SpECTRE: A Task-based Discontinuous Galerkin Code for Relativistic Astrophysics

We introduce a new relativistic astrophysics code, SpECTRE, that combines a discontinuous Galerkin method with a task-based parallelism model. SpECTRE's goal is to achieve more accurate solutions for challenging relativistic astrophysics problems such as core-collapse supernovae and binary neutron star mergers. The robustness of the discontinuous Galerkin method allows for the use of high-resolution shock capturing methods in regions where (relativistic) shocks are found, while exploiting high-order accuracy in smooth regions. A task-based parallelism model allows efficient use of the largest supercomputers for problems with a heterogeneous workload over disparate spatial and temporal scales. We argue that the locality and algorithmic structure of discontinuous Galerkin methods will exhibit good scalability within a task-based parallelism framework. We demonstrate the code on a wide variety of challenging benchmark problems in (non)-relativistic (magneto)-hydrodynamics. We demonstrate the code's scalability including its strong scaling on the NCSA Blue Waters supercomputer up to the machine's full capacity of 22,380 nodes using 671,400 threads.Comment: 41 pages, 13 figures, and 7 tables. Ancillary data contains simulation input file

Discontinuous Galerkin methods for general-relativistic hydrodynamics: formulation and application to spherically symmetric spacetimes

We have developed the formalism necessary to employ the discontinuous-Galerkin approach in general-relativistic hydrodynamics. The formalism is firstly presented in a general 4-dimensional setting and then specialized to the case of spherical symmetry within a 3+1 splitting of spacetime. As a direct application, we have constructed a one-dimensional code, EDGES, which has been used to asses the viability of these methods via a series of tests involving highly relativistic flows in strong gravity. Our results show that discontinuous Galerkin methods are able not only to handle strong relativistic shock waves but, at the same time, to attain very high orders of accuracy and exponential convergence rates in smooth regions of the flow. Given these promising prospects and their affinity with a pseudospectral solution of the Einstein equations, discontinuous Galerkin methods could represent a new paradigm for the accurate numerical modelling in relativistic astrophysics.Comment: 24 pages, 19 figures. Small changes; matches version to appear in PR

On the effect of different flux limiters on the performance of an engine gas exchange gas-dynamic model

[EN] A suitable tool for the design of intake and exhaust systems of internal combustion engines is provided by time domain non-linear finite volume models. These models, however, are affected by overshoots at discontinuities and numerical dispersion unless some flux limiter is used. In this paper, the effect of the most relevant of such flux limiters on a non-linear staggered-mesh finite-volume model is evaluated. Flux-Corrected-Transport (FCT) and Total Variation Diminishing (TVD) schemes, together with a Momentum Diffusion Term (MDT) are presented for such a model, and the performance of the resulting methods is checked in different problems representative of the influence of engine gas exchange flows on engine performance and intake and exhaust noise. First, two one-dimensional cases are considered: the shock-tube problem, and the propagation of a finite amplitude pressure pulse. Secondly, a simple but representative three-dimensional geometry is studied. From the results obtained, it can be concluded that, even if none of the methods is able to handle properly the three problems considered, the FCT method provides the best overall performance. (C) 2017 Elsevier Ltd. All rights reserved.M. Hernandez is partially supported through contract FPI-S2-2015-1064 of Programa de Apoyo para la Investigacion y Desarrollo (PAID) of Universitat Politecnica de Valencia.Torregrosa, AJ.; Broatch, A.; Arnau Martínez, FJ.; Hernández-Marco, M. (2017). On the effect of different flux limiters on the performance of an engine gas exchange gas-dynamic model. International Journal of Mechanical Sciences. 133:740-751. https://doi.org/10.1016/j.ijmecsci.2017.09.029S74075113

Dynamic earthquake rupture modelled with an unstructured 3-D spectral element method applied to the 2011 M9 Tohoku earthquake

An important goal of computational seismology is to simulate dynamic earthquake rupture and strong ground motion in realistic models that include crustal heterogeneities and complex fault geometries. To accomplish this, we incorporate dynamic rupture modelling capabilities in a spectral element solver on unstructured meshes, the 3-D open source code SPECFEM3D, and employ state-of-the-art software for the generation of unstructured meshes of hexahedral elements. These tools provide high flexibility in representing fault systems with complex geometries, including faults with branches and non-planar faults. The domain size is extended with progressive mesh coarsening to maintain an accurate resolution of the static field. Our implementation of dynamic rupture does not affect the parallel scalability of the code. We verify our implementation by comparing our results to those of two finite element codes on benchmark problems including branched faults. Finally, we present a preliminary dynamic rupture model of the 2011 M_w 9.0 Tohoku earthquake including a non-planar plate interface with heterogeneous frictional properties and initial stresses. Our simulation reproduces qualitatively the depth-dependent frequency content of the source and the large slip close to the trench observed for this earthquake

Dynamic earthquake rupture modelled with an unstructured 3-D spectral element method applied to the 2011 M9 Tohoku earthquake

An important goal of computational seismology is to simulate dynamic earthquake rupture and strong ground motion in realistic models that include crustal heterogeneities and complex fault geometries. To accomplish this, we incorporate dynamic rupture modelling capabilities in a spectral element solver on unstructured meshes, the 3-D open source code SPECFEM3D, and employ state-of-the-art software for the generation of unstructured meshes of hexahedral elements. These tools provide high flexibility in representing fault systems with complex geometries, including faults with branches and non-planar faults. The domain size is extended with progressive mesh coarsening to maintain an accurate resolution of the static field. Our implementation of dynamic rupture does not affect the parallel scalability of the code. We verify our implementation by comparing our results to those of two finite element codes on benchmark problems including branched faults. Finally, we present a preliminary dynamic rupture model of the 2011 Mw 9.0 Tohoku earthquake including a non-planar plate interface with heterogeneous frictional properties and initial stresses. Our simulation reproduces qualitatively the depth-dependent frequency content of the source and the large slip close to the trench observed for this earthquak