MAESTROeX: A Massively Parallel Low Mach Number Astrophysical Solver

Abstract

We present MAESTROeX, a massively parallel solver for low Mach number astrophysical flows. The underlying low Mach number equation set allows for efficient, long-time integration for highly subsonic flows compared to compressible approaches. MAESTROeX is suitable for modeling full spherical stars as well as well as planar simulations of dynamics within localized regions of a star, and can robustly handle several orders of magnitude of density and pressure stratification. Previously, we have described the development of the predecessor of MAESTROeX, called MAESTRO, in a series of papers. Here, we present a new, greatly simplified temporal integration scheme that retains the same order of accuracy as our previous approaches. We also explore the use of alternative spatial mapping of the one-dimensional base state onto the full Cartesian grid. The code leverages the new AMReX software framework for block-structured adaptive mesh refinement (AMR) applications, allowing for scalability to large fractions of leadership-class machines. Using our previous studies on the convective phase of single-degenerate progenitor models of Type Ia supernovae as a guide, we characterize the performance of the code and validate the new algorithmic features. Like MAESTRO, MAESTROeX is fully open source.

A hybrid pseudo-incompressible–hydrostatic model

“…We emphasise that in order to obtain this result, we needed to use the momentum equation (2.21), which includes an additional force not present in previous pseudo-incompressible models (e.g. Durran 1989; Almgren et al 2008; Klein & Pauluis 2012; Vasil et al 2013; O'Neill & Klein 2014; Fan et al 2019 a ). The presence of this force follows directly from Hamilton's principle.…”

“…This function will depend on the choice of boundary condition at the upper boundary. For example, in the case where the upper boundary is impenetrable it is convenient to eliminate between (2.36) and (2.37), leading to a constraint equation for the velocity field: where we have defined to match the notation used in the low-Mach-number literature (Fan et al 2019 a ). If we neglect the term here then in general this equation has no solutions that meet the impenetrable boundary conditions; this is just an example of the problem mentioned in § 2.2, and indicates that the velocity constraint is degenerate for this choice of boundary conditions.…”

“…To avoid inessential complications, in what follows we consider an ideal gas, so that the relations between the thermodynamic variables can be stated explicitly. Our complete set of equations is then The MAESTROeX code (Fan et al 2019 a , b ) is a massively parallel, finite-volume solver for low-Mach-number astrophysical flows. It allows us to solve the above equations after having modified the code to include the terms involving and for planar geometry (avoiding the additional complexity of the spherical implementation for now).…”

“…(The fork of the code can be found at .) Here we compare results obtained using this implementation, in a number of test problems, with results obtained using the existing pseudo-incompressible implementation in MAESTROeX (Fan et al 2019 a ) and the fully compressible CASTRO code (Almgren et al 2010). To demonstrate the effect of each of our separate changes to the model, we consider four levels of refinement: denotes the original implementation; , as , but including the term; , as , but including the term in the momentum equation; and , as , but also using the thermodynamically consistent , rather than .…”

“…(Such a force is expected whenever an additional constraint is imposed, though this point does not always seem to have been recognised in the literature.) As a proof of concept we present an implementation of our hybrid equations using the MAESTROeX code (Fan et al 2019 a ).…”