A Multiparameter, Numerical Stability Analysis of a Standing Cantilever Conveying Fluid

In this paper, we numerically examine the stability of a standing cantilever conveying fluid in a multiparameter space. Based on nonlinear beam theory, our mathematical model turns out to be replete with exciting behavior, some of which was totally unexpected and novel, and some of which confirm our intuition as well as the work of others. The numerical bifurcation results obtained from applying the Library of Continuation Algorithms (LOCA) reveal a plethora of one, two, and higher codimension bifurcations. For a vertical or standing cantilever beam, bifurcations to buckled solutions (via symmetry breaking) and oscillating solutions are detected as a function of gravity and the fluid-structure interaction. The unfolding of these results as a function of the orientation of the beam compared to gravity is also revealed

Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry

In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the bifurcation problem associated with the steady incompressible Navier-Stokes equations. Particular attention is given to the reliable error estimation of the critical Reynolds number at which a steady pitchfork or Hopf bifurcation occurs when the underlying physical system possesses reflectional or Z_2 symmetry. Here, computable a posteriori error bounds are derived based on employing the generalization of the standard Dual-Weighted-Residual approach, originally developed for the estimation of target functionals of the solution, to bifurcation problems. Numerical experiments highlighting the practical performance of the proposed a posteriori error indicator on adaptively refined computational meshes are presented

Automating embedded analysis capabilities and managing software complexity in multiphysics simulation part II: application to partial differential equations

A template-based generic programming approach was presented in a previous paper that separates the development effort of programming a physical model from that of computing additional quantities, such as derivatives, needed for embedded analysis algorithms. In this paper, we describe the implementation details for using the template-based generic programming approach for simulation and analysis of partial differential equations (PDEs). We detail several of the hurdles that we have encountered, and some of the software infrastructure developed to overcome them. We end with a demonstration where we present shape optimization and uncertainty quantification results for a 3D PDE application

Albany: Using Component-based Design to Develop a Flexible, Generic Multiphysics Analysis Code

Abstract: Albany is a multiphysics code constructed by assembling a set of reusable, general components. It is an implicit, unstructured grid finite element code that hosts a set of advanced features that are readily combined within a single analysis run. Albany uses template-based generic programming methods to provide extensibility and flexibility; it employs a generic residual evaluation interface to support the easy addition and modification of physics. This interface is coupled to powerful automatic differentiation utilities that are used to implement efficient nonlinear solvers and preconditioners, and also to enable sensitivity analysis and embedded uncertainty quantification capabilities as part of the forward solve. The flexible application programming interfaces in Albany couple to two different adaptive mesh libraries; it internally employs generic integration machinery that supports tetrahedral, hexahedral, and hybrid meshes of user specified order. We present the overall design of Albany, and focus on the specifics of the integration of many of its advanced features. As Albany and the components that form it are openly available on the internet, it is our goal that the reader might find some of the design concepts useful in their own work. Albany results in a code that enables the rapid development of parallel, numerically efficient multiphysics software tools. In discussing the features and details of the integration of many of the components involved, we show the reader the wide variety of solution components that are available and what is possible when they are combined within a simulation capability. Key Words: partial differential equations, finite element analysis, template-based generic programmin

The DOE E3SM Coupled Model Version 1: Overview and Evaluation at Standard Resolution

This work documents the first version of the U.S. Department of Energy (DOE) new Energy Exascale Earth System Model (E3SMv1). We focus on the standard resolution of the fully coupled physical model designed to address DOE mission-relevant water cycle questions. Its components include atmosphere and land (110-km grid spacing), ocean and sea ice (60 km in the midlatitudes and 30 km at the equator and poles), and river transport (55 km) models. This base configuration will also serve as a foundation for additional configurations exploring higher horizontal resolution as well as augmented capabilities in the form of biogeochemistry and cryosphere configurations. The performance of E3SMv1 is evaluated by means of a standard set of Coupled Model Intercomparison Project Phase 6 (CMIP6) Diagnosis, Evaluation, and Characterization of Klima simulations consisting of a long preindustrial control, historical simulations (ensembles of fully coupled and prescribed SSTs) as well as idealized CO2 forcing simulations. The model performs well overall with biases typical of other CMIP-class models, although the simulated Atlantic Meridional Overturning Circulation is weaker than many CMIP-class models. While the E3SMv1 historical ensemble captures the bulk of the observed warming between preindustrial (1850) and present day, the trajectory of the warming diverges from observations in the second half of the twentieth century with a period of delayed warming followed by an excessive warming trend. Using a two-layer energy balance model, we attribute this divergence to the model’s strong aerosol-related effective radiative forcing (ERFari+aci = -1.65 W/m2) and high equilibrium climate sensitivity (ECS = 5.3 K).Plain Language SummaryThe U.S. Department of Energy funded the development of a new state-of-the-art Earth system model for research and applications relevant to its mission. The Energy Exascale Earth System Model version 1 (E3SMv1) consists of five interacting components for the global atmosphere, land surface, ocean, sea ice, and rivers. Three of these components (ocean, sea ice, and river) are new and have not been coupled into an Earth system model previously. The atmosphere and land surface components were created by extending existing components part of the Community Earth System Model, Version 1. E3SMv1’s capabilities are demonstrated by performing a set of standardized simulation experiments described by the Coupled Model Intercomparison Project Phase 6 (CMIP6) Diagnosis, Evaluation, and Characterization of Klima protocol at standard horizontal spatial resolution of approximately 1° latitude and longitude. The model reproduces global and regional climate features well compared to observations. Simulated warming between 1850 and 2015 matches observations, but the model is too cold by about 0.5 °C between 1960 and 1990 and later warms at a rate greater than observed. A thermodynamic analysis of the model’s response to greenhouse gas and aerosol radiative affects may explain the reasons for the discrepancy.Key PointsThis work documents E3SMv1, the first version of the U.S. DOE Energy Exascale Earth System ModelThe performance of E3SMv1 is documented with a set of standard CMIP6 DECK and historical simulations comprising nearly 3,000 yearsE3SMv1 has a high equilibrium climate sensitivity (5.3 K) and strong aerosol-related effective radiative forcing (-1.65 W/m2)Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/151288/1/jame20860_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151288/2/jame20860.pd

Adaptivity and a posteriori error control for bifurcation problems I: the Bratu problem

This article is concerned with the numerical detection of bifurcation points of nonlinear partial differential equations as some parameter of interest is varied. In particular, we study in detail the numerical approximation of the Bratu problem, based on exploiting the symmetric version of the interior penalty discontinuous Galerkin finite element method. A framework for a posteriori control of the discretization error in the computed critical parameter value is developed based upon the application of the dual weighted residual (DWR) approach. Numerical experiments are presented to highlight the practical performance of the proposed a posteriori error estimator

Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry

In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the bifurcation problem associated with the steady incompressible Navier-Stokes equations. Particular attention is given to the reliable error estimation of the critical Reynolds number at which a steady pitchfork or Hopf bifurcation occurs when the underlying physical system possesses reflectional or Z_2 symmetry. Here, computable a posteriori error bounds are derived based on employing the generalization of the standard Dual-Weighted-Residual approach, originally developed for the estimation of target functionals of the solution, to bifurcation problems. Numerical experiments highlighting the practical performance of the proposed a posteriori error indicator on adaptively refined computational meshes are presented