EARLY EXPERIENCES WITH THE 360TF IBM BLUE GENE/L PLATFORM

2008 ◽  
Vol 05 (02) ◽  
pp. 237-253 ◽  
Author(s):  
G. BHANOT ◽  
J. M. DENNIS ◽  
J. EDWARDS ◽  
W. GRABOWSKI ◽  
M. GUPTA ◽  
...  
Keyword(s):  
Test Problem ◽  
Time Integration ◽  
Atmospheric Model ◽  
Horizontal Resolution ◽  
Implicit Time ◽  
Preconditioned Conjugate Gradient ◽  
Time Step ◽  
Climate System Model ◽  
Vertical Coordinate ◽  
Blue Gene

The High Order Method Modeling Environment is a scalable, spectral-element-based prototype for the Community Atmospheric Model component of the Community Climate System Model. The 3D moist primitive equations are solved on the cubed sphere with a hybrid pressure η vertical coordinate using an Emanuel convective parametrization for moist processes. Semi-implicit time integration, based on a preconditioned conjugate gradient solver, circumvents the time step restrictions associated with gravity waves. Benchmarks for two standard tests problems at 10 km horizontal resolution have been run on Blue Gene/L. Results obtained on a 32-rack Blue Gene/L system (65,536 processors, 183.5-teraflop peak) show sustained performance of 8.0 teraflops on 32,768 processors for the moist Held–Suarez test problem in coprocessor mode and 11.3 teraflops on 32,768 processors for the aquaplanet test problem, running in virtual node mode.

scholarly journals Investigation of Air Pocket Behavior in Pipelines Using Rigid Column Model and Contributions of Time Integration Schemes

Water ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 785
Author(s):  
Arman Rokhzadi ◽  
Musandji Fuamba
Keyword(s):  
Transient Flow ◽  
Time Integration ◽  
Driving Pressure ◽  
Implicit Time ◽  
Numerical Dissipation ◽  
Integration Scheme ◽  
Time Step ◽  
Column Model ◽  
Integration Schemes ◽  
Backward Euler

This paper studies the air pressurization problem caused by a partially pressurized transient flow in a reservoir-pipe system. The purpose of this study is to analyze the performance of the rigid column model in predicting the attenuation of the air pressure distribution. In this regard, an analytic formula for the amplitude and frequency will be derived, in which the influential parameters, particularly, the driving pressure and the air and water lengths, on the damping can be seen. The direct effect of the driving pressure and inverse effect of the product of the air and water lengths on the damping will be numerically examined. In addition, these numerical observations will be examined by solving different test cases and by comparing to available experimental data to show that the rigid column model is able to predict the damping. However, due to simplified assumptions associated with the rigid column model, the energy dissipation, as well as the damping, is underestimated. In this regard, using the backward Euler implicit time integration scheme, instead of the classical fourth order explicit Runge–Kutta scheme, will be proposed so that the numerical dissipation of the backward Euler implicit scheme represents the physical dissipation. In addition, a formula will be derived to calculate the appropriate time step size, by which the dissipation of the heat transfer can be compensated.

scholarly journals A Semi-Implicit Version of the MPAS-Atmosphere Dynamical Core

2015 ◽  
Vol 143 (9) ◽  
pp. 3838-3855 ◽  
Author(s):  
Steven Sandbach ◽  
John Thuburn ◽  
Danail Vassilev ◽  
Michael G. Duda
Keyword(s):  
Time Integration ◽  
Standard Test ◽  
Newton Iteration ◽  
Atmospheric Modeling ◽  
Implicit Time ◽  
Integration Scheme ◽  
Baroclinic Wave ◽  
Time Step ◽  
Integration Schemes ◽  
Helmholtz Problem

Abstract An important question for atmospheric modeling is the viability of semi-implicit time integration schemes on massively parallel computing architectures. Semi-implicit schemes can provide increased stability and accuracy. However, they require the solution of an elliptic problem at each time step, creating concerns about their parallel efficiency and scalability. Here, a semi-implicit (SI) version of the Model for Prediction Across Scales (MPAS) is developed and compared with the original model version, which uses a split Runge–Kutta (SRK3) time integration scheme. The SI scheme is based on a quasi-Newton iteration toward a Crank–Nicolson scheme. Each Newton iteration requires the solution of a Helmholtz problem; here, the Helmholtz problem is derived, and its solution using a geometric multigrid method is described. On two standard test cases, a midlatitude baroclinic wave and a small-planet nonhydrostatic gravity wave, the SI and SRK3 versions produce almost identical results. On the baroclinic wave test, the SI version can use somewhat larger time steps (about 60%) than the SRK3 version before losing stability. The SI version costs 10%–20% more per step than the SRK3 version, and the weak and strong scalability characteristics of the two versions are very similar for the processor configurations the authors have been able to test (up to 1920 processors). Because of the spatial discretization of the pressure gradient in the lowest model layer, the SI version becomes unstable in the presence of realistic orography. Some further work will be needed to demonstrate the viability of the SI scheme in this case.

scholarly journals WAVETRISK-2.1: an adaptive dynamical core for ocean modelling

2021 ◽  
Author(s):  
Nicholas Keville-Reynolds Kevlahan ◽  
Florian Lemarié
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Time Integration ◽  
Ocean Model ◽  
Mesh Adaptivity ◽  
Time Step ◽  
Vertical Coordinate ◽  
Slip Boundary ◽  
Modelling Framework ◽  
Atmosphere Model

Abstract. This paper introduces WAVETRISK-2.1 (i.e. WAVETRISK-OCEAN), an incompressible version of the atmosphere model wavetrisk-1.x with free-surface. This new model is built on the same wavelet-based dynamically adaptive core as wavetrisk, which itself uses DYNANICO's mimetic vector-invariant multilayer rotating shallow water formulation. Both codes use a Lagrangian vertical coordinate with conservative remapping. The ocean variant solves the incompressible multilayer shallow water equations with inhomogeneous density layers. Time integration uses barotropic--baroclinic mode splitting via an semi-implicit free surface formulation, which is about 34–44 times faster than an unsplit explicit time-stepping. The barotropic and baroclinic estimates of the free surface are reconciled at each time step using layer dilation. No slip boundary conditions at coastlines are approximated using volume penalization. The vertical eddy viscosity and diffusivity coefficients are computed from a closure model based on turbulent kinetic energy (TKE). Results are presented for a standard set of ocean model test cases adapted to the sphere (seamount, upwelling and baroclinic turbulence). An innovative feature of wavetrisk-ocean is that it could be coupled easily to the wavetrisk atmosphere model, thus providing a first building block toward an integrated Earth-system model using a consistent modelling framework with dynamic mesh adaptivity and mimetic properties.

scholarly journals Staggered Vertical Discretization of the Canadian Environmental Multiscale (GEM) Model Using a Coordinate of the Log-Hydrostatic-Pressure Type

2014 ◽  
Vol 142 (3) ◽  
pp. 1183-1196 ◽  
Author(s):  
Claude Girard ◽  
André Plante ◽  
Michel Desgagné ◽  
Ron McTaggart-Cowan ◽  
Jean Côté ◽  
...  
Keyword(s):  
Hydrostatic Pressure ◽  
Solution Method ◽  
Time Integration ◽  
Atmospheric Model ◽  
Integration Scheme ◽  
Limited Area ◽  
Vertical Coordinate ◽  
Global Environmental ◽  
Time Integration Scheme ◽  
Global Environmental Multiscale

Abstract The Global Environmental Multiscale (GEM) model is the Canadian atmospheric model used for meteorological forecasting at all scales. A limited-area version now also exists. It is a gridpoint model with an implicit semi-Lagrangian iterative space–time integration scheme. In the “horizontal,” the equations are written in spherical coordinates with the traditional shallow atmosphere approximations and are discretized on an Arakawa C grid. In the “vertical,” the equations were originally defined using a hydrostatic-pressure coordinate and discretized on a regular (unstaggered) grid, a configuration found to be particularly susceptible to noise. Among the possible alternatives, the Charney–Phillips grid, with its unique characteristics, and, as the vertical coordinate, log-hydrostatic pressure are adopted. In this paper, an attempt is made to justify these two choices on theoretical grounds. The resulting equations and their vertical discretization are described and the solution method of what is forming the new dynamical core of GEM is presented, focusing on these two aspects.

scholarly journals Accuracy Analysis of a Spectral Element Atmospheric Model Using a Fully Implicit Solution Framework

2010 ◽  
Vol 138 (8) ◽  
pp. 3333-3341 ◽  
Author(s):  
Katherine J. Evans ◽  
Mark A. Taylor ◽  
John B. Drake
Keyword(s):  
Shallow Water Equation ◽  
Time Integration ◽  
Atmospheric Model ◽  
Test Cases ◽  
Implicit Methods ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Fully Implicit ◽  
Stability Limits

Abstract A fully implicit (FI) time integration method has been implemented into a spectral finite-element shallow-water equation model on a sphere, and it is compared to existing fully explicit leapfrog and semi-implicit methods for a suite of test cases. This experiment is designed to determine the time step sizes that minimize simulation time while maintaining sufficient accuracy for these problems. For test cases without an analytical solution from which to compare, it is demonstrated that time step sizes 30–60 times larger than the gravity wave stability limits and 6–20 times larger than the advective-scale stability limits are possible using the FI method without a loss in accuracy, depending on the problem being solved. For a steady-state test case, the FI method produces error within machine accuracy limits as with existing methods, but using an arbitrarily large time step size.

Studies on the Accuracy Stability and Efficiency of a New Time Integration Scheme for Ballast Modeling Using the Discrete Element Method

2014 ◽  
Author(s):  
G. F. Mathews ◽  
R. L. Mullen ◽  
D. C. Rizos
Keyword(s):  
Particle Interaction ◽  
Time Integration ◽  
Discrete Element ◽  
Critical Discussion ◽  
Implicit Time ◽  
Integration Scheme ◽  
Computationally Efficient ◽  
Time Step ◽  
Central Difference ◽  
Time Integration Scheme

This paper presents the development of a semi-implicit time integration scheme, originally developed for structural dynamics in the 1970’s, and its implementation for use in Discrete Element Methods (DEM) for rigid particle interaction, and interaction of elastic bodies that are modeled as a cluster of rigid interconnected particles. The method is developed in view of ballast modeling that accounts for the flexibility of aggregates and the arbitrary shape and size of granules. The proposed scheme does not require any matrix inversions and is expressed in an incremental form making it appropriate for non-linear problems. The proposed method focuses on improving the efficiency, stability and accuracy of the solutions, as compared to current practice. A critical discussion of the findings of the studies is presented. Extended verification and assessment studies demonstrate that the proposed algorithm is unconditionally stable and accurate even for large time step sizes. It is demonstrated that the proposed method is at least as computationally efficient as the Central Difference Method. Guidelines for the implementation of the method to ballast modeling are discussed.

scholarly journals Efficient extrapolation methods for electro- and magnetoquasistatic field simulations

2003 ◽  
Vol 1 ◽  
pp. 81-86 ◽  
Author(s):  
M. Clemens ◽  
M. Wilke ◽  
T. Weiland
Keyword(s):  
Taylor Series Expansion ◽  
Iterative Solvers ◽  
Gradient Algorithm ◽  
Implicit Time ◽  
Preconditioned Conjugate Gradient ◽  
Test Problems ◽  
Time Step ◽  
Time Stepping ◽  
Multi Stage ◽  
Runge Kutta

Abstract. In magneto- and electroquasi-static time domain simulations with implicit time stepping schemes the iterative solvers applied to the large sparse (non-)linear systems of equations are observed to converge faster if more accurate start solutions are available. Different extrapolation techniques for such new time step solutions are compared in combination with the preconditioned conjugate gradient algorithm. Simple extrapolation schemes based on Taylor series expansion are used as well as schemes derived especially for multi-stage implicit Runge-Kutta time stepping methods. With several initial guesses available, a new subspace projection extrapolation technique is proven to produce an optimal initial value vector. Numerical tests show the resulting improvements in terms of computational efficiency for several test problems. In quasistatischen elektromagnetischen Zeitbereichsimulationen mit impliziten Zeitschrittverfahren zeigt sich, dass die iterativen Lösungsverfahren für die großen dünnbesetzten (nicht-)linearen Gleichungssysteme schneller konvergieren, wenn genauere Startlösungen vorgegeben werden. Verschiedene Extrapolationstechniken werden für jeweils neue Zeitschrittlösungen in Verbindung mit dem präkonditionierten Konjugierte Gradientenverfahren vorgestellt. Einfache Extrapolationsverfahren basierend auf Taylorreihenentwicklungen werden ebenso benutzt wie speziell für mehrstufige implizite Runge-Kutta-Verfahren entwickelte Verfahren. Sind verschiedene Startlösungen verfügbar, so erlaubt ein neues Unterraum-Projektion- Extrapolationsverfahren die Konstruktion eines optimalen neuen Startvektors. Numerische Tests zeigen die aus diesen Verfahren resultierenden Verbesserungen der numerischen Effizienz.

WAVETRISK-OCEAN: an adaptive dynamical core for ocean modelling

2021 ◽  
Author(s):  
Kevlahan Nicholas
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Time Integration ◽  
Ocean Model ◽  
Time Step ◽  
Vertical Coordinate ◽  
Modelling Framework ◽  
Standard Set ◽  
Atmosphere Model ◽  
Multilayer Shallow Water Equations

<p>This talk introduces WAVETRISK-OCEAN, an incompressible version of the atmosphere model WAVETRISK.  This new model is built on the same wavelet-based dynamically adaptive core as WAVETRISK, which itself uses DYNAMICO's mimetic vector-invariant multilayer shallow water formulation. Both codes use a Lagrangian vertical coordinate with conservative remapping.  The ocean variant solves the incompressible multilayer shallow water equations with a Ripa type thermodynamic treatment of horizontal density gradients.  Time integration uses barotropic-baroclinic mode splitting via an implicit free surface formulation, which is about 15 times faster than explicit time stepping.  The barotropic and baroclinic estimates of the free surface are reconciled at each time step using layer dilation. No slip boundary conditions at coastlines are approximated using volume penalization.  Results are presented for a standard set of ocean model test cases adapted to the sphere (seamount,  upwelling and baroclinic jet) as well as  turbulent wind-driven gyre flow in simplified geometries.  An innovative feature of WAVETRISK-OCEAN is that it could be coupled easily to the WAVETRISK atmosphere model, providing a simple integrated Earth system model using a consistent modelling framework.</p>

Impact Analysis of Sandwich Composites

2008 ◽  
Author(s):  
Laura Ferrero ◽  
Ugo Icardi
Keyword(s):  
Impact Analysis ◽  
Time Integration ◽  
Nonlinear Problems ◽  
Implicit Time ◽  
Contact Radius ◽  
Integration Scheme ◽  
Sandwich Composites ◽  
Time Step ◽  
Wide Range ◽  
The Impact

A finite element simulation of impacts on sandwich composites with laminated faces is presented; it is based on a refined multilayered plate model with a high-order zig-zag representation of displacements, which is incorporated through a strain energy updating process. This allows the implementation into existing commercial finite elements codes, preserving their program structure. As customary, the Hertzian law and the Newmark implicit time integration scheme are used for solving the contact problem. The contact radius and the force are computed within each time step by an iterative algorithm which forces the impacted top surface to conform, in the least-squares sense, to the shape of the impactor. Nonlinear strains of von Karman type are used. As appearing by the comparison with experimental results, the present model is able to accurately predict the impact force, the core damage and the damage of face sheets in sandwich composites with foam and or honeycomb core. Moreover, this paper also assesses the accuracy and the range of application of stress based criteria in predicting the onset and evolution of delamination in service. These criteria are widespread by virtue of their low run time and storage costs, although no exhaustive proofs are known weather they are accurate enough for a reasonably wide range of applications. Since where highly iterative solutions are involved (e.g., impact and geometric, or material nonlinear problems) they are the only currently affordable failure models, it appears of primary importance to fill this gap. Aimed to contribute to the knowledge advancement in this field, a comparison is presented with more sophisticate fracture mechanics and progressive delamination models.

scholarly journals Overview of the 2018 Workshop on Iterative Errors in Unsteady Flow Simulations

2020 ◽  
Vol 5 (2) ◽  
Author(s):  
L. Eça ◽  
G. Vaz ◽  
M. Hoekstra ◽  
S. Pal ◽  
E. Muller ◽  
...  
Keyword(s):  
Unsteady Flow ◽  
Time Integration ◽  
Implicit Time ◽  
Test Case ◽  
Convergence Criteria ◽  
Courant Number ◽  
Time Step ◽  
Flow Solver ◽  
Flow Simulations ◽  
Implicit Time Integration

Abstract Two workshops were held at the ASME V&V Symposiums of 2017 and 2018 dedicated to Iterative Errors in Unsteady Flow Simulations. The focus was on the effect of iterative errors on numerical simulations performed with implicit time integration, which require the solution of a nonlinear set of equations at each time-step. The main goal of these workshops was to create awareness to the problem and to confirm that different flow solvers exhibited the same trends. The test case was a simple two-dimensional, laminar flow of a single-phase, incompressible, Newtonian fluid around a circular cylinder at the Reynolds number of 100. A set of geometrically similar multiblock structured grids was available and boundary conditions to perform the simulations were proposed to the participants. Results from seven flow solvers were submitted, but not all of them followed exactly the proposed conditions. One set of results was obtained with adaptive grid and time refinement using triangular elements (CADYF) and another used a compressible flow solver with a dual time stepping technique and a Mach number of 0.2 (DLR-Tau). The remaining five submissions were obtained with five different incompressible flow solvers (ansyscfx 14.5, pimplefoam, refresco, saturne, starccm+ v12.06.010-R8) using implicit time integration in the proposed grids. The results obtained in this simple test case showed that iterative errors may have a significant impact on the numerical accuracy of unsteady flow simulations performed with implicit time integration. Iterative errors can be significantly larger (one to two orders of magnitude) than the residuals and/or solution changes used as convergence criteria at each time-step. The Courant number affected the magnitude of the iterative errors obtained in the proposed exercise. For the same iterative convergence criteria at each time-step, increasing the Courant number tends to increase the iterative error.

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