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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.
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Arbitrarily high-order accurate simulations of compressible rotationally constrained convection using a transfinite mapping on cubed-sphere grids
We present two major improvements over the Compressible High-ORder Unstructured Spectral difference (CHORUS) code published in Wang et al., “A compressible high-order unstructured spectral difference code for stratified convection in rotating spherical shells,” J. Comput. Phys. 290, 90–111 (2015). The new code is named CHORUS++ in this paper. Subsequently, we perform a series of efficient simulations for rotationally constrained convection (RCC) in spherical shells. The first improvement lies in the integration of the high-order spectral difference method with a boundary-conforming transfinite mapping on cubed-sphere grids, thus ensuring exact geometric representations of spherical surfaces on arbitrary sparse grids. The second improvement is on the adoption of higher-order elements (sixth-order) in CHORUS++ vs third-order elements for the original CHORUS code. CHORUS++ enables high-fidelity RCC simulations using sixth-order elements on very coarse grids. To test the accuracy and efficiency of using elements of different orders, CHORUS++ is applied to a laminar solar benchmark, which is characterized by columnar banana-shaped convective cells. By fixing the total number of solution degrees of freedom, the computational cost per time step remains unchanged. Nevertheless, using higher-order elements in CHORUS++ resolves components of the radial energy flux much better than using third-order elements. To obtain converged predictions, using sixth-order elements is 8.7 times faster than using third-order elements. This significant speedup allows global-scale fully compressible RCC simulations to reach equilibration of the energy fluxes on a small cluster of just 40 cores. In contrast, CHORUS simulations were performed by Wang et al. on supercomputers using approximately 10 000 cores. Using sixth-order elements in CHORUS++, we further carry out global-scale solar convection simulations with decreased rotational velocities. Interconnected networks of downflow lanes emerge and surround broader and weaker regions of upflow fields. A strong inward kinetic energy flux compensated by an enhanced outward enthalpy flux appears. These observations are all consistent with those published in the literature. Furthermore, CHORUS++ can be extended to magnetohydrodynamic simulations with potential applications to the hydromagnetic dynamo processes in the interiors of stars and planets.
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- Award ID(s):
- 2310372
- PAR ID:
- 10488554
- Publisher / Repository:
- AIP Publishing
- Date Published:
- Journal Name:
- Physics of Fluids
- Volume:
- 35
- Issue:
- 8
- ISSN:
- 1070-6631
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1063/5.0158146
