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MAESTRO: Low Mach Number Astrophysics


Overview

Many astrophysical phenomena of interest occur in the low Mach number regime, where the characteristic fluid velocity is small compared to the speed of sound. Some well-known examples are the convective phase of Type Ia supernovae, classical novae, convection in stars, and Type I X-ray bursts. Such problems require a numerical approach capable of resolving phenomena over time scales much longer than the characteristic time required for an acoustic wave to propagate across the computational domain.

As part of the SciDAC Computational Astrophysics Consortium we have developed a new low Mach number hydrodynamics code, MAESTRO, that includes stellar equations of state and nuclear reaction networks. We are currently using MAESTRO to study the convective phase of Type Ia supernovae and Type I X-ray bursts.

Development of MAESTRO is in collaboration with Mike Zingale at Stony Brook Univeristy.


MAESTRO Download

To get a copy of the latest version of the MAESTRO repository using git, please visit our Downloads page.


MAESTRO Email Support List

We have set up a mailing list for MAESTRO users to communicate with one another and with the developers. We will be using this list to announce new features in MAESTRO, as well as any changes in MAESTRO or BoxLib which may affect people running the MAESTRO code.

To learn more about the help list, and to subscribe, go here.




White Dwarf Convection

This movie shows the convection patterns in a carbon-oxygen white dwarf during the final seconds before ignition. This full-star, 3D simulation used over 500,000 CPU hours on the Jaguar supercomputer at the Oak Ridge National Laboratory. This movie was created using the VisIt visualization software. For more about this simulation, click here.

For a great overview of our white dwarf convection and ignition studies using MAESTRO, see Mike Zingale's White Dwarf Convection page.




Why A Low Mach Number Approach?

A large number of interesting astrophysical phenomena occur in the low Mach number regime, where the characteristic fluid velocity is small compared to the speed of sound. Evolving these flows with a fully compressible simulation code is inefficient because these codes compute the effect of sound waves, which are unimportant for our problems of interest.

For an explicit time-discretization (i.e., the new state is expressed solely in terms of the present state), a fundamental limitation exists on the size of the allowable timesteps -- the CFL condition. A timestep is restricted such that information may only propagate across one zone in the computational grid per timestep. In compressible flow, information propagates at the speeds: u, u + c, and u - c, where c is the sound speed. Mathematically the timestep restriction is expressed as

Δ t < min { Δ x / (|u| + c) }

For very low Mach number flows, this is
Δ t ~ Δ x / c

This means that for an interface moving at a Mach number M << 1, it takes 1/M timesteps for that interface to move just one zone!

Our desire is to reformulate the equations of hydrodynamics to filter out sound waves, while retaining the compressibility effects important to the problem at hand. This will result in a timestep constraint of the form

Δ t < min{ Δ x / |u| }

Therefore, our algorithm will require far fewer timesteps (~1/M fewer) to simulate low Mach number flows.



MAESTRO Features

Coordinate Systems

MAESTRO supports calculations in 2D and 3D Cartesian coordinates.

Unsplit PPM Hydrodynamics

MAESTRO uses an unsplit version of the piecewise parabolic method (PPM), with new limiters that avoid reducing the accuracy of the scheme at smooth extrema.

Modular Equation of State and Reaction Networks

MAESTRO is written in a modular fashion so that the routines for the equation of state and reaction network can be supplied by the user. The reactions are included in the time integration scheme in a second-order accurate operator-split formulation (Strang splitting).

AMR in MAESTRO

Our approach to adaptive refinement in MAESTRO uses a nested hierarchy of logically-rectangular grids with refinement of the grids only in space, i.e. all levels are advanced with the same time step. The integration algorithm on the grid hierarchy is such that each substep of a time step is completed at all levels before proceding to the next substep. Data is synchronized between levels at the completion of each substep.

During the regridding step, increasingly finer grids are recursively embedded in coarse grids until the solution is sufficiently resolved. An error estimation procedure based on user-specified criteria evaluates where additional refinement is needed and grid generation procedures dynamically create or remove rectangular fine grid patches as resolution requirements change.

Visualization

  • Amrvis2d and Amrvis3d are visualization tools developed by CCSE particularly for the BoxLib style of plotfile which MAESTRO generates. A particularly useful feature in AmrVis is View/Dataset, which allows you to actually view the data -- not just a color or contour plot -- this can be handy for debugging. You can modify how many levels of data you want to see, whether you want to see the grid boxes or not, what palette you use, etc.

  • VisIt is also a great visualization tool, and it directly handles our plotfile format (which it calls Boxlib). For more information check out the VisIt home page.

  • Software Framework

    The MAESTRO software is written in the Fortran90 BoxLib software framework developed by CCSE.

    Questions?

    Contact Ann Almgren.





    MAESTRO in the News: First Full Simulation of Star's Final Hours.

    The precise conditions inside a white dwarf star in the hours leading up to its explosive end as a Type Ia supernova are one of the mysteries confronting astrophysicists studying these massive stellar explosions. But now, a team of researchers, composed of three applied mathematicians at the U.S. Department of Energy's (DOE) Lawrence Berkeley National Laboratory and two astrophysicists, has created the first full-star simulation of the hours preceding the largest thermonuclear explosions in the universe... more

    MAESTRO-related Publications

    M. Zingale, C. M. Malone, A. Nonaka, A. S. Almgren, and J. B. Bell, "Comparisons of Two- and Three-Dimensional Convection in Type I X-ray Bursts," submitted for publication [pdf].

    Ann Almgren, John Bell, Andy Nonaka and Michael Zingale, "Low Mach Number Modeling of Stratified Flows," Finite Volumes for Complex Applications VII -- Methods and Theoretical Apsects, Springer Proceedings in Mathematics and Statistics, eds. J. Fuhrmann, M. Ohlberger, C. Rohde, Berlin, June 2014. [link]

    C. M. Malone, M. Zingale, A. Nonaka, A. S. Almgren, and J. B. Bell, "Multidimensional Modeling of Type I X-ray Bursts. II. Two-Dimensional Convection in a Mixed H/He Accretor", Astrophysical Journal, 788, 115, 2014. [arxiv]

    C. Gilet, A.S. Almgren, J.B. Bell, A. Nonaka, S.E. Woosley and M. Zingale, "Low-Mach Number Modeling of Core Convection in Massive Stars", Astrophysical Journal, 773, 137, 2013. [pdf]

    A. Nonaka, A. J. Aspden, M. Zingale, A. S. Almgren, J. B. Bell, and S. E. Woosley, "High-Resolution Simulations of Convection Preceding Ignition in Type Ia Supernovae Using Adaptive Mesh Refinement", Astrophysical Journal, 745, 73, 2012. [pdf]

    M. Zingale, A. Nonaka, A. S. Almgren, J. B. Bell, C. M. Malone, and S. E. Woosley, "The Convective Phase Preceding Type Ia Supernovae", Astrophysical Journal, 740, 8, 2011. [pdf]

    A. Nonaka, A. S. Almgren, J. B. Bell, H. Ma, S. E. Woosley, and M. Zingale, "From Convection to Explosion: End-to-End Simulation of Type Ia Supernovae," Proceedings of SciDAC 2011, Denver, CO, July 2011. [pdf]

    C. M. Malone, A. Nonaka, A. S. Almgren, J. B. Bell, and M. Zingale "Multidimensional Modeling of Type I X-ray Bursts. I. Two-Dimensional Convection Prior to the Outburst of a pure 4He Accretor", Astrophysical Journal, 728, 118, Feb. 2011. [arxiv]

    A. Almgren, J. Bell, D. Kasen, M. Lijewski, A. Nonaka, P. Nugent, C. Rendleman, R. Thomas, M. Zingale, "MAESTRO, CASTRO and SEDONA -- Petascale Codes for Astrophysical Applications," SciDAC 2010, J. of Physics: Conference Series, Chattanooga, Tennessee, July 2010. [arxiv]

    H. Ma, M. Zingale, S. E. Woosley, A. J. Aspden, J. B. Bell, A. S. Almgren, A. Nonaka, and S. Dong, "Type Ia Supernovae: Advances in Large Scale Simulation," Proceedings of SciDAC 2010, Chattanooga, TN, July 2010. [pdf]

    A. Nonaka, A. S. Almgren, J. B. Bell, M. J. Lijewski, C. M. Malone, and M. Zingale, "MAESTRO: An Adaptive Low Mach Number Hydrodynamics Algorithm for Stellar Flows", Astrophysical Journal Supplement Series, 188, 358-383, June 2010. [pdf] [arxiv]

    M. Zingale, A. S. Almgren, J. B. Bell, A. Nonaka, and S. E. Woosley, "Low Mach Number Modeling of Type Ia Supernovae. IV. White Dwarf Convection", Astrophysical Journal, 704, 196-210, 2009. [pdf]

    S. E. Woosley, A. S. Almgren, A. J. Aspden, J. B. Bell, D. Kasen, A. R. Kerstein, H. Ma, A. Nonaka, and M. Zingale, "Type Ia Supernovae: Advances in Large Scale Simulation ", SciDAC 2009, J. of Physics: Conference Series, 180, July 2009. [pdf]

    A. S. Almgren, J. B. Bell, A. Nonaka, M. Zingale, "A New Low Mach Number Approach in Astrophysics", Computers in Science and Engineering, vol. 11, no. 2, pp. 24-33, March/April 2009. [CiSE]

    M. Zingale, A. S. Almgren, J. B. Bell, C. M. Malone and A. Nonaka, "Astrophysical Applications of the MAESTRO Code", SciDAC 2008, J. of Physics: Conference Series, 125, Seattle Washington, July 2008. [pdf]

    A. S. Almgren, J. B. Bell, and M. Zingale, "MAESTRO: A Low Mach Number Stellar Hydrodynamics Code ", SciDAC 2007, J. of Physics: Conference Series, Boston, Massachusetts, July 2007.

    A. S. Almgren, J. B. Bell, A. Nonaka, and M. Zingale, "Low Mach Number Modeling of Type Ia Supernovae. III. Reactions", Astrophysical Journal, 684, 449-470, 2008. LBNL Report LBNL-58673 Pt. III. [pdf]

    A. S. Almgren, J. B. Bell, C. A. Rendleman, and M. Zingale, "Low Mach Number Modeling of Type Ia Supernovae. II. Energy Evolution", Astrophysical Journal, 649, 927-938, 2006. LBNL Report LBNL-58673 Pt. II. [pdf]

    A. S. Almgren, J. B. Bell, C. A. Rendleman, and M. Zingale, "Low Mach Number Modeling of Type Ia Supernovae. I. Hydrodynamics", Astrophysical Journal, 637, 922-936, 2006. LBNL Report LBNL-58673. [pdf](revised)

    Acknowledgements

    This work was supported by the SciDAC Program of the DOE Office of Mathematics, Information, and Computational Sciences under the U.S. Department of Energy under contract No. DE-AC02-05CH11231 to LBNL and by a DOE Office of Nuclear Physics Outstanding Junior Investigator award (No. DE-FG02-06ER41448) to Mike Zingale at Stony Brook Univeristy.
    SciDAC