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Abstract Global solar photospheric magnetic maps play a critical role in solar and heliospheric physics research. Routine magnetograph measurements of the field occur only along the Sun–Earth line, leaving the far side of the Sun unobserved. Surface flux transport (SFT) models attempt to mitigate this by modeling the surface evolution of the field. While such models have long been established in the community (with several releasing public full-Sun maps), none are open source. The Open-source Flux Transport (OFT) model seeks to fill this gap by providing an open and user-extensible SFT model that also builds on the knowledge of previous models with updated numerical and data acquisition/assimilation methods along with additional user-defined features. In this first of a series of papers on OFT, we introduce its computational core: the High-performance Flux Transport (HipFT) code (https://github.com/predsci/hipft). HipFT implements advection, diffusion, and data assimilation in a modular design that supports a variety of flow models and options. It can compute multiple realizations in a single run across model parameters to create ensembles of maps for uncertainty quantification and is high-performance through the use of multi-CPU and multi-GPU parallelism. HipFT is designed to enable users to write extensions easily, enhancing its flexibility and adaptability. We describe HipFT’s model features, validations of its numerical methods, performance of its parallel and GPU-accelerated code implementation, analysis/postprocessing options, and example use cases. 

Abstract We present the HelioCubed, a high-order magnetohydrodynamic (MHD) code designed for modeling the inner heliosphere. The code is designed to achieve 4th order accuracy both in space and in time. In addition, HelioCubed can perform simulations on mapped grids, such as those based on cubed spheres, which makes it possible to overcome stability limitations caused by the geometrical singularity at the polar axis of a spherical grid, thus enabling substantially larger time steps. HelioCubed has been developed using the high-level Proto library, ensures performance portability across CPU and GPU architectures, and supports back-end implementations, e.g., CUDA, HIP, OpenMP, and MPI. The code is compatible with the HDF5 library, which facilitates seamless data handling for simulations and boundary conditions derived from semi-empirical and MHD models of the solar corona. While presenting the results of preliminary simulations, we demonstrate that our simulations are indeed performed with 4th order of accuracy. Our approach ensures that HelioCubed solves the MHD equations preserving the radial flow to machine round-off error even on cubed-sphere grids. Solar wind simulations are performed using the boundary conditions provided by the Wang–Sheeley–Arge coronal model of the ambient solar wind. It also allows us to to simulate coronal mass ejections using observation-driven flux rope models. These capabilities make HelioCubed a versatile and powerful tool to advance heliophysics research and space weather forecasting. 

Abstract Interplanetary coronal mass ejections (ICMEs) are the primary sources of geomagnetic storms at Earth. The negative out-of-ecliptic component (B_z) of magnetic field in the ICME or its associated sheath region is necessary for it to be geoeffective. For this reason, magnetohydrodynamic simulations of CMEs containing data-constrained flux ropes are more suitable for forecasting their geoeffectiveness as compared to hydrodynamic models of the CME. ICMEs observed in situ by radially aligned spacecraft can provide an important setup to validate the physics-based heliospheric modeling of CMEs. In this work, we use the constant-turn flux rope (CTFR) model to study an ICME that was observed in situ by Solar Orbiter (SolO) and at Earth, when they were in a near-radial alignment. This was a stealth CME that erupted on 2020 April 14 and reached Earth on 2020 April 20 with a weak shock and a smoothly rotating magnetic field signature. We found that the CTFR model was able to reproduce the rotating magnetic field signature at both SolO and Earth with very good accuracy. The simulated ICME arrived 5 hr late at SolO and 5 hr ahead at Earth, when compared to the observed ICME. We compare the propagation of the CME front through the inner heliosphere using synthetic J-maps and those observed in the heliospheric imager data and discuss the role of incorrect ambient solar wind background on kinematics of the simulated CME. This study supports the choice of the CTFR model for reproducing the magnetic field of ICMEs. 

Abstract The Wang–Sheeley–Arge (WSA) model has been in use for decades and remains a popular, economical approach to modeling the solar coronal magnetic field and forecasting conditions in the inner heliosphere. Given its usefulness, it is unsurprising that a number of WSA implementations have been developed by various groups with different computational approaches. While the WSA magnetic field model has traditionally been calculated using a spherical harmonic expansion of the solar magnetic field, finite-difference potential field solutions can offer speed and/or accuracy advantages. However, the creation of new versions of WSA requires that we ensure the solutions from these new models are consistent with established versions and that we quantify for the user community to what degree and in what ways they differ. In this paper, we present side-by-side comparisons of WSA models produced using the traditional, spherical harmonic–based implementation developed by Wang, Sheeley, and Arge with WSA models produced using a recently open-sourced finite-difference code from the CORHEL modeling suite called POT3D. We present comparisons of the terminal solar wind speed and magnetic field at the outer boundaries of the models, weighing these against the variation of the WSA model in the presence of small perturbations in the computational procedure, parameters, and inputs. We also compare the footpoints of magnetic field lines traced from the outer boundaries and the locations of open field in the models. We find that the traced field-line footpoints show remarkable agreement, with the greatest differences near the magnetic neutral line and in the polar regions. 

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. 

Abstract The arrival time prediction of coronal mass ejections (CMEs) is an area of active research. Many methods with varying levels of complexity have been developed to predict CME arrival. However, the mean absolute error (MAE) of predictions remains above 12 hr, even with the increasing complexity of methods. In this work we develop a new method for CME arrival time prediction that uses magnetohydrodynamic simulations involving data-constrained flux-rope-based CMEs, which are introduced in a data-driven solar wind background. We found that for six CMEs studied in this work the MAE in arrival time was ∼8 hr. We further improved our arrival time predictions by using ensemble modeling and comparing the ensemble solutions with STEREO-A and STEREO-B heliospheric imager data. This was done by using our simulations to create synthetic J-maps. A machine-learning (ML) method called the lasso regression was used for this comparison. Using this approach, we could reduce the MAE to ∼4 hr. Another ML method based on the neural networks (NNs) made it possible to reduce the MAE to ∼5 hr for the cases when HI data from both STEREO-A and STEREO-B were available. NNs are capable of providing similar MAE when only the STEREO-A data are used. Our methods also resulted in very encouraging values of standard deviation (precision) of arrival time. The methods discussed in this paper demonstrate significant improvements in the CME arrival time predictions. Our work highlights the importance of using ML techniques in combination with data-constrained magnetohydrodynamic modeling to improve space weather predictions. 

Abstract Drawing connections between heliospheric spacecraft and solar wind sources is a vital step in understanding the evolution of the solar corona into the solar wind and contextualizing in situ timeseries. Furthermore, making advanced predictions of this linkage for ongoing heliospheric missions, such as Parker Solar Probe (Parker), is necessary for achieving useful coordinated remote observations and maximizing scientific return. The general procedure for estimating such connectivity is straightforward (i.e., magnetic field line tracing in a coronal model) but validating the resulting estimates is difficult due to the lack of an independent ground truth and limited model constraints. In its most recent orbits, Parker has reached perihelia of 13.3R_⊙and moreover travels extremely fast prograde relative to the solar surface, covering over 120° longitude in 3 days. Here we present footpoint predictions and subsequent validation efforts for Parker Encounter 10, the first of the 13.3R_⊙orbits, which occurred in November 2021. We show that the longitudinal dependence of in situ plasma data from these novel orbits provides a powerful method of footpoint validation. With reference to other encounters, we also illustrate that the conditions under which source mapping is most accurate for near‐ecliptic spacecraft (such as Parker) occur when solar activity is low, but also require that the heliospheric current sheet is strongly warped by mid‐latitude or equatorial coronal holes. Lastly, we comment on the large‐scale coronal structure implied by the Encounter 10 mapping, highlighting an empirical equatorial cut of the Alfvèn surface consisting of localized protrusions above unipolar magnetic separatrices. 

The Sun’s corona is its tenuous outer atmosphere of hot plasma, which is difficult to observe. Most models of the corona extrapolate its magnetic field from that measured on the photosphere (the Sun’s optical surface) over a full 27-day solar rotational period, providing a time-stationary approximation. We present a model of the corona that evolves continuously in time, by assimilating photospheric magnetic field observations as they become available. This approach reproduces dynamical features that do not appear in time-stationary models. We used the model to predict coronal structure during the total solar eclipse of 8 April 2024 near the maximum of the solar activity cycle. There is better agreement between the model predictions and eclipse observations in coronal regions located above recently assimilated photospheric data. 

The solar wind (SW) is a vital component of space weather, providing a background for solar transients such as coronal mass ejections, stream interaction regions, and energetic particles propagating toward Earth. Accurate prediction of space weather events requires a precise description and thorough understanding of physical processes occurring in the ambient SW plasma. Ensemble simulations of the three-dimensional SW flow are performed using an empirically-driven magnetohydrodynamic heliosphere model implemented in the Multi-Scale Fluid-Kinetic Simulation Suite (MS-FLUKSS). The effect of uncertainties in the photospheric boundary conditions on the simulation outcome is investigated. The results are in good overall agreement with the observations from the Parker Solar Probe, Solar Orbiter, Solar Terrestrial Relations Observatory, and OMNI data at Earth, specifically during 2020-2021. This makes it possible to shed more light on the properties of the SW propagating through the heliosphere and perspectives for improving space weather forecasts.