An Example of Code Verification in the Simulation of Wave Propagation

2011 ◽  
Author(s):  
Fahd Fathi ◽  
Lui´s Ec¸a ◽  
Mart Borsboom
Keyword(s):  
Wave Propagation ◽  
Numerical Solution ◽  
Physical Reality ◽  
Verification And Validation ◽  
Cfd Modeling ◽  
Code Verification ◽  
Complex Flows ◽  
Solution Verification ◽  
The Mathematical Model

Thanks to advances in modeling and hardware the range of applications available to CFD modeling is continuously increasing. As CFD has moved from demonstration of capability to production of engineering results of practical value, there is an increased awareness in the field that Verification and Validation are systematically required. Verification deals with the numerical accuracy of a given set of results. Its object is the assessment of the numerical uncertainty due to discretization and iterative errors of a numerical solution (Solution Verification) performed with a Code that has been previously checked to be free of errors (Code Verification). Both activities are required to ensure that errors are controlled and that quality of the results is maintained. Complementarily, Validation addresses the modeling error, i.e. the comparison of the mathematical model with the (physical) reality. Therefore, it requires comparison with experimental data. Validating CFD results is only meaningful when preceded by carefully verified calculations (Solution Verification) with verified codes (Code Verification). The topic of Verification and Validation is developing and standardized procedures are still under discussion. Nevertheless, there are techniques available to perform careful Code and Solution Verification for flows with engineering relevance. This paper presents a Code Verification exercise for the simulation of wave propagation with a VOF code. Systematically refined grids and time steps are applied in the calculation of waves with a known analytical solution to assess the convergence properties of the numerical solution. The aim of the exercise is to demonstrate the advantages of such exercises for the knowledge of the numerical properties of a code that is applied in complex flows. The study is not a pure Code Verification exercise. Modeling errors introduced by approximate outlet boundary conditions (allowing wave reflections) are also quantified for a linear and a high-order wave. However, these are still based on (numerical) error evaluations for known analytical solutions and so they can still be classified as Code Verification.

Workshop on Verification and Validation of CFD for Offshore Flows

2012 ◽  
Author(s):  
L. Eça ◽  
G. Vaz
Keyword(s):  
Reynolds Numbers ◽  
Verification And Validation ◽  
Test Cases ◽  
Code Verification ◽  
Complex Flow ◽  
Solution Verification ◽  
Manufactured Solution ◽  
Cylinder Flow ◽  
Flow Case ◽  
Paper Submission

This document introduces the Workshop on Verification and Validation (V&V) of CFD for Offshore Flows, to be held during OMAE2012. It presents a brief introduction to the purpose of Verification and Validation with the identification of the goals of code and solution verification and validation. Within this context, three test-cases are proposed: Case-I of code verification, Case-II of solution verification and Case-III of solution verification and validation. Case-I consists on a 3D manufactured solution of an unsteady turbulent flow. Case-II is an exercise on the canonical problem of the infinite smooth circular cylinder flow at different Reynolds numbers. Case-III is a more complex flow around a straked-riser. The participants are asked to perform at least one of these test-cases. The objectives for the three proposed test-cases are presented, together with a detailed description of the numerical settings to be used, and the results to be obtained and sent to the Workshop organization. At the end some considerations on general conditions, paper submission, deadlines, and encouragements are stated.

Effective Use of V&V20 Solution Verification Methodology

2010 ◽  
Author(s):  
Christopher J. Freitas
Keyword(s):  
Heat Transfer ◽  
Verification And Validation ◽  
Code Verification ◽  
Flow And Heat Transfer ◽  
Time Period ◽  
Solution Verification ◽  
Particular Solution ◽  
American Society ◽  
Effective Use ◽  
Verification Methodology

Methods for the quantification of numerical uncertainty have been a subject of interest to the American Society of Mechanical Engineers (ASME) and the mechanical engineering community as a whole for over a decade. During this time period, ASME has promulgated three statements of standards for the reporting of numerical uncertainty in archival publications (Journal of Fluids Engineering). This paper summarizes the work that has gone into the specification of these standards and the continuing effort in formulation of methods and procedures for quantifying numerical uncertainty. Specifically, this paper discusses the efforts of the ASME V&V 20 Committee (Verification and Validation in Computational Fluid Dynamics and Heat Transfer) to lay a foundation and structure to verification and validation for fluid flow and heat transfer simulations. Issues and methods related to code verification and in particular solution verification are presented and discussed in the context of the recently released V&V20 Standard.

Code Verification, Solution Verification and Validation in RANS Solvers

2010 ◽  
Author(s):  
Lui´s Ec¸a ◽  
Guilherme Vaz ◽  
Martin Hoekstra
Keyword(s):  
Turbulent Flows ◽  
Verification And Validation ◽  
Test Cases ◽  
Simple Test ◽  
Error Evaluation ◽  
Code Verification ◽  
Engineering Activity ◽  
Solution Verification ◽  
The Right ◽  
Comparison With Experimental Data

The maturing of CFD codes for practical calculations of complex turbulent flows implies the need to establish the credibility of the results by Verification & Validation. These two activities have different goals: Verification is a purely mathematical exercise that intends to show that we are “solving the equations right”, whereas Validation is a science/engineering activity that intends to show that we are “solving the right equations”. Verification is in fact composed of two different activities: Code Verification and Solution Verification. Code Verification intends to verify that a given code solves correctly the equations of the model that it contains by error evaluation. On the other hand, Solution Verification intends to estimate the error of a given calculation, for which in general the exact solution is not known. Validation intends to estimate modelling errors by comparison with experimental data. The paper gives an overview of procedures for Code Verification, Solution Verification and Validation. Examples of the three types of exercises are presented for simple test cases demonstrating the advantages of performing Verification and Validation exercises.

Boundary conditions for the numerical solution of wave propagation problems

Geophysics ◽  
1978 ◽  
Vol 43 (6) ◽  
pp. 1099-1110 ◽  
Author(s):  
Albert C. Reynolds
Keyword(s):  
Wave Propagation ◽  
Reflection Coefficient ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Neumann Boundary ◽  
Synthetic Seismograms ◽  
Neumann Boundary Conditions ◽  
Numerical Calculations ◽  
Reflection Coefficients

Many finite difference models in use for generating synthetic seismograms produce unwanted reflections from the edges of the model due to the use of Dirichlet or Neumann boundary conditions. In this paper we develop boundary conditions which greatly reduce this edge reflection. A reflection coefficient analysis is given which indicates that, for the specified boundary conditions, smaller reflection coefficients than those obtained for Dirichlet or Neumann boundary conditions are obtained. Numerical calculations support this conclusion.

Evaluation of Uncertainty for the Determination of Magnesium Oxide Content in Limestone by the Atomic Absorption Spectrometry

2014 ◽  
Vol 707 ◽  
pp. 283-288
Author(s):  
Xiang Dong Wen ◽  
Zheng Zhou ◽  
Wen Yang Pan ◽  
Mei Shao
Keyword(s):  
Atomic Absorption Spectrometry ◽  
Atomic Absorption ◽  
Magnesium Oxide ◽  
Influence Factors ◽  
Absorption Spectrometry ◽  
Oxide Content ◽  
Standard Solution ◽  
The Mathematical Model

According to GB/T3286.1-2012(The determination of calcium oxide and magnesium oxide content in limestone and dolomite), the mathematical model of magnesium oxide content determination in limestone by atomic absorption spectrometry was established. The various uncertainty factors of different elements for a sample were discussed and compared in the testing process. The confidence interval for the measurement result was (0.74±0.03)%,k=2 in uncertainty evaluation .The results showed that the variability of working curve and accuracy of standard solution volume for working curve were main influence factors of uncertainty. It could effectively reduce the uncertainty from the perspective of the main factors,and improve the quality of analysis.

scholarly journals Research on the Influencing Factors of "Scale Veins" of Single Point Incremental Forming Workpieces Surface

2015 ◽  
Vol 9 (1) ◽  
pp. 1025-1032
Author(s):  
Shi Pengtao ◽  
Li Yan ◽  
Yang Mingshun ◽  
Yao Zimeng
Keyword(s):  
Surface Quality ◽  
Incremental Forming ◽  
Single Point ◽  
Spindle Speed ◽  
Experimental Results ◽  
Feed Speed ◽  
Single Point Incremental Forming ◽  
Machining Parameters ◽  
The Mathematical Model

To furthermore optimize the machining parameters and improve the surface quality of the workpieces manufactured by single point incremental forming method, the formation mechanism of the sacle veins on the metal incremental froming workpieces was studied through experiment method. The influence principle of the spindle speed, the feed speed and the material of tip of tools on the length of scale veins was obtained through analyzing the experimental results and building the mathematical model among the length of scale veins were feed speed and spindle speed through measuring the roughness of surfaces and observing the appearance of the forming workpieces. The experimental results showed that, the spindle speed, the feed speed and the material of tool tips have a significant effect on the scale veins formation on the surface of forming workpieces. Therefore, an appropriate group of spindle speed and feed speed can reduce the effect of scale veins on the roughness of single point incremental forming workpieces and furthermore improve the surface quality of forming workpieces.

scholarly journals Dynamic positioning system design for “blue lady”. simulation tests

2012 ◽  
Vol 19 (Special) ◽  
pp. 57-65 ◽  
Author(s):  
Mirosław Tomera
Keyword(s):  
Dynamic Positioning ◽  
Positioning System ◽  
System Operation ◽  
Training Centre ◽  
Dynamic Positioning System ◽  
Operational Quality ◽  
The Mathematical Model ◽  
And Training ◽  
Ship Handling

ABSTRACT The dynamical positioning system is a complex control consisting of a number of components, including: filters, observers, controllers, and propeller allocation systems. The design and preliminary analysis of operational quality of system operation are usually done based on numerical simulations performed with the aid of the mathematical model of the ship. The article presents a concept of the dynamic positioning system applied to steering the training ship Blue Lady used for training captains in the ship handling research and training centre owned by the Foundation for Safety of Navigation and Environment Protection in Ilawa/Kamionka. The simulation tests performed in the numerical environment of Matlab/Simulink have proved the usability of the designed system for steering a ship at low speed.

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