APSARA: A multi-dimensional unsplit fourth-order explicit Eulerian hydrodynamics code for arbitrary curvilinear grids

Abstract

We present a new fourth-order, finite-volume hydrodynamics code named Apsara. The code employs a high-order, finite-volume method for mapped coordinates with extensions for nonlinear hyperbolic conservation laws. Apsara can handle arbitrary structured curvilinear meshes in three spatial dimensions. The code has successfully passed several hydrodynamic test problems, including the advection of a Gaussian density profile and a nonlinear vortex and the propagation of linear acoustic waves. For these test problems, Apsara produces fourth-order accurate results in case of smooth grid mappings. The order of accuracy is reduced to first-order when using the nonsmooth circular grid mapping. When applying the high-order method to simulations of low-Mach number flows, for example, the Gresho vortex and the Taylor-Green vortex, we discover that Apsara delivers superior results to codes based on the dimensionally split, piecewise parabolic method (PPM) widely used in astrophysics. Hence, Apsara is a suitable tool for simulating highly subsonic flows in astrophysics. In the first astrophysical application, we perform implicit large eddy simulations (ILES) of anisotropic turbulence in the context of core collapse supernova (CCSN) and obtain results similar to those previously reported.

Three-dimensional simulations of neutrino-driven core-collapse supernovae from low-mass single and binary star progenitors

“…Aside from giving up the spherical coordinate geometry altogether in favour of Cartesian geometry and adaptive mesh refinement, various approaches have been applied to alleviate the time step constraints near the axis without sacrificing the advantages of spherical geometry. Overset orthogonal grids (Kageyama & Sato 2004;Wongwathanarat et al 2010a) and non-orthogonal grids (Wongwathanarat et al 2016) are excellent solutions, but add some complexity to the grid geometry. An alternative approach is to retain the basic structure of a spherical polar grid, but to adaptively combine ("coarsen") cells to at high latitudes and (optionally) also close to the origin.…”

Hydrodynamics of core-collapse supernovae and their progenitors

“…As a downside, it is more complicated-but possible (Peng et al 2006)-to implement overset grids in a strictly conservative manner. In future, non-orthogonal grids spherical grids (Ronchi et al 1996;Calhoun et al 2008;Wongwathanarat et al 2016) may provide another solution that avoids the axis problem and ensures conservation in a straightforward manner, but applications Alternative spherical grids that avoid the tight time step constraint at the axis of standard spherical polar grids: a Grid with mesh coarsening in the u-direction only. Only an octant of the entire grid is shown.…”

“…First, such methods open up the regime of low Mach numbers to explicit Godunv-based codes. Using their APSARA code, Wongwathanarat et al (2016) were able to solve the Gresho vortex problem (Gresho and Chan 1990) with little dissipation down to a Mach number of 10 À4 with the extremum-preserving PPM method of Colella and Sekora (2008), which is about two orders of magnitude better than for the MC limiter (Miczek et al 2015), and about one order of magnitude better than for standard PPM.…”

An FFT-based Solution Method for the Poisson Equation on 3D Spherical Polar Grids

“…This, however, is not a fundamental restriction and could be remedied by using more general algorithms for the parallel FFT and matrix-vector multiplication. A more serious limitation is that the algo-rithm cannot readily be generalized to overset spherical grids (Kageyama & Sato 2004;Wongwathanarat et al 2010) or spherical grids with non-orthogonal patches like the cubedsphere grid (Wongwathanarat et al 2016). One option would be to map to an auxiliary global spherical polar grid for the Poisson solver.…”