Analysis Of Boundary Conditions For Factorizable Discretizations Of The Euler Equations
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Analysis Of Boundary Conditions For Factorizable Discretizations Of The Euler Equations
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Author : Boris Diskin
language : en
Publisher:
Release Date : 2002
Analysis Of Boundary Conditions For Factorizable Discretizations Of The Euler Equations written by Boris Diskin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.
In this article, several sets of boundary conditions or factorizable schemes corresponding to the steady-state compressible Euler equations are evaluated. The analyzed model is a one-dimensional constant-coefficient problem. Numerical tests have been performed for a fully subsonic quasi-one-dimensional flow in a convergent/divergent channel. This paper focuses on the effect of boundary-condition equations on stability and accuracy of the discrete solutions. Explicit correspondence between solutions and boundary conditions is established through a boundary-condition-sensitivity (BCS) matrix. The following new findings are reported: (1) Examples of stable discrete problems contradicting a wide-spread belief that employment of a one-order-lower approximation schemes in an O(h)-small region does not affect the overall accuracy order of the solution have been found and explained. Such counterexamples can only be constructed for systems of differential equations. For scalar equations, the conventional wisdom is correct. (2) A negative effect of overspecified (although, exact) boundary conditions on accuracy and stability of the solution has been observed and explained. (3) Sets of practical boundary conditions for factorizable schemes providing stable second-order accurate solutions have been formulated. These schemes belong to a family of second-order schemes requiring second-order accuracy for some numerical-closure boundary conditions.
Icase Semiannual Report
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Author :
language : en
Publisher:
Release Date : 2002
Icase Semiannual Report written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.
This report summarizes research conducted at ICASE in applied mathematics, computer science, fluid mechanics, and structures and material sciences during the period October 1, 2000 through March 31, 2001.
New Factorizable Discretizations For The Euler Equations
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Author : Boris Diskin
language : en
Publisher:
Release Date : 2002
New Factorizable Discretizations For The Euler Equations written by Boris Diskin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.
A multigrid method is defined as having textbook multigrid efficiency (TME) if solutions to the governing system of equations are attained in a computational work that is a small (less than 10) multiple of the operation count in one target-grid residual evaluation. Away to achieve TME for the Euler and Navier-Stokes equations is to apply the distributed relaxation method thereby separating the elliptic and hyperbolic partitions of the equations. Design of a distributed relaxation scheme can be significantly simplified if the target discretization possesses two properties: (1) factorizability, and (2) consistent approximations for the separate factors. The first property implies that the discrete system determinant can be represented as a product of discrete factors, each of them approximating a corresponding factor of the determinant of the differential equations. The second property requires that the discrete factors reflect the physical anisotropies, be stable, and be easily solvable. In this paper, discrete schemes for the nonconservative Euler equations possessing properties (1) and (2) have been derived and analyzed. The accuracy of these scheme has been tested for subsonic flow regimes and is comparable with the accuracy of standard schemes. TME has been demonstrated in solving fully subsonic quasi-one-dimensional flow in a convergent/divergent channel.
Applied Mechanics Reviews
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Author :
language : en
Publisher:
Release Date : 2004
Applied Mechanics Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mechanical engineering categories.
Extension Of Latin Hypercube Samples With Correlated Variables
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Author : William L. Oberkampf
language : en
Publisher:
Release Date : 2007
Extension Of Latin Hypercube Samples With Correlated Variables written by William L. Oberkampf and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Computer programs categories.
Verification and validation (V & V) are the primary means to assess the accuracy and reliability of computational simulations. V & V methods and procedures have fundamentally improved the credibility of simulations in several high-consequence fields, such as nuclear reactor safety, underground nuclear waste storage, and nuclear weapon safety. Although the terminology is not uniform across engineering disciplines, code verification deals with assessing the reliability of the software coding, and solution verification deals with assessing the numerical accuracy of the solution to a computational model. Validation addresses the physics modeling accuracy of a computational simulation by comparing the computational results with experimental data. Code verification benchmarks and validation benchmarks have been constructed for a number of years in every field of computational simulation. However, no comprehensive guidelines have been proposed for the construction and use of V & V benchmarks. For example, the field of nuclear reactor safety has not focused on code verification benchmarks, but it has placed great emphasis on developing validation benchmarks. Many of these validation benchmarks are closely related to the operations of actual reactors at near-safety-critical conditions, as opposed to being more fundamental-physics benchmarks. This paper presents recommendations for the effective design and use of code verification benchmarks based on manufactured solutions, classical analytical solutions, and highly accurate numerical solutions. In addition, this paper presents recommendations for the design and use of validation benchmarks, highlighting the careful design of building-block experiments, the estimation of experimental measurement uncertainty for both inputs and outputs to the code, validation metrics, and the role of model calibration in validation. It is argued that the understanding of predictive capability of a computational model is built on the level of achievement in V & V activities, how closely related the V & V benchmarks are to the actual application of interest, and the quantification of uncertainties related to the application of interest.
Verification Validation And Predictive Capability In Computational Engineering And Physics
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Author : William L. Oberkampf
language : en
Publisher:
Release Date : 2003
Verification Validation And Predictive Capability In Computational Engineering And Physics written by William L. Oberkampf and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Computer simulation categories.
Developers of computer codes, analysts who use the codes, and decision makers who rely on the results of the analyses face a critical question: How should confidence in modeling and simulation be critically assessed? Verification and validation (V & V) of computational simulations are the primary methods for building and quantifying this confidence. Briefly, verification is the assessment of the accuracy of the solution to a computational model. Validation is the assessment of the accuracy of a computational simulation by comparison with experimental data. In verification, the relationship of the simulation to the real world is not an issue. In validation, the relationship between computation and the real world, i.e., experimental data, is the issue. This paper presents our viewpoint of the state of the art in V & V in computational physics. (In this paper we refer to all fields of computational engineering and physics, e.g., computational fluid dynamics, computational solid mechanics, structural dynamics, shock wave physics, computational chemistry, etc., as computational physics.) We do not provide a comprehensive review of the multitudinous contributions to V & V, although we do reference a large number of previous works from many fields. We have attempted to bring together many different perspectives on V & V, highlight those perspectives that are effective from a practical engineering viewpoint, suggest future research topics, and discuss key implementation issues that are necessary to improve the effectiveness of V & V. We describe our view of the framework in which predictive capability relies on V & V, as well as other factors that affect predictive capability. Our opinions about the research needs and management issues in V & V are very practical: What methods and techniques need to be developed and what changes in the views of management need to occur to increase the usefulness, reliability, and impact of computational physics for decision making about engineering systems? We review the state of the art in V & V over a wide range of topics, for example, prioritization of V & V activities using the Phenomena Identification and Ranking Table (PIRT), code verification, software quality assurance (SQA), numerical error estimation, hierarchical experiments for validation, characteristics of validation experiments, the need to perform nondeterministic computational simulations in comparisons with experimental data, and validation metrics. We then provide an extensive discussion of V & V research and implementation issues that we believe must be addressed for V & V to be more effective in improving confidence in computational predictive capability. Some of the research topics addressed are development of improved procedures for the use of the PIRT for prioritizing V & V activities, the method of manufactured solutions for code verification, development and use of hierarchical validation diagrams, and the construction and use of validation metrics incorporating statistical measures. Some of the implementation topics addressed are the needed management initiatives to better align and team computationalists and experimentalists in conducting validation activities, the perspective of commercial software companies, the key role of analysts and decision makers as code customers, obstacles to the improved effectiveness of V & V, effects of cost and schedule constraints on practical applications in industrial settings, and the role of engineering standards committees in documenting best practices for V & V.
Recent Advances In Achieving Textbook Multigrid Efficiency For Computational Fluid Dynamics Simulations
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Author : Achi Brandt
language : en
Publisher:
Release Date : 2002
Recent Advances In Achieving Textbook Multigrid Efficiency For Computational Fluid Dynamics Simulations written by Achi Brandt and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.
Recent advances in achieving textbook multigrid efficiency for fluid simulations are presented. Textbook multigrid efficiency is defined as attaining the solution to the governing system of equations in a computational work which is a small multiple of the operation counts associated with discretizing the system. Strategies are reviewed to attain this efficiency by exploiting the factorizability properties inherent to a range of fluid simulations, including the compressible Navier-Stokes equations. factorizability is used to separate the elliptic and hyperbolic factors contributing to the target system; each of the factors can then be treated individually and optimally. Boundary regions and discontinuities are addressed with separate (local) treatments. New formulations and recent calculations demonstrating the attainment of textbook efficiency for aerodynamic simulations are shown.
On The Combined Performance Of Non Local Artificial Boundary Conditions With The New Generation Of Advanced Multigrid Flow Solvers
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Author : T. W. Roberts
language : en
Publisher:
Release Date : 2000
On The Combined Performance Of Non Local Artificial Boundary Conditions With The New Generation Of Advanced Multigrid Flow Solvers written by T. W. Roberts and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Aerodynamics categories.
We develop theoretically and implement numerically a unified flow solution methodology that combines the advantages relevant to two independent groups of methods in CFD that have recently proven successful: The new factorizable schemes for the equations of hydrodynamics that facilitate the construction of optimally convergent multigrid algorithms, and highly accurate global far-field artificial boundary conditions (ABCs). The primary result that we have obtained is the following. Global ABCs do not hamper the optimal (i.e., unimprovable) multigrid convergence rate pertinent to the solver. At the same time, contrary to the standard local ABCs, the solution accuracy provided by the global ABCs deteriorates very slightly or does not deteriorate at all when the computational domain shrinks, which clearly translates into substantial savings of computer resources.
Siam Journal On Scientific Computing
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Author :
language : en
Publisher:
Release Date : 2004
Siam Journal On Scientific Computing written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Electronic journals categories.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2005
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.