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MPI-AMRVAC 2.0 for Solar and Astrophysical Applications
C. Xia, J. Teunissen, I. El Mellah, E. Chane, R. Keppens
TL;DR
MPI-AMRVAC 2.0 addresses the need for scalable, grid-adaptive simulations spanning multiple spatial scales in astrophysical and solar-physics applications. It combines radial grid stretching with AMR, generic magnetic-field splitting, three-dimensional anisotropic thermal conduction, and framework modernization, demonstrating these capabilities across accretion, solar, and scaling tests. The reported results include robust thermal-conduction tests and satisfactory strong scaling for 3D coronal-rain simulations up to 2000 cores.
Problem
Astrophysical and solar-physics simulations require parallel, grid-adaptive methods that handle multiple spatial scales, curvilinear flows, low-plasma-beta magnetic fields, anisotropic conduction, and realistic computational workloads.
Method
The paper develops MPI-AMRVAC 2.0 by combining radial grid stretching with AMR, generic background-field splitting, 3D anisotropic thermal conduction, and modernized software infrastructure.
Results
Satisfactory strong scaling is demonstrated for 3D AMR simulations of solar coronal rain up to 2000 cores, while ring diffusion tests show accurate and robust anisotropic-conduction treatment that prevents unphysical thermal flux.
Takeaways & Limitations
The updated framework supports a broad range of hydrodynamic and MHD applications, including multiscale accretion flows, solar magnetic structures, reconnection, and coronal-rain simulations.
Takeaways & Limitations
The Bondi analysis uses analytic expressions assuming zero speed at infinity, although the authors state that the qualitative conclusions remain similar for the general subsonic case.
Abstract
from arXiv · showhide
We report on the development of MPI-AMRVAC version 2.0, which is an open-source framework for parallel, grid-adaptive simulations of hydrodynamic and magnetohydrodynamic (MHD) astrophysical applications. The framework now supports radial grid stretching in combination with adaptive mesh refinement (AMR). The advantages of this combined approach are demonstrated with one-dimensional, two-dimensional and three-dimensional examples of spherically symmetric Bondi accretion, steady planar Bondi-Hoyle-Lyttleton flows, and wind accretion in Supergiant X-ray binaries. Another improvement is support for the generic splitting of any background magnetic field. We present several tests relevant for solar physics applications to demonstrate the advantages of field splitting on accuracy and robustness in extremely low plasma $β$ environments: a static magnetic flux rope, a magnetic null-point, and magnetic reconnection in a current sheet with either uniform or anomalous resistivity. Our implementation for treating anisotropic thermal conduction in multi-dimensional MHD applications is also described, which generalizes the original slope limited symmetric scheme from 2D to 3D. We perform ring diffusion tests that demonstrate its accuracy and robustness, and show that it prevents the unphysical thermal flux present in traditional schemes. The improved parallel scaling of the code is demonstrated with 3D AMR simulations of solar coronal rain, which show satisfactory strong scaling up to 2000 cores. Other framework improvements are also reported: the modernization and reorganization into a library, the handling of automatic regression tests, the use of inline/online Doxygen documentation, and a new future-proof data format for input/output
1. INTRODUCTION
MPI-AMRVAC has evolved into a versatile, open-source multiphysics framework for parallel AMR simulations across hydrodynamic and MHD applications. Version 2.0 builds on this foundation with expanded coordinate, dimensional, coupling, and solar-physics capabilities.
- MPI-AMRVAC is an open-source framework for parallel simulations of hydrodynamic and MHD systems using patch-based or hybrid-block-based AMR meshes.
- The framework supports one-to-three-dimensional AMR meshes in Cartesian, polar, cylindrical, and spherical coordinate systems.
- Its multiphysics modules cover special relativistic hydrodynamics and MHD, while localized domain regions can couple different PDE models across block-based AMR meshes.
- The AMR strategy evolved to a pure quadtree-octree block-based hierarchy to support efficient scaling on realistic applications.
- Solar-physics functionality includes magnetofrictional extrapolation of vector magnetic fields into coronal volumes, alongside linear-force-free extrapolation in local Cartesian or global spherical coordinates.
2. RADIALLY STRETCHED MESHES
MPI-AMRVAC 2.0 combines radial grid stretching with AMR to resolve astrophysical flows spanning large spatial ranges. Tests cover Bondi accretion, Bondi–Hoyle–Lyttleton flow, wind accretion, and solar-wind MHD simulations.
- Radial stretching principle: Radial stretching supports multi-scale spherical, polar, and cylindrical simulations by adapting cell sizes across large radial domains.The radial step is proportional to local radius, producing a self-similar grid while helping maintain cell aspect ratios.
- 1D Bondi transonic accretion: The Bondi test reproduces the analytic sonic radius across adiabatic indices on non-stretched, stretched, and stretched-AMR meshes.The computed sonic radii are visually indistinguishable from the analytic solution, while density-profile agreement improves with additional AMR levels.
- Radial stretching principle: Stretched meshes reduce the cell count needed for an accurate Bondi solution by two orders of magnitude and resolve off-centered features without lowering the time step.This combination is especially useful when the inner and outer radii differ by more than a few tens.
- Wind accretion applications: For wind-dominated X-ray binaries, the accretor can be 4 to 5 orders of magnitude smaller than the surrounding shock, making stretched grids necessary to bridge the scales.The framework applies the approach to planar Bondi–Hoyle–Lyttleton flow and three-dimensional clumpy wind accretion.
- 3D clumpy wind accretion: Three-dimensional spherical simulations face a CFL time step about 40 times smaller than their two-dimensional counterparts at the stated polar resolution.AMR deliberately lowers polar resolution while refining upstream regions containing small-scale inflow clumps.
- Trans-Alfvénic solar wind: Solar-wind simulations with and without magnetic-field splitting produce nearly identical global structures and velocity profiles, with differences mainly in localized magnetic-field strength.The magnetic field is up to 30% stronger with splitting in a small fast–slow wind transition region.
3. MAGNETIC FIELD SPLITTING
MPI-AMRVAC generalizes magnetic-field splitting to arbitrary time-independent backgrounds and extends it to resistive MHD. Tests show improved preservation of low-β equilibria and agreement with reference resistive solutions, while the implementation stores background-field data per AMR block.
- Governing equations: Magnetic field splitting decomposes B into a dominant, time-independent background B0 and a deviation B1 to improve calculations in strong-field, low-β regions.The background must satisfy ∂B0/∂t = 0 and ∇·B0 = 0.
- Governing equations: The method supports arbitrary time-independent background fields, rather than only potential current-free fields, and is extended to resistive MHD.The resistive formulation adds magnetic diffusion and Ohmic-heating terms to the induction and energy equations.
- Governing equations: In the split ideal-MHD equations, background-field interactions appear as source terms involving the background current and electric field.The momentum equation includes a term related to J0×B0, while the energy equation contains E·J0; the induction equation retains background-field advection.
- Implementation: MPI-AMRVAC computes and stores B0 at cell centers and interfaces for each AMR block, then evaluates and stores J0 numerically or analytically.Stored background values are discarded when a block is deleted from the AMR mesh.
- Validation tests: At 5 time units, the non-MFS flux-rope run changed magnetic energy by 0.02%, current by 0.15%, and internal energy by 1.8%, while MFS changes were exactly zero.For resistive current-sheet tests, MFS and the reference solution differed by less than 0.1% for the reported quantities, and anomalous-resistivity simulations reproduced reconnection and flare-loop evaporation.
4. ANISOTROPIC THERMAL CONDUCTION
MPI-AMRVAC 2.0 generalizes slope-limited anisotropic thermal conduction from 2D to 3D, including parallel and perpendicular transport with flux limiting and saturation. Ring-diffusion tests show accurate, robust behavior, consistency between 2D and 3D implementations, and prevention of unphysical heat fluxes.
- Method: Anisotropic conduction is solved independently from the MHD equations using operator splitting, with field-aligned conductivity typically dominating perpendicular conductivity.In the solar corona, κ⊥ is about 12 orders of magnitude smaller than κ∥; both are implemented, and κ∥ can use Spitzer conductivity.
- Method: Traditional centered-difference schemes can produce unphysical heat flow from cold to hot regions across strong temperature gradients.Such fluxes can lead to negative temperatures, motivating slope limiting of transverse heat-flux components.
- Test problems: The 3D implementation reproduces the 2D ring-diffusion extrema, with a temperature transition region about 4% broader at the tested resolution.The 3D setup used a 200 × 200 × 20 mesh and yielded an x-y slice close to the corresponding 2D result.
5. PERFORMANCE AND SCALING
MPI-AMRVAC 2.0 improves parallel performance through Morton ordering of root-level blocks and related optimizations. Strong-scaling tests cover an ideal-MHD blast wave and a 3D AMR coronal-rain application, with the latter retaining more than 60% efficiency to about 2000 cores.
- Parallelization: MPI-AMRVAC 2.0 applies a Morton-ordered space-filling curve to root-level blocks to improve data locality and reduce inter-processor communication.The implementation also addresses rectangular domains where a pure Morton curve cannot be applied directly.
- Strong scaling tests: The ideal-MHD strong-scaling test uses a uniform 512^3-cell mesh decomposed into 32^3 blocks and compares MPI-AMRVAC 2.0 with version 1.0.The test varies the processor count from 28 to 3584 cores; version 1.0 stops speeding up after 1729 cores.
- Strong scaling tests: The 3D thermodynamic AMR-MHD coronal-rain test evolves about 46.4 million cells in 26,652 blocks across five AMR levels.The simulation includes heating, radiative cooling, anisotropic conduction, and mesh reevaluation during the scaling run.
- Results: More than 60% strong-scaling efficiency is obtained with up to about 2000 cores and more than 5 × 10^4 cells per core in the coronal-rain test.This test represents an actual solar application rather than an idealized uniform-mesh benchmark.
6. GENERIC FRAMEWORK IMPROVEMENTS
MPI-AMRVAC 2.0 reorganizes the framework into a static library with simplified preprocessing, automated regression testing, integrated Doxygen documentation, and a future-proof binary format. These changes target maintainability, reproducibility, usability, and data handling.
- Framework modernization: The preprocessor now handles only dimensionality, while standard Fortran modules allow the full framework to compile into a static library.Users select major physics modules and functionality through input parameters rather than frequent recompilation.
- Regression testing: Regression tests compare reduced simulation outputs with stored reference results to detect changes in conservation properties and solution shape.Default comparison tolerances are ε_abs = 10^-5 and ε_rel = 10^-8, accounting for numerical roundoff.
- Regression testing: The framework aims to provide at least one automated regression test for each major functionality, dimensionality, equation set, or algorithmic approach.Tests are designed to run quickly and can also help new users explore the framework.
- Documentation: Doxygen documentation is written close to the code, generated automatically each day, and published online for users and maintainers.This makes documentation easier to update when code changes and provides a starting point for new users.
- Data format: The revised binary format adds versioning, a leading header, byte offsets, block metadata, and optional ghost-cell storage.These changes simplify reading files, support future variables, and facilitate data access.
7. CONCLUSIONS AND OUTLOOK
MPI-AMRVAC 2.0 extends an open-source AMR framework for hydrodynamic and MHD astrophysical applications with grid stretching, generic magnetic-field splitting, multidimensional anisotropic conduction, improved scaling, and framework modernization. The authors identify future extensions including particle dynamics, Poisson problems, and improved radiative-loss treatment.
- Scientific capabilities: MPI-AMRVAC 2.0 combines grid stretching with block adaptivity and demonstrates the approach in accretion, wind, and solar-wind scenarios from 1D through 3D.The update targets parallel, grid-adaptive hydrodynamic and MHD astrophysical computations.
- Scientific capabilities: Generic magnetic-field splitting is demonstrated for low-plasma-β solar-physics problems including a force-free flux rope, a magnetic null point, and resistive reconnection.The reconnection examples use either uniform or anomalous resistivity.
- Scientific capabilities: The multidimensional conduction implementation generalizes the slope-limited symmetric scheme from 2D to 3D and prevents unphysical thermal flux in ring-diffusion tests.The tests are reported as demonstrating good accuracy and robustness.
- Performance: The improved code shows satisfactory strong scaling up to 2000 cores in 3D AMR simulations of solar coronal rain.The coronal-rain application includes anisotropic thermal conduction and thermal-instability-driven dynamics.
- Outlook: Future work includes particle-dynamics solvers, Poisson problems on the AMR hierarchy, and improved treatment of radiative losses beyond the optically thin assumption.Particle dynamics are identified for a forthcoming paper, while Poisson and radiative-loss improvements are longer-term possibilities.