1.  Pereira, Filipe; Eca, Luis; Vaz, Guilherme: Verification and Validation exercises for the flow around the KVLCC2 tanker at model and fullscale Reynolds numbers. In: Ocean Engineering, 129 , pp. 133148, 2017. (Type: Journal Article  Abstract  Links  BibTeX) @article{2017OEPereiraVazEca_KVLCC2, title = {Verification and Validation exercises for the flow around the KVLCC2 tanker at model and fullscale Reynolds numbers}, author = {Filipe Pereira and Luis Eca and Guilherme Vaz}, url = {http://www.refresco.org/download/2017oepereiravazeca_kvlcc2vv/}, doi = {http://dx.doi.org/10.1016/j.oceaneng.2016.11.005}, year = {2017}, date = {20170109}, journal = {Ocean Engineering}, volume = {129}, pages = {133148}, abstract = {This paper presents the quantification of numerical and modelling errors for the solution of the flow around the KVLCC2 tanker at modelscale Reynolds number. Numerical errors are also quantified for fullscale Reynolds number simulations to address the numerical accuracy of the prediction of scaleeffects. The calculations are performed with the solver ReFRESCO using fourteen distinct ReynoldsAveraged NavierStokes (RANS) equations models. The quantities of interest for the Validation exercises at modelscale are the resistance coefficient and the velocity and turbulence kinetic energy fields at the propeller plane. Modelling errors are estimated using the ASME V & $2V20 procedure which requires numerical and experimental data with their respective uncertainties. Numerical uncertainties are dominated by the contribution of the discretization error, which is determined by grid refinement studies. Scaleeffects are also assessed for the wakefraction and formfactor. The outcome shows that quantifying modelling errors is not a trivial exercise that depends on the quality and details of simulations and experiments. Nonetheless, it is also evident that a quantitative evaluation of modelling errors is more reliable than traditional graphical comparisons of simulations and experiments. Fullscale results show scaleeffects larger than numerical uncertainties that are illustrated for the formfactor and wakefraction.}, keywords = {}, pubstate = {published}, tppubtype = {article} } This paper presents the quantification of numerical and modelling errors for the solution of the flow around the KVLCC2 tanker at modelscale Reynolds number. Numerical errors are also quantified for fullscale Reynolds number simulations to address the numerical accuracy of the prediction of scaleeffects. The calculations are performed with the solver ReFRESCO using fourteen distinct ReynoldsAveraged NavierStokes (RANS) equations models. The quantities of interest for the Validation exercises at modelscale are the resistance coefficient and the velocity and turbulence kinetic energy fields at the propeller plane. Modelling errors are estimated using the ASME V & $2V20 procedure which requires numerical and experimental data with their respective uncertainties. Numerical uncertainties are dominated by the contribution of the discretization error, which is determined by grid refinement studies. Scaleeffects are also assessed for the wakefraction and formfactor. The outcome shows that quantifying modelling errors is not a trivial exercise that depends on the quality and details of simulations and experiments. Nonetheless, it is also evident that a quantitative evaluation of modelling errors is more reliable than traditional graphical comparisons of simulations and experiments. Fullscale results show scaleeffects larger than numerical uncertainties that are illustrated for the formfactor and wakefraction. 
2.  Rocha A.L., Eca L; G., Vaz: On the Numerical Convergence Properties of the Calculation of the Flow around the KVLCC2 Tanker in Unstructured Grids. VII International Conference on Computational Methods in Marine Engineering, Wageningen, The Netherlands, 2017. (Type: Conference  Abstract  Links  BibTeX) @conference{2017MarineRocha, title = {On the Numerical Convergence Properties of the Calculation of the Flow around the KVLCC2 Tanker in Unstructured Grids}, author = {Rocha A.L., Eca L. and Vaz G.}, url = {http://www.refresco.org/download/numericalconvergencepropertiescalculationflowaroundkvlcc2tankerunstructuredgrids/ }, year = {2017}, date = {20170101}, booktitle = {VII International Conference on Computational Methods in Marine Engineering}, address = {Wageningen, The Netherlands}, abstract = {This paper addresses the estimation of numerical errors in the calculation of the flow around the KVLCC2 tanker at modelscale Reynolds number inunstrctured grids.The flow solution is based on the ReynoldsAveraged NavierStokes equations supplemented by the k−SSTtwoequation eddyviscosity model using the socalled doublebody approach, i.e. free surface effects are neglected. Grid refinement studies are performed for sets of grids generated with the open source code SnappyHexMesh and with the HEXPRESSTM grid generator. Definition of grid refinemen tratioin unstructured grids and itsconsequencesfortheestimati onofnumericalerrorsisdiscussed.FrictionandpressureresistancecoefficientsandmeanvelocitycomponentsatthepropellerplanearecomparedwithreferencesolutionsobtainedinearlyorthogonalmultiblockstructuredgridswiththesameflowsolverReFRESCO.}, keywords = {}, pubstate = {published}, tppubtype = {conference} } This paper addresses the estimation of numerical errors in the calculation of the flow around the KVLCC2 tanker at modelscale Reynolds number inunstrctured grids.The flow solution is based on the ReynoldsAveraged NavierStokes equations supplemented by the k−SSTtwoequation eddyviscosity model using the socalled doublebody approach, i.e. free surface effects are neglected. Grid refinement studies are performed for sets of grids generated with the open source code SnappyHexMesh and with the HEXPRESSTM grid generator. Definition of grid refinemen tratioin unstructured grids and itsconsequencesfortheestimati onofnumericalerrorsisdiscussed.FrictionandpressureresistancecoefficientsandmeanvelocitycomponentsatthepropellerplanearecomparedwithreferencesolutionsobtainedinearlyorthogonalmultiblockstructuredgridswiththesameflowsolverReFRESCO. 
3.  Eca, Luis; Klaij, Christiaan; Vaz, Guilherme; Hoekstra, Martin; Pereira, Filipe: On code verification of RANS solvers. In: Journal of Computational Physics, 310 , pp. 418439, 2016. (Type: Journal Article  Abstract  Links  BibTeX) @article{2016JCPEcaKlaijVazPereiraHoekstra, title = {On code verification of RANS solvers}, author = {Luis Eca and Christiaan Klaij and Guilherme Vaz and Martin Hoekstra and Filipe Pereira}, url = {http://www.refresco.org/download/2016jcpecaklaijvazpereirahoekstra_codeverification/}, year = {2016}, date = {20160113}, journal = {Journal of Computational Physics}, volume = {310}, pages = {418439}, abstract = {This article discusses Code Verification of ReynoldsAveraged Navier Stokes (RANS) solvers that rely on face based finite volume discretizations for volumes of arbitrary shape. The study includes test cases with known analytical solutions (generated with the method of manufactured solutions) corresponding to laminar and turbulent flow, with the latter using eddyviscosity turbulence models. The procedure to perform Code Verification based on grid refinement studies is discussed and the requirements for its correct application are illustrated in a simple onedimensional problem. It is shown that geometrically similar grids are recommended for proper Code Verification and so the data should not have scatter making the use of least square fits unnecessary. Results show that it may be advantageous to determine the extrapolated error to cell size/time step zero instead of assuming that it is zero, especially when it is hard to determine the asymptotic order of grid convergence. In the RANS examples, several of the features of the ReFRESCO solver are checked including the effects of the available turbulence models in the convergence properties of the code. It is shown that it is required to account for nonorthogonality effects in the discretization of the diffusion terms and that the turbulence quantities transport equations can deteriorate the order of grid convergence of mean flow quantities.}, keywords = {}, pubstate = {published}, tppubtype = {article} } This article discusses Code Verification of ReynoldsAveraged Navier Stokes (RANS) solvers that rely on face based finite volume discretizations for volumes of arbitrary shape. The study includes test cases with known analytical solutions (generated with the method of manufactured solutions) corresponding to laminar and turbulent flow, with the latter using eddyviscosity turbulence models. The procedure to perform Code Verification based on grid refinement studies is discussed and the requirements for its correct application are illustrated in a simple onedimensional problem. It is shown that geometrically similar grids are recommended for proper Code Verification and so the data should not have scatter making the use of least square fits unnecessary. Results show that it may be advantageous to determine the extrapolated error to cell size/time step zero instead of assuming that it is zero, especially when it is hard to determine the asymptotic order of grid convergence. In the RANS examples, several of the features of the ReFRESCO solver are checked including the effects of the available turbulence models in the convergence properties of the code. It is shown that it is required to account for nonorthogonality effects in the discretization of the diffusion terms and that the turbulence quantities transport equations can deteriorate the order of grid convergence of mean flow quantities. 
4.  Eca, Luis; Vaz, Guilherme; Hoekstra, Martin: ASSESSING CONVERGENCE PROPERTIES OF RANS SOLVERS WITH MANUFACTURED SOLUTIONS. ECCOMAS Vienna, Austria, 2012. (Type: Conference  Abstract  Links  BibTeX) @conference{2012ECCOMAS_Eca_Vaz_Hoekstra, title = {ASSESSING CONVERGENCE PROPERTIES OF RANS SOLVERS WITH MANUFACTURED SOLUTIONS}, author = {Luis Eca and Guilherme Vaz and Martin Hoekstra }, url = {http://www.refresco.org/download/2012eccomas_eca_vaz_hoekstra/}, year = {2012}, date = {20120910}, address = {Vienna, Austria}, organization = {ECCOMAS}, abstract = {This paper addresses the effects of eddyviscosity turbulence models  namely, the oneequation model of Spalart & Allmaras and the TNT version of the twoequation k  w model  on the convergence properties of RANS solvers. These effects are examined with Manufactured Solutions that mimic nearwall turbulent flows, allowing the evaluation of the discretization error of the numerical solutions (contributions of the iterative and roundoff errors being negligible). Grid refinement studies are performed with two completely different RANS solvers to determine the asymptotic order of convergence of the L1 and L2 norms of the discretization error of mean flow and turbulence quantities. Two types of exercises are performed: calculation of all transport equations with the manufactured eddyviscosity field (no influence of the turbulence model on the mean flow solution); calculation of all transport equations, i.e. continuity, momentum equations and transport equations of turbulence quantities. Furthermore, techniques with different orders of accuracy are tested in the discretization of the convective terms of the turbulence quantities transport equations to assess its impact on the convergence properties of the mean flow quantities. The selected examples show that the solution of the turbulence quantities transport equations may disturb the expected convergence properties of the discretization error of the mean flow quantities.}, keywords = {}, pubstate = {published}, tppubtype = {conference} } This paper addresses the effects of eddyviscosity turbulence models  namely, the oneequation model of Spalart & Allmaras and the TNT version of the twoequation k  w model  on the convergence properties of RANS solvers. These effects are examined with Manufactured Solutions that mimic nearwall turbulent flows, allowing the evaluation of the discretization error of the numerical solutions (contributions of the iterative and roundoff errors being negligible). Grid refinement studies are performed with two completely different RANS solvers to determine the asymptotic order of convergence of the L1 and L2 norms of the discretization error of mean flow and turbulence quantities. Two types of exercises are performed: calculation of all transport equations with the manufactured eddyviscosity field (no influence of the turbulence model on the mean flow solution); calculation of all transport equations, i.e. continuity, momentum equations and transport equations of turbulence quantities. Furthermore, techniques with different orders of accuracy are tested in the discretization of the convective terms of the turbulence quantities transport equations to assess its impact on the convergence properties of the mean flow quantities. The selected examples show that the solution of the turbulence quantities transport equations may disturb the expected convergence properties of the discretization error of the mean flow quantities. 
2017 

Pereira, Filipe; Eca, Luis; Vaz, Guilherme Verification and Validation exercises for the flow around the KVLCC2 tanker at model and fullscale Reynolds numbers Journal Article Ocean Engineering, 129 , pp. 133148, 2017. Abstract  Links  BibTeX  Tags: EARSM, KVLCC2, Modelling error, Numerical error, RANS, ScaleEffects, SST, Turbulence modelling, Validation, Verification @article{2017OEPereiraVazEca_KVLCC2, title = {Verification and Validation exercises for the flow around the KVLCC2 tanker at model and fullscale Reynolds numbers}, author = {Filipe Pereira and Luis Eca and Guilherme Vaz}, url = {http://www.refresco.org/download/2017oepereiravazeca_kvlcc2vv/}, doi = {http://dx.doi.org/10.1016/j.oceaneng.2016.11.005}, year = {2017}, date = {20170109}, journal = {Ocean Engineering}, volume = {129}, pages = {133148}, abstract = {This paper presents the quantification of numerical and modelling errors for the solution of the flow around the KVLCC2 tanker at modelscale Reynolds number. Numerical errors are also quantified for fullscale Reynolds number simulations to address the numerical accuracy of the prediction of scaleeffects. The calculations are performed with the solver ReFRESCO using fourteen distinct ReynoldsAveraged NavierStokes (RANS) equations models. The quantities of interest for the Validation exercises at modelscale are the resistance coefficient and the velocity and turbulence kinetic energy fields at the propeller plane. Modelling errors are estimated using the ASME V & $2V20 procedure which requires numerical and experimental data with their respective uncertainties. Numerical uncertainties are dominated by the contribution of the discretization error, which is determined by grid refinement studies. Scaleeffects are also assessed for the wakefraction and formfactor. The outcome shows that quantifying modelling errors is not a trivial exercise that depends on the quality and details of simulations and experiments. Nonetheless, it is also evident that a quantitative evaluation of modelling errors is more reliable than traditional graphical comparisons of simulations and experiments. Fullscale results show scaleeffects larger than numerical uncertainties that are illustrated for the formfactor and wakefraction.}, keywords = {EARSM, KVLCC2, Modelling error, Numerical error, RANS, ScaleEffects, SST, Turbulence modelling, Validation, Verification}, pubstate = {published}, tppubtype = {article} } This paper presents the quantification of numerical and modelling errors for the solution of the flow around the KVLCC2 tanker at modelscale Reynolds number. Numerical errors are also quantified for fullscale Reynolds number simulations to address the numerical accuracy of the prediction of scaleeffects. The calculations are performed with the solver ReFRESCO using fourteen distinct ReynoldsAveraged NavierStokes (RANS) equations models. The quantities of interest for the Validation exercises at modelscale are the resistance coefficient and the velocity and turbulence kinetic energy fields at the propeller plane. Modelling errors are estimated using the ASME V & $2V20 procedure which requires numerical and experimental data with their respective uncertainties. Numerical uncertainties are dominated by the contribution of the discretization error, which is determined by grid refinement studies. Scaleeffects are also assessed for the wakefraction and formfactor. The outcome shows that quantifying modelling errors is not a trivial exercise that depends on the quality and details of simulations and experiments. Nonetheless, it is also evident that a quantitative evaluation of modelling errors is more reliable than traditional graphical comparisons of simulations and experiments. Fullscale results show scaleeffects larger than numerical uncertainties that are illustrated for the formfactor and wakefraction.  
Rocha A.L., Eca L; G., Vaz VII International Conference on Computational Methods in Marine Engineering, Wageningen, The Netherlands, 2017. Abstract  Links  BibTeX  Tags: KVLCC2, Numerical error, RANS, Unstructured grid @conference{2017MarineRocha, title = {On the Numerical Convergence Properties of the Calculation of the Flow around the KVLCC2 Tanker in Unstructured Grids}, author = {Rocha A.L., Eca L. and Vaz G.}, url = {http://www.refresco.org/download/numericalconvergencepropertiescalculationflowaroundkvlcc2tankerunstructuredgrids/ }, year = {2017}, date = {20170101}, booktitle = {VII International Conference on Computational Methods in Marine Engineering}, address = {Wageningen, The Netherlands}, abstract = {This paper addresses the estimation of numerical errors in the calculation of the flow around the KVLCC2 tanker at modelscale Reynolds number inunstrctured grids.The flow solution is based on the ReynoldsAveraged NavierStokes equations supplemented by the k−SSTtwoequation eddyviscosity model using the socalled doublebody approach, i.e. free surface effects are neglected. Grid refinement studies are performed for sets of grids generated with the open source code SnappyHexMesh and with the HEXPRESSTM grid generator. Definition of grid refinemen tratioin unstructured grids and itsconsequencesfortheestimati onofnumericalerrorsisdiscussed.FrictionandpressureresistancecoefficientsandmeanvelocitycomponentsatthepropellerplanearecomparedwithreferencesolutionsobtainedinearlyorthogonalmultiblockstructuredgridswiththesameflowsolverReFRESCO.}, keywords = {KVLCC2, Numerical error, RANS, Unstructured grid}, pubstate = {published}, tppubtype = {conference} } This paper addresses the estimation of numerical errors in the calculation of the flow around the KVLCC2 tanker at modelscale Reynolds number inunstrctured grids.The flow solution is based on the ReynoldsAveraged NavierStokes equations supplemented by the k−SSTtwoequation eddyviscosity model using the socalled doublebody approach, i.e. free surface effects are neglected. Grid refinement studies are performed for sets of grids generated with the open source code SnappyHexMesh and with the HEXPRESSTM grid generator. Definition of grid refinemen tratioin unstructured grids and itsconsequencesfortheestimati onofnumericalerrorsisdiscussed.FrictionandpressureresistancecoefficientsandmeanvelocitycomponentsatthepropellerplanearecomparedwithreferencesolutionsobtainedinearlyorthogonalmultiblockstructuredgridswiththesameflowsolverReFRESCO.  
2016 

Eca, Luis; Klaij, Christiaan; Vaz, Guilherme; Hoekstra, Martin; Pereira, Filipe On code verification of RANS solvers Journal Article Journal of Computational Physics, 310 , pp. 418439, 2016. Abstract  Links  BibTeX  Tags: Code Verification, Manufactured solutions, Numerical error, Order of grid convergence, RANS @article{2016JCPEcaKlaijVazPereiraHoekstra, title = {On code verification of RANS solvers}, author = {Luis Eca and Christiaan Klaij and Guilherme Vaz and Martin Hoekstra and Filipe Pereira}, url = {http://www.refresco.org/download/2016jcpecaklaijvazpereirahoekstra_codeverification/}, year = {2016}, date = {20160113}, journal = {Journal of Computational Physics}, volume = {310}, pages = {418439}, abstract = {This article discusses Code Verification of ReynoldsAveraged Navier Stokes (RANS) solvers that rely on face based finite volume discretizations for volumes of arbitrary shape. The study includes test cases with known analytical solutions (generated with the method of manufactured solutions) corresponding to laminar and turbulent flow, with the latter using eddyviscosity turbulence models. The procedure to perform Code Verification based on grid refinement studies is discussed and the requirements for its correct application are illustrated in a simple onedimensional problem. It is shown that geometrically similar grids are recommended for proper Code Verification and so the data should not have scatter making the use of least square fits unnecessary. Results show that it may be advantageous to determine the extrapolated error to cell size/time step zero instead of assuming that it is zero, especially when it is hard to determine the asymptotic order of grid convergence. In the RANS examples, several of the features of the ReFRESCO solver are checked including the effects of the available turbulence models in the convergence properties of the code. It is shown that it is required to account for nonorthogonality effects in the discretization of the diffusion terms and that the turbulence quantities transport equations can deteriorate the order of grid convergence of mean flow quantities.}, keywords = {Code Verification, Manufactured solutions, Numerical error, Order of grid convergence, RANS}, pubstate = {published}, tppubtype = {article} } This article discusses Code Verification of ReynoldsAveraged Navier Stokes (RANS) solvers that rely on face based finite volume discretizations for volumes of arbitrary shape. The study includes test cases with known analytical solutions (generated with the method of manufactured solutions) corresponding to laminar and turbulent flow, with the latter using eddyviscosity turbulence models. The procedure to perform Code Verification based on grid refinement studies is discussed and the requirements for its correct application are illustrated in a simple onedimensional problem. It is shown that geometrically similar grids are recommended for proper Code Verification and so the data should not have scatter making the use of least square fits unnecessary. Results show that it may be advantageous to determine the extrapolated error to cell size/time step zero instead of assuming that it is zero, especially when it is hard to determine the asymptotic order of grid convergence. In the RANS examples, several of the features of the ReFRESCO solver are checked including the effects of the available turbulence models in the convergence properties of the code. It is shown that it is required to account for nonorthogonality effects in the discretization of the diffusion terms and that the turbulence quantities transport equations can deteriorate the order of grid convergence of mean flow quantities.  
2012 

Eca, Luis; Vaz, Guilherme; Hoekstra, Martin ASSESSING CONVERGENCE PROPERTIES OF RANS SOLVERS WITH MANUFACTURED SOLUTIONS Conference ECCOMAS Vienna, Austria, 2012. Abstract  Links  BibTeX  Tags: convergence properties, Manufactured solutions, Numerical error, RANS solvers @conference{2012ECCOMAS_Eca_Vaz_Hoekstra, title = {ASSESSING CONVERGENCE PROPERTIES OF RANS SOLVERS WITH MANUFACTURED SOLUTIONS}, author = {Luis Eca and Guilherme Vaz and Martin Hoekstra }, url = {http://www.refresco.org/download/2012eccomas_eca_vaz_hoekstra/}, year = {2012}, date = {20120910}, address = {Vienna, Austria}, organization = {ECCOMAS}, abstract = {This paper addresses the effects of eddyviscosity turbulence models  namely, the oneequation model of Spalart & Allmaras and the TNT version of the twoequation k  w model  on the convergence properties of RANS solvers. These effects are examined with Manufactured Solutions that mimic nearwall turbulent flows, allowing the evaluation of the discretization error of the numerical solutions (contributions of the iterative and roundoff errors being negligible). Grid refinement studies are performed with two completely different RANS solvers to determine the asymptotic order of convergence of the L1 and L2 norms of the discretization error of mean flow and turbulence quantities. Two types of exercises are performed: calculation of all transport equations with the manufactured eddyviscosity field (no influence of the turbulence model on the mean flow solution); calculation of all transport equations, i.e. continuity, momentum equations and transport equations of turbulence quantities. Furthermore, techniques with different orders of accuracy are tested in the discretization of the convective terms of the turbulence quantities transport equations to assess its impact on the convergence properties of the mean flow quantities. The selected examples show that the solution of the turbulence quantities transport equations may disturb the expected convergence properties of the discretization error of the mean flow quantities.}, keywords = {convergence properties, Manufactured solutions, Numerical error, RANS solvers}, pubstate = {published}, tppubtype = {conference} } This paper addresses the effects of eddyviscosity turbulence models  namely, the oneequation model of Spalart & Allmaras and the TNT version of the twoequation k  w model  on the convergence properties of RANS solvers. These effects are examined with Manufactured Solutions that mimic nearwall turbulent flows, allowing the evaluation of the discretization error of the numerical solutions (contributions of the iterative and roundoff errors being negligible). Grid refinement studies are performed with two completely different RANS solvers to determine the asymptotic order of convergence of the L1 and L2 norms of the discretization error of mean flow and turbulence quantities. Two types of exercises are performed: calculation of all transport equations with the manufactured eddyviscosity field (no influence of the turbulence model on the mean flow solution); calculation of all transport equations, i.e. continuity, momentum equations and transport equations of turbulence quantities. Furthermore, techniques with different orders of accuracy are tested in the discretization of the convective terms of the turbulence quantities transport equations to assess its impact on the convergence properties of the mean flow quantities. The selected examples show that the solution of the turbulence quantities transport equations may disturb the expected convergence properties of the discretization error of the mean flow quantities. 