Radiation hydrodynamics are a challenging multiscale and multiphysics set of equations. To capture the relevant physics of interest, one typically must time step on the hydrodynamics timescale, making explicit integration the obvious choice. On the other hand, the coupled radiation equations have a scaling such that implicit integration is effectively necessary in non-relativistic regimes. A first-order Lie-Trotter-like operator split is the most common time integration scheme used in practice, alternating between an explicit hydrodynamics step and an implicit radiation solve and energy deposition step. However, such a scheme is limited to first-order accuracy, and non- linear coupling between the radiation and hydrodynamics equations makes a more general additive partitioning of the equations non-trivial. Here, we develop a new formulation and partitioning of radiation hydrodynamics with gray diffusion that allows us to apply (linearly) implicit-explicit Runge-Kutta time integration schemes. We prove conservation of total energy in the new framework, and demonstrate 2nd-order convergence in time on multiple radiative shock problems, achieving error 3–5 orders of magnitude smaller than the first-order Lie-Trotter operator split at the hydrodynamic CFL, even when Lie-Trotter applies a 3rd-order TVD Runge-Kutta scheme to the hydrodynamics equations.

We present an open-source code, Xyst, intended for the simulation of complex-geometry 3D compressible flows. The software implementation facilitates the effective use of the largest distributed-memory machines, combining data-, and task-parallelism on top of the Charm++ runtime system. Charm++'s execution model is asynchronous by default, allowing arbitrary overlap of computation and communication. Built-in automatic load balancing enables redistribution of arbitrarily heterogeneous computational load based on real-time CPU load measurement at negligible cost. The runtime system also features automatic checkpointing, fault tolerance, resilience against hardware failure, and supports power- and energy-aware computation. We verify and validate the numerical method and demonstrate the benefits of automatic load balancing for irregular workloads.

impractical if A is large and sparse. Iterative methods such as Gauss-Seidel, SOR, Chebyshev semi-iterative, and related methods also often depend upon parameters that require calibration and which are sometimes hard to choose properly. An iterative method which surmounts many of these difficulties is the method of conjugate gradient. Algorithms of this type find solutions iteratively, by optimally calculating the next approximation from the residuals.

3 The role of Ristra at LANL post-ATDM 88Nodes

The persistently growing resilience concerns of large-scale computing systems today require not only generic fault tolerance approaches, but also application-level resilience, due to demanding efficiency and various domain-specific requirements. Scientific applications within a particular domain generally comply with domain conservation laws, which can be leveraged as an error detection criterion to study the resilience of this domain of applications sharing similar program characteristics. However, it is challenging to achieve application resilience: (a) how to identify the invariants of a given domain of applications, knowing the conservation laws, and (b) how to utilize the invariants to efficiently detect and recover from failures in application runs. In this work, we target several continuum dynamics software packages, FleCSALE [1] and CODY [2] (with intrinsic invariants during computation), study their resilience to soft errors online (injected using an open-source fault injector), and investigate the opportunities for non-intrusive and lightweight failure recovery (checksum-based invariant checking). We propose a checksum-retry approach to achieve our goals, and experimental results on a virtualized platform with extensive fault injection campaigns demonstrate the effectiveness and efficiency of the proposed approach.

From the very origins of numerical hydrodynamics in the Lagrangian work of von Neumann and Richtmyer [83], the issue of total energy conservation as well as entropy production has been problematic. Because of well known problems with mesh deformation, Lagrangian schemes have evolved into Arbitrary Lagrangian-Eulerian (ALE) methods [39] that combine the best properties of Lagrangian and Eulerian methods. Energy issues have persisted for this class of methods. We believe that fundamental issues of energy conservation and entropy production in ALE require further examination. The context of the paper is an ALE scheme that is extended in the sense that it permits cyclic or periodic remap of data between grids of the same or differing connectivity. The principal design goals for a remap method then consist of total energy conservation, bounded internal energy, and compatibility of kinetic energy and momentum. We also have secondary objectives of limiting velocity and stress in a non-directional manner, keeping primitive variables monotone, and providing a higher than second order reconstruction of remapped variables. In particular, the new contributions fall into three categories associated with: energy conservation and entropy production, reconstruction and bounds preservation of scalar and tensor fields, and conservative remap of nonlinear fields. The paper presents a derivation of the methods, details of implementation, and numerical results for a number of test problems. The methods requires volume integration of polynomial functions in polytopal cells with planar facets, and the requisite expressions are derived for arbitrary order. (c) 2017 Elsevier Inc. All rights reserved.

The Ziman formulation of electrical conductivity is tested in warm and hot dense matter using the pseudo-atom molecular dynamics method. Several implementation options that have been widely used in the literature are systematically tested through a comparison to the accurate, but expensive Kohn–Sham density functional theory molecular dynamics (KS-DFT-MD) calculations. The comparison is made for several elements and mixtures and for a wide range of temperatures and densities, and reveals a preferred method that generally gives very good agreement with the KS-DFT-MD results, but at a fraction of the computational cost.

Several next generation high performance computing platforms are or will be based on the so-called many-core architectures, which represent a significant departure from commodity multi-core architectures. A key issue in transitioning large-scale simulation codes from multi-core to many-core systems is closing the serial performance gap, that is, overcoming the large difference in single-core performance between multi-core and many-core systems. In this paper, we discuss how this problem was addressed for a 3D unstructured mesh hydrodynamics code, describe how Amdahl's law can be used to estimate performance targets and guide optimization efforts, and present timing studies performed on multi-core and many-core platforms. Published 2014. This article is a U.S. Government work and is in the public domain in the USA.

We present a three dimensional (3D) arbitrary Lagrangian Eulerian (ALE) hydrodynamic scheme suitable for modeling complex compressible flows on tetrahedral meshes. The new approach stores the conserved variables (mass, momentum, and total energy) at the nodes of the mesh and solves the conservation equations on a control volume surrounding the point. This type of an approach is termed a point-centered hydrodynamic (PCH) method. The conservation equations are discretized using an edge-based finite element (FE) approach with linear basis functions. All fluxes in the new approach are calculated at the center of each tetrahedron. A multidirectional Riemann-like problem is solved at the center of the tetrahedron. The advective fluxes are calculated by solving a 1D Riemann problem on each face of the nodal control volume. A 2-stage Runge–Kutta method is used to evolve the solution forward in time, where the advective fluxes are part of the temporal integration. The mesh velocity is smoothed by solving a Laplacian equation. The details of the new ALE hydrodynamic scheme are discussed. Results from a range of numerical test problems are presented.

The Ziman formulation of electrical conductivity is tested in warm and hot dense matter using the pseudo-atom molecular dynamics method. Several implementation options that have been widely used in the literature are systematically tested through a comparison to accurate but expensive Kohn-Sham density functional theory molecular dynamics (KS-DFT-MD) calculations. The comparison is made for several elements and mixtures and for a wide range of temperatures and densities, and reveals a preferred method that generally gives very good agreement with the KSDFT-MD results, but at a fraction of the computational cost.

High-order discretization techniques offer the potential to significantly reduce the computational costs necessary to obtain accurate predictions when compared to lower-order methods. However, efficient and universally-applicable high-order discretizations remain somewhat illusive, especially for more arbitrary unstructured meshes and for incompressible/low-speed flows. A novel, high-order, central essentially non-oscillatory (CENO), cell-centered, finite-volume scheme is proposed for the solution of the conservation equations of viscous, incompressible flows on three-dimensional unstructured meshes. Similar to finite element methods, coordinate transformations are used to maintain the scheme's order of accuracy even when dealing with arbitrarily-shaped cells having non-planar faces. The proposed scheme is applied to the pseudo-compressibility formulation of the steady and unsteady Navier-Stokes equations and the resulting discretized equations are solved with a parallel implicit Newton-Krylov algorithm. For unsteady flows, a dual-time stepping approach is adopted and the resulting temporal derivatives are discretized using the family of high-order backward difference formulas (BDF). The proposed finite-volume scheme for fully unstructured mesh is demonstrated to provide both fast and accurate solutions for steady and unsteady viscous flows.

Arbitrary Lagrangian-Eulerian (ALE) methods incorporate dynamic mesh motion in an attempt to combine the advantages of both Eulerian and Lagrangian kinematic descriptions. They are especially attractive for modelling compressible flows since their moving meshes are able to capture large distortions of the continuum without excessively smearing free surfaces or material/fluid interfaces. It is desirable to combine these ALE descriptions with high-order spatial and temporal discretizations because, for a given accuracy, high-order methods offer the potential to greatly reduce computational costs. However, the application of high-order methods to ALE is complicated by changing mesh geometry and certain stability requirements such as geometric conservation. In addition to these challenges, it is also difficult to obtain accurate high-order discretizations of conservation laws without any unphysical oscillations across discontinuities, especially on multi-dimensional unstructured meshes. One high-order method that was proved to be efficient and robust for static meshes is the central essentially non-oscillatory (CENO) finite-volume method. Here, the CENO approach was extended to an ALE formulation on tetrahedral meshes. The proposed unstructured method is vertex-based and uses a direct ALE approach that avoids the temporal splitting errors introduced by traditional “Lagrange-plus-remap” ALE methods. The new approach was applied to the conservation equations governing compressible flows and assessed in terms of accuracy and computational cost. For all problems considered, which included various idealized flows, CENO demonstrated excellent reliability and robustness. High-order accuracy was achieved in smooth regions and essentially non-oscillatory solutions were obtained near discontinuities. The high-order schemes were also more computationally efficient for high-accuracy solutions, i.e., they took less wall time to achieve a desired level of error than the lower-order schemes.

•A high-order, central essentially non-oscillatory finite-volume method is proposed.•The method is vertex-based and applied to tetrahedral meshes.•Up to fifth-order accuracy was achieved in smooth regions.•Essentially non-oscillatory solutions were obtained near discontinuities.•The high-order schemes were more computationally efficient for high accuracy.

We present a three-dimensional (3D) finite element (FE) arbitrary Lagrangian–Eulerian (ALE) method for shock hydrodynamics on unstructured grids. The method is based on an FE Eulerian Godunov scheme for linear tetrahedra that has been extended to include mesh motion in an unsplit, flux-conservative formulation. The proposed method eliminates the splitting errors present in traditional Lagrange-plus-remap methods that occur during the remap phase. Unlike typical unsplit approaches, the mesh velocity is not determined by boundary motion but is instead based on the local fluid velocity. Smoothing operations are then applied to the mesh velocity to avoid mesh tangling. This approach allows the mesh to follow the fluid motion in a robust manner and leverage one of the primary advantages of Lagrangian schemes for shock hydrodynamics, namely that the resolution follows the flow. An approximate Riemann solver is used to calculate fluxes in the co-moving frame of the mesh. Results for a number of standard test problems are presented for 3D meshes of up to 107 tetrahedra. Global convergence rates of 0.8–1.0 are observed for shock dominated flows and 1.9 for smooth flows. We also demonstrate that the method satisfies the discrete geometric conservation law to truncation error, conserves total energy to machine precision, and preserves symmetry.