21 Matching Results

Search Results

Advanced search parameters have been applied.

R7 VU Born-Assessed Demo Plan

Description: This is an initial draft of a born-assessed VU plan for the RELAP7 (R7) code development effort. The plan will continue to evolve based on the growth of code capability. This growth will be reflected as additional testing is identified and done. Later versions of this document will reflect that growth.
Date: February 1, 2010
Creator: Nourgaliev, Robert
Partner: UNT Libraries Government Documents Department

A CLASS OF RECONSTRUCTED DISCONTINUOUS GALERKIN METHODS IN COMPUTATIONAL FLUID DYNAMICS

Description: A class of reconstructed discontinuous Galerkin (DG) methods is presented to solve compressible flow problems on arbitrary grids. The idea is to combine the efficiency of the reconstruction methods in finite volume methods and the accuracy of the DG methods to obtain a better numerical algorithm in computational fluid dynamics. The beauty of the resulting reconstructed discontinuous Galerkin (RDG) methods is that they provide a unified formulation for both finite volume and DG methods, and contain both classical finite volume and standard DG methods as two special cases of the RDG methods, and thus allow for a direct efficiency comparison. Both Green-Gauss and least-squares reconstruction methods and a least-squares recovery method are presented to obtain a quadratic polynomial representation of the underlying linear discontinuous Galerkin solution on each cell via a so-called in-cell reconstruction process. The devised in-cell reconstruction is aimed to augment the accuracy of the discontinuous Galerkin method by increasing the order of the underlying polynomial solution. These three reconstructed discontinuous Galerkin methods are used to compute a variety of compressible flow problems on arbitrary meshes to assess their accuracy. The numerical experiments demonstrate that all three reconstructed discontinuous Galerkin methods can significantly improve the accuracy of the underlying second-order DG method, although the least-squares reconstructed DG method provides the best performance in terms of both accuracy, efficiency, and robustness.
Date: May 1, 2011
Creator: Luo, Hong; Xia, Yidong & Nourgaliev, Robert
Partner: UNT Libraries Government Documents Department

General purpose steam table library : CASL L3:THM.CFD.P7.04 milestone report.

Description: Completion of the CASL L3 milestone THM.CFD.P7.04 provides a general purpose tabular interpolation library for material properties to support, in particular, standardized models for steam properties. The software consists of three parts, implementations of analytic steam models, a code to generate tables from those models, and an interpolation package to interface the tables to CFD codes such as Hydra-TH. Verification of the standard model is maintained through the entire train of routines. The performance of interpolation package exceeds that of freely available analytic implementation of the steam properties by over an order of magnitude.
Date: August 1, 2013
Creator: Carpenter, John H.; Belcourt, Noel & Nourgaliev, Robert
Partner: UNT Libraries Government Documents Department

Notes on Newton-Krylov based Incompressible Flow Projection Solver

Description: The purpose of the present document is to formulate Jacobian-free Newton-Krylov algorithm for approximate projection method used in Hydra-TH code. Hydra-TH is developed by Los Alamos National Laboratory (LANL) under the auspices of the Consortium for Advanced Simulation of Light-Water Reactors (CASL) for thermal-hydraulics applications ranging from grid-to-rod fretting (GTRF) to multiphase flow subcooled boiling. Currently, Hydra-TH is based on the semi-implicit projection method, which provides an excellent platform for simulation of transient single-phase thermalhydraulics problems. This algorithm however is not efficient when applied for very slow or steady-state problems, as well as for highly nonlinear multiphase problems relevant to nuclear reactor thermalhydraulics with boiling and condensation. These applications require fully-implicit tightly-coupling algorithms. The major technical contribution of the present report is the formulation of fully-implicit projection algorithm which will fulfill this purpose. This includes the definition of non-linear residuals used for GMRES-based linear iterations, as well as physics-based preconditioning techniques.
Date: September 1, 2012
Creator: Nourgaliev, Robert; Christon, Mark & Bakosi, J.
Partner: UNT Libraries Government Documents Department

A Parallel Reconstructed Discontinuous Galerkin Method for the Compressible Flows on Aritrary Grids

Description: A reconstruction-based discontinuous Galerkin method is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids. In this method, an in-cell reconstruction is used to obtain a higher-order polynomial representation of the underlying discontinuous Galerkin polynomial solution and an inter-cell reconstruction is used to obtain a continuous polynomial solution on the union of two neighboring, interface-sharing cells. The in-cell reconstruction is designed to enhance the accuracy of the discontinuous Galerkin method by increasing the order of the underlying polynomial solution. The inter-cell reconstruction is devised to remove an interface discontinuity of the solution and its derivatives and thus to provide a simple, accurate, consistent, and robust approximation to the viscous and heat fluxes in the Navier-Stokes equations. A parallel strategy is also devised for the resulting reconstruction discontinuous Galerkin method, which is based on domain partitioning and Single Program Multiple Data (SPMD) parallel programming model. The RDG method is used to compute a variety of compressible flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results demonstrate that this RDG method is third-order accurate at a cost slightly higher than its underlying second-order DG method, at the same time providing a better performance than the third order DG method, in terms of both computing costs and storage requirements.
Date: January 1, 2010
Creator: Luo, Hong; Ali, Amjad; Nourgaliev, Robert & Mousseau, Vincent A.
Partner: UNT Libraries Government Documents Department

A Reconstructed Discontinuous Galerkin Method for the Compressible Euler Equations on Arbitrary Grids

Description: A reconstruction-based discontinuous Galerkin (DG) method is presented for the solution of the compressible Euler equations on arbitrary grids. By taking advantage of handily available and yet invaluable information, namely the derivatives, in the context of the discontinuous Galerkin methods, a solution polynomial of one degree higher is reconstructed using a least-squares method. The stencils used in the reconstruction involve only the van Neumann neighborhood (face-neighboring cells) and are compact and consistent with the underlying DG method. The resulting DG method can be regarded as an improvement of a recovery-based DG method in the sense that it shares the same nice features as the recovery-based DG method, such as high accuracy and efficiency, and yet overcomes some of its shortcomings such as a lack of flexibility, compactness, and robustness. The developed DG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate the accuracy and efficiency of the method. The numerical results indicate that this reconstructed DG method is able to obtain a third-order accurate solution at a slightly higher cost than its second-order DG method and provide an increase in performance over the third order DG method in terms of computing time and storage requirement.
Date: June 1, 2009
Creator: Luo, Hong; Luo, Luquing; Nourgaliev, Robert & Mousseau, Vincent
Partner: UNT Libraries Government Documents Department

A Reconstructed Discontinuous Galerkin Method for the Compressible Flows on Unstructured Tetrahedral Grids

Description: A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier-Stokes equations on unstructured tetrahedral grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier-Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not need to judiciously choose a proper form of a recovered polynomial, thus is simple, flexible, and robust, and can be used on unstructured grids. The preliminary results indicate that this RDG method is stable on unstructured tetrahedral grids, and provides a viable and attractive alternative for the discretization of the viscous and heat fluxes in the Navier-Stokes equations.
Date: June 1, 2011
Creator: Luo, Hong; Xia, Yidong; Nourgaliev, Robert & Cai, Chunpei
Partner: UNT Libraries Government Documents Department

A Reconstructed Discontinuous Galerkin Method for the Compressible Navier-Stokes Equations on Arbitrary Grids

Description: A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier-Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not need to judiciously choose a proper form of a recovered polynomial, thus is simple, flexible, and robust, and can be used on arbitrary grids. The developed RDG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG method is able to deliver the same accuracy as the well-known Bassi-Rebay II scheme, at a half of its computing costs for the discretization of the viscous fluxes in the Navier-Stokes equations, clearly demonstrating its superior performance over the existing DG methods for solving the compressible Navier-Stokes equations.
Date: January 1, 2010
Creator: Luo, Hong; Luo, Luqing; Nourgaliev, Robert & Mousseau, Vincent A.
Partner: UNT Libraries Government Documents Department

A Novel Hyperbolization Procedure for The Two-Phase Six-Equation Flow Model

Description: We introduce a novel approach for the hyperbolization of the well-known two-phase six equation flow model. The six-equation model has been frequently used in many two-phase flow applications such as bubbly fluid flows in nuclear reactors. One major drawback of this model is that it can be arbitrarily non-hyperbolic resulting in difficulties such as numerical instability issues. Non-hyperbolic behavior can be associated with complex eigenvalues that correspond to characteristic matrix of the system. Complex eigenvalues are often due to certain flow parameter choices such as the definition of inter-facial pressure terms. In our method, we prevent the characteristic matrix receiving complex eigenvalues by fine tuning the inter-facial pressure terms with an iterative procedure. In this way, the characteristic matrix possesses all real eigenvalues meaning that the characteristic wave speeds are all real therefore the overall two-phase flowmodel becomes hyperbolic. The main advantage of this is that one can apply less diffusive highly accurate high resolution numerical schemes that often rely on explicit calculations of real eigenvalues. We note that existing non-hyperbolic models are discretized mainly based on low order highly dissipative numerical techniques in order to avoid stability issues.
Date: October 1, 2011
Creator: Kadioglu, Samet Y.; Nourgaliev, Robert & Dinh, Nam
Partner: UNT Libraries Government Documents Department

A Comparative Study of Different Reconstruction Schemes for a Reconstructed Discontinuous Galerkin Method on Arbitrary Grids

Description: A comparative study of different reconstruction schemes for a reconstruction-based discontinuous Galerkin, termed RDG(P1P2) method is performed for compressible flow problems on arbitrary grids. The RDG method is designed to enhance the accuracy of the discontinuous Galerkin method by increasing the order of the underlying polynomial solution via a reconstruction scheme commonly used in the finite volume method. Both Green-Gauss and least-squares reconstruction methods and a least-squares recovery method are implemented to obtain a quadratic polynomial representation of the underlying discontinuous Galerkin linear polynomial solution on each cell. These three reconstruction/recovery methods are compared for a variety of compressible flow problems on arbitrary meshes to access their accuracy and robustness. The numerical results demonstrate that all three reconstruction methods can significantly improve the accuracy of the underlying second-order DG method, although the least-squares reconstruction method provides the best performance in terms of both accuracy and robustness.
Date: June 1, 2011
Creator: Luo, Hong; Xiao, Hanping; Nourgaliev, Robert & Cai, Chunpei
Partner: UNT Libraries Government Documents Department

A Comparative Study of the Harmonic and Arithmetic Averaging of Diffusion Coefficients for Non-linear Heat Conduction Problems

Description: We perform a comparative study for the harmonic versus arithmetic averaging of the heat conduction coefficient when solving non-linear heat transfer problems. In literature, the harmonic average is the method of choice, because it is widely believed that the harmonic average is more accurate model. However, our analysis reveals that this is not necessarily true. For instance, we show a case in which the harmonic average is less accurate when a coarser mesh is used. More importantly, we demonstrated that if the boundary layers are finely resolved, then the harmonic and arithmetic averaging techniques are identical in the truncation error sense. Our analysis further reveals that the accuracy of these two techniques depends on how the physical problem is modeled.
Date: March 1, 2008
Creator: Kadioglu, Samet Y.; Nourgaliev, Robert R. & Mousseau, Vincent A.
Partner: UNT Libraries Government Documents Department

Jacobian-free Newton Krylov discontinuous Galerkin method and physics-based preconditioning for nuclear reactor simulations

Description: We present high-order accurate spatiotemporal discretization of all-speed flow solvers using Jacobian-free Newton Krylov framework. One of the key developments in this work is the physics-based preconditioner for the all-speed flow, which makes use of traditional semi-implicit schemes. The physics-based preconditioner is developed in the primitive variable form, which allows a straightforward separation of physical phenomena. Numerical examples demonstrate that the developed preconditioner effectively reduces the number of the Krylov iterations, and the efficiency is independent of the Mach number and mesh sizes under a fixed CFL condition.
Date: September 1, 2008
Creator: Park, HyeongKae; Nourgaliev, Robert R.; Martineau, Richard C. & Knoll, Dana A.
Partner: UNT Libraries Government Documents Department

Direct Numerical Simulation of Interfacial Flows: Implicit Sharp-Interface Method (I-SIM)

Description: In recent work (Nourgaliev, Liou, Theofanous, JCP in press) we demonstrated that numerical simulations of interfacial flows in the presence of strong shear must be cast in dynamically sharp terms (sharp interface treatment or SIM), and that moreover they must meet stringent resolution requirements (i.e., resolving the critical layer). The present work is an outgrowth of that work aiming to overcome consequent limitations on the temporal treatment, which become still more severe in the presence of phase change. The key is to avoid operator splitting between interface motion, fluid convection, viscous/heat diffusion and reactions; instead treating all these non-linear operators fully-coupled within a Newton iteration scheme. To this end, the SIM’s cut-cell meshing is combined with the high-orderaccurate implicit Runge-Kutta and the “recovery” Discontinuous Galerkin methods along with a Jacobian-free, Krylov subspace iteration algorithm and its physics-based preconditioning. In particular, the interfacial geometry (i.e., marker’s positions and volumes of cut cells) is a part of the Newton-Krylov solution vector, so that the interface dynamics and fluid motions are fully-(non-linearly)-coupled. We show that our method is: (a) robust (L-stable) and efficient, allowing to step over stability time steps at will while maintaining high-(up to the 5th)-order temporal accuracy; (b) fully conservative, even near multimaterial contacts, without any adverse consequences (pressure/velocity oscillations); and (c) highorder-accurate in spatial discretization (demonstrated here up to the 12th-order for smoothin-the-bulk-fluid flows), capturing interfacial jumps sharply, within one cell. Performance is illustrated with a variety of test problems, including low-Mach-number “manufactured” solutions, shock dynamics/tracking with slow dynamic time scales, and multi-fluid, highspeed shock-tube problems. We briefly discuss preconditioning, and we introduce two physics-based preconditioners – “Block-Diagonal” and “Internal energy-Pressure-Velocity Partially Decoupled”, demonstrating the ability to efficiently solve all-speed flows with strong effects from viscous dissipation and heat conduction.
Date: January 1, 2008
Creator: Nourgaliev, Robert; Theofanous, Theo; Park, HyeongKae; Mousseau, Vincent & Knoll, Dana
Partner: UNT Libraries Government Documents Department

Recovery Discontinuous Galerkin Jacobian-free Newton-Krylov Method for all-speed flows

Description: There is an increasing interest to develop the next generation simulation tools for the advanced nuclear energy systems. These tools will utilize the state-of-art numerical algorithms and computer science technology in order to maximize the predictive capability, support advanced reactor designs, reduce uncertainty and increase safety margins. In analyzing nuclear energy systems, we are interested in compressible low-Mach number, high heat flux flows with a wide range of Re, Ra, and Pr numbers. Under these conditions, the focus is placed on turbulent heat transfer, in contrast to other industries whose main interest is in capturing turbulent mixing. Our objective is to develop singlepoint turbulence closure models for large-scale engineering CFD code, using Direct Numerical Simulation (DNS) or Large Eddy Simulation (LES) tools, requireing very accurate and efficient numerical algorithms. The focus of this work is placed on fully-implicit, high-order spatiotemporal discretization based on the discontinuous Galerkin method solving the conservative form of the compressible Navier-Stokes equations. The method utilizes a local reconstruction procedure derived from weak formulation of the problem, which is inspired by the recovery diffusion flux algorithm of van Leer and Nomura [?] and by the piecewise parabolic reconstruction [?] in the finite volume method. The developed methodology is integrated into the Jacobianfree Newton-Krylov framework [?] to allow a fully-implicit solution of the problem.
Date: July 1, 2008
Creator: Park, HyeongKae; Nourgaliev, Robert; Mousseau, Vincent & Knoll, Dana
Partner: UNT Libraries Government Documents Department

Recovery Discontinuous Galerkin Jacobian-Free Newton-Krylov Method for All-Speed Flows

Description: A novel numerical algorithm (rDG-JFNK) for all-speed fluid flows with heat conduction and viscosity is introduced. The rDG-JFNK combines the Discontinuous Galerkin spatial discretization with the implicit Runge-Kutta time integration under the Jacobian-free Newton-Krylov framework. We solve fully-compressible Navier-Stokes equations without operator-splitting of hyperbolic, diffusion and reaction terms, which enables fully-coupled high-order temporal discretization. The stability constraint is removed due to the L-stable Explicit, Singly Diagonal Implicit Runge-Kutta (ESDIRK) scheme. The governing equations are solved in the conservative form, which allows one to accurately compute shock dynamics, as well as low-speed flows. For spatial discretization, we develop a “recovery” family of DG, exhibiting nearly-spectral accuracy. To precondition the Krylov-based linear solver (GMRES), we developed an “Operator-Split”-(OS) Physics Based Preconditioner (PBP), in which we transform/simplify the fully-coupled system to a sequence of segregated scalar problems, each can be solved efficiently with Multigrid method. Each scalar problem is designed to target/cluster eigenvalues of the Jacobian matrix associated with a specific physics.
Date: July 1, 2008
Creator: Park, HyeongKae; Nourgaliev, Robert; Mousseau, Vincent & Knoll, Dana
Partner: UNT Libraries Government Documents Department

Exploration of High-Dimensional Scalar Function for Nuclear Reactor Safety Analysis and Visualization

Description: The next generation of methodologies for nuclear reactor Probabilistic Risk Assessment (PRA) explicitly accounts for the time element in modeling the probabilistic system evolution and uses numerical simulation tools to account for possible dependencies between failure events. The Monte-Carlo (MC) and the Dynamic Event Tree (DET) approaches belong to this new class of dynamic PRA methodologies. A challenge of dynamic PRA algorithms is the large amount of data they produce which may be difficult to visualize and analyze in order to extract useful information. We present a software tool that is designed to address these goals. We model a large-scale nuclear simulation dataset as a high-dimensional scalar function defined over a discrete sample of the domain. First, we provide structural analysis of such a function at multiple scales and provide insight into the relationship between the input parameters and the output. Second, we enable exploratory analysis for users, where we help the users to differentiate features from noise through multi-scale analysis on an interactive platform, based on domain knowledge and data characterization. Our analysis is performed by exploiting the topological and geometric properties of the domain, building statistical models based on its topological segmentations and providing interactive visual interfaces to facilitate such explorations. We provide a user’s guide to our software tool by highlighting its analysis and visualization capabilities, along with a use case involving dataset from a nuclear reactor safety simulation.
Date: May 1, 2013
Creator: Maljovec, Dan; Wang, Bei; Pascucci, Valerio; Bremer, Peer-Timo; Pernice, Michael & Nourgaliev, Robert
Partner: UNT Libraries Government Documents Department

Exploratory Nuclear Reactor Safety Analysis and Visualization via Integrated Topological and Geometric Techniques

Description: A recent trend in the nuclear power engineering field is the implementation of heavily computational and time consuming algorithms and codes for both design and safety analysis. In particular, the new generation of system analysis codes aim to embrace several phenomena such as thermo-hydraulic, structural behavior, and system dynamics, as well as uncertainty quantification and sensitivity analyses. The use of dynamic probabilistic risk assessment (PRA) methodologies allows a systematic approach to uncertainty quantification. Dynamic methodologies in PRA account for possible coupling between triggered or stochastic events through explicit consideration of the time element in system evolution, often through the use of dynamic system models (simulators). They are usually needed when the system has more than one failure mode, control loops, and/or hardware/process/software/human interaction. Dynamic methodologies are also capable of modeling the consequences of epistemic and aleatory uncertainties. The Monte-Carlo (MC) and the Dynamic Event Tree (DET) approaches belong to this new class of dynamic PRA methodologies. The major challenges in using MC and DET methodologies (as well as other dynamic methodologies) are the heavier computational and memory requirements compared to the classical ET analysis. This is due to the fact that each branch generated can contain time evolutions of a large number of variables (about 50,000 data channels are typically present in RELAP) and a large number of scenarios can be generated from a single initiating event (possibly on the order of hundreds or even thousands). Such large amounts of information are usually very difficult to organize in order to identify the main trends in scenario evolutions and the main risk contributors for each initiating event. This report aims to improve Dynamic PRA methodologies by tackling the two challenges mentioned above using: 1) adaptive sampling techniques to reduce computational cost of the analysis and 2) topology-based methodologies to interactively visualize ...
Date: October 1, 2013
Creator: Maljovec, Dan; Wang, Bei; Pascucci, Valerio; Bremer, Peer-Timo; Mandelli, Diego; Pernice, Michael et al.
Partner: UNT Libraries Government Documents Department

A Framework to Expand and Advance Probabilistic Risk Assessment to Support Small Modular Reactors

Description: During the early development of nuclear power plants, researchers and engineers focused on many aspects of plant operation, two of which were getting the newly-found technology to work and minimizing the likelihood of perceived accidents through redundancy and diversity. As time, and our experience, has progressed, the realization of plant operational risk/reliability has entered into the design, operation, and regulation of these plants. But, to date, we have only dabbled at the surface of risk and reliability technologies. For the next generation of small modular reactors (SMRs), it is imperative that these technologies evolve into an accepted, encompassing, validated, and integral part of the plant in order to reduce costs and to demonstrate safe operation. Further, while it is presumed that safety margins are substantial for proposed SMR designs, the depiction and demonstration of these margins needs to be better understood in order to optimize the licensing process.
Date: September 1, 2012
Creator: Smith, Curtis; Schwieder, David; Nourgaliev, Robert; Phelan, Cherie; Mandelli, Diego; Kvarfordt, Kellie et al.
Partner: UNT Libraries Government Documents Department