWx predictions by decreasing the time-of-arrival mismatch. The tests show that our software is formally more accurate and performs much faster than its predecessors used for SWx predictions. 

This white paper is on the HMCS Firefly mission concept study. Firefly focuses on the global structure and dynamics of the Sun's interior, the generation of solar magnetic fields, the deciphering of the solar cycle, the conditions leading to the explosive activity, and the structure and dynamics of the corona as it drives the heliosphere.