GENASIS Mathematics: Object-oriented manifolds, operations, and solvers for large-scale physics simulations

The large-scale computer simulation of a system of physical fields governed by partial differential equations requires some means of approximating the mathematical limit of continuity. For example, conservation laws are often treated with a ‘finite-volume’ approach in which space is partitioned into a large number of small ‘cells,’ with fluxes through cell faces providing an intuitive discretization modeled on the mathematical definition of the divergence operator. Here we describe and make available Fortran 2003 classes furnishing extensible object-oriented implementations of simple meshes and the evolution of generic conserved currents thereon, along with individual ‘unit test’ programs and larger example problems demonstrating their use. These classes inaugurate the Mathematics division of our developing astrophysics simulation code GENASIS (Gen eral A strophysical Si mulation S ystem), which will be expanded over time to include additional meshing options, mathematical operations, solver types, and solver variations appropriate for many multiphysics applications. Program Summary Program Title: SineWave, SawtoothWave, RiemannProblem, RayleighTaylor, SedovTaylor, and FishboneMoncrief (fluid dynamics example problems illustrating GENASISMathematics) Program Files doi: http://dx.doi.org/10.17632/mzvxngwtw6.1 Licensing provisions: GPLv3 Programming language: Fortran 2003 (tested with gfortran 6.2.0, Intel Fortran 16.0.3, Cray Compiler 8.5.3) External routines/libraries: MPI [1] and Silo [2] Nature of problem: By way of illustrating GENASISMathematics functionality, solve example fluid dynamics problems. Solution method: Finite-volume discretization; second-order slope-limited reconstruction; HLL Riemann Solver; Runge–Kutta time integration. Additional comments including Restrictions and Unusual features: The example problems named above are not ends in themselves, but serve to illustrate the functionality available though GENASISMathematics. In addition to these more substantial examples, we provide individual unit test programs for the classes comprised by GENASISMathematics. GENASISMathematics is available in the CPC Program Library and also at https://github.com/GenASiS. [1] http://www.mcs.anl.gov/mpi/[2] https://wci.llnl.gov/simulation/computer-codes/silo