1.  Eca, Luis; Hoekstra, Martin; Vaz, Guilherme: Verification of Solutions in Unsteady Flows. In Proceedings of ASME 2015 V&V Symposium, Las Vegas, Nevada, USA, 2015. (Type: Conference  Links  BibTeX) @conference{2015ASMEV&V_Eca_et_al_SolVerificationUnstd, title = {Verification of Solutions in Unsteady Flows}, author = {Luis Eca and Martin Hoekstra and Guilherme Vaz}, url = {http://www.refresco.org/?p=1422}, year = {2015}, date = {20150511}, booktitle = {In Proceedings of ASME 2015 V&V Symposium, Las Vegas, Nevada, USA}, keywords = {}, pubstate = {published}, tppubtype = {conference} } 
2.  Pereira, Filipe: Verication of ReFRESCO with the Method of Manufactured Solutions. IST, Lisbon, Portugal, 2012. (Type: Masters Thesis  Abstract  Links  BibTeX) @mastersthesis{2012Msc_Thesis_FilipePereira, title = {Verication of ReFRESCO with the Method of Manufactured Solutions}, author = {Filipe Pereira}, url = {http://www.refresco.org/?wpdmpro=2012msc_thesis_filipepereirapdf}, year = {2012}, date = {20121001}, school = {IST, Lisbon, Portugal}, abstract = {The purpose of this Thesis was to Verify the RANS solver ReFRESCO. This analysis was executed over three distinct parts of the code: convection schemes, nonorthogonality and excentricity correctors. Moreover, it was performed the implementation and evaluation of the numerical properties of two nonorthogonality and three excentricity new correction methods. In order to execute the Verification of ReFRESCO, grid refinement studies were performed to check if the numerical error tend to zero with the correct order of grid convergence (theoretical order). The calculation of the numerical error required the use of the Method of Manufactured Solutions to create exact solutions of the RANS equations. Thus, three manufactured solutions were used, each one resembling a different flow. The main conclusions of the present Thesis were: the convection schemes are correctly coded; the Hybrid scheme order of grid convergence did not vary linearly with the blending factor and it tended to a step function with the increase of the ow complexity; the tests performed over the nonorthogonality correctors showed that these methods maintained the secondorder of the code while discarding the correctors originated a constant numerical error in the solution; in grids where the excentricity factor was independent from grid renement, compared to the noncorrected case (constant numerical error), the excentricity correctors (correctly implemented) decreased significantly the magnitude of the numerical error. However, these correctors only guaranteed rstorder accuracy.}, keywords = {}, pubstate = {published}, tppubtype = {mastersthesis} } The purpose of this Thesis was to Verify the RANS solver ReFRESCO. This analysis was executed over three distinct parts of the code: convection schemes, nonorthogonality and excentricity correctors. Moreover, it was performed the implementation and evaluation of the numerical properties of two nonorthogonality and three excentricity new correction methods. In order to execute the Verification of ReFRESCO, grid refinement studies were performed to check if the numerical error tend to zero with the correct order of grid convergence (theoretical order). The calculation of the numerical error required the use of the Method of Manufactured Solutions to create exact solutions of the RANS equations. Thus, three manufactured solutions were used, each one resembling a different flow. The main conclusions of the present Thesis were: the convection schemes are correctly coded; the Hybrid scheme order of grid convergence did not vary linearly with the blending factor and it tended to a step function with the increase of the ow complexity; the tests performed over the nonorthogonality correctors showed that these methods maintained the secondorder of the code while discarding the correctors originated a constant numerical error in the solution; in grids where the excentricity factor was independent from grid renement, compared to the noncorrected case (constant numerical error), the excentricity correctors (correctly implemented) decreased significantly the magnitude of the numerical error. However, these correctors only guaranteed rstorder accuracy. 
3.  Eca, Luis; Hoekstra, Martin; Vaz, Guilherme: Manufactured solutions for steady flow Reynoldsaveraged Navier–Stokes solvers. In: International Journal of Computational Fluid Dynamics, 26 (5), pp. 313332, 2012. (Type: Journal Article  Abstract  Links  BibTeX) @article{2012IJCFD_Eca_et_al_MMS, title = {Manufactured solutions for steady flow Reynoldsaveraged Navier–Stokes solvers}, author = {Luis Eca and Martin Hoekstra and Guilherme Vaz}, editor = {Taylor & Francis}, url = {http://www.refresco.org/?post_type=wpdmpro&p=844 }, doi = {DOI: 10.1080/10618562.2012.717617}, year = {2012}, date = {20120911}, journal = {International Journal of Computational Fluid Dynamics}, volume = {26}, number = {5}, pages = {313332}, abstract = {This paper presents manufactured solutions (MS’s) for code verification of incompressible flow solvers based on the Reynoldsaveraged Navier–Stokes (RANS) equations. The proposed solutions mimic statistically steady, twodimensional or threedimensional nearwall turbulent flows in a simple domain (rectangle or rectangular box) at a given Reynolds number. The proposed analytical functions cover the mean flow quantities and the dependent variables of several eddyviscosity turbulence models. Namely, the undamped eddyviscosity of the Spalart and Allmaras and Menter oneequations models, the one (SKL) and twoequation (KSKL) models proposed by Menter, the turbulence kinetic energy and the turbulence frequency included in twoequation KOmega models. A basic flow field resembling a turbulent flat plate flow is constructed with the turbulence quantities defined from ‘automatic wall functions’ that are supposed to reproduce more or less the normal behaviour of these variables. Alternative flow fields are constructed superposing a perturbation flow field that creates a ‘recirculation zone’. However, the nearwall solution of the basic flow is kept to avoid zero friction at the wall. Threedimensional MS’s are obtained from the blending of the basic twodimensional MS’s in the transverse direction. All flow fields satisfy mass conservation, i.e. mean velocity fields are divergencefree. The source functions required for the balancing of momentum and turbulence quantities transport equations and all the dependent variables and their derivatives are available in Fortran 90 modules.}, keywords = {}, pubstate = {published}, tppubtype = {article} } This paper presents manufactured solutions (MS’s) for code verification of incompressible flow solvers based on the Reynoldsaveraged Navier–Stokes (RANS) equations. The proposed solutions mimic statistically steady, twodimensional or threedimensional nearwall turbulent flows in a simple domain (rectangle or rectangular box) at a given Reynolds number. The proposed analytical functions cover the mean flow quantities and the dependent variables of several eddyviscosity turbulence models. Namely, the undamped eddyviscosity of the Spalart and Allmaras and Menter oneequations models, the one (SKL) and twoequation (KSKL) models proposed by Menter, the turbulence kinetic energy and the turbulence frequency included in twoequation KOmega models. A basic flow field resembling a turbulent flat plate flow is constructed with the turbulence quantities defined from ‘automatic wall functions’ that are supposed to reproduce more or less the normal behaviour of these variables. Alternative flow fields are constructed superposing a perturbation flow field that creates a ‘recirculation zone’. However, the nearwall solution of the basic flow is kept to avoid zero friction at the wall. Threedimensional MS’s are obtained from the blending of the basic twodimensional MS’s in the transverse direction. All flow fields satisfy mass conservation, i.e. mean velocity fields are divergencefree. The source functions required for the balancing of momentum and turbulence quantities transport equations and all the dependent variables and their derivatives are available in Fortran 90 modules. 
2015 

Eca, Luis; Hoekstra, Martin; Vaz, Guilherme Verification of Solutions in Unsteady Flows Conference In Proceedings of ASME 2015 V&V Symposium, Las Vegas, Nevada, USA, 2015. Links  BibTeX  Tags: Iterative error, MMS, SST, URANS, Verification @conference{2015ASMEV&V_Eca_et_al_SolVerificationUnstd, title = {Verification of Solutions in Unsteady Flows}, author = {Luis Eca and Martin Hoekstra and Guilherme Vaz}, url = {http://www.refresco.org/?p=1422}, year = {2015}, date = {20150511}, booktitle = {In Proceedings of ASME 2015 V&V Symposium, Las Vegas, Nevada, USA}, keywords = {Iterative error, MMS, SST, URANS, Verification}, pubstate = {published}, tppubtype = {conference} }  
2012 

Pereira, Filipe Verication of ReFRESCO with the Method of Manufactured Solutions Masters Thesis IST, Lisbon, Portugal, 2012. Abstract  Links  BibTeX  Tags: Code Verification, Convection schemes, Excentricity, MMS, Nonorthogonality, RANS, SST, Validation, Verification @mastersthesis{2012Msc_Thesis_FilipePereira, title = {Verication of ReFRESCO with the Method of Manufactured Solutions}, author = {Filipe Pereira}, url = {http://www.refresco.org/?wpdmpro=2012msc_thesis_filipepereirapdf}, year = {2012}, date = {20121001}, school = {IST, Lisbon, Portugal}, abstract = {The purpose of this Thesis was to Verify the RANS solver ReFRESCO. This analysis was executed over three distinct parts of the code: convection schemes, nonorthogonality and excentricity correctors. Moreover, it was performed the implementation and evaluation of the numerical properties of two nonorthogonality and three excentricity new correction methods. In order to execute the Verification of ReFRESCO, grid refinement studies were performed to check if the numerical error tend to zero with the correct order of grid convergence (theoretical order). The calculation of the numerical error required the use of the Method of Manufactured Solutions to create exact solutions of the RANS equations. Thus, three manufactured solutions were used, each one resembling a different flow. The main conclusions of the present Thesis were: the convection schemes are correctly coded; the Hybrid scheme order of grid convergence did not vary linearly with the blending factor and it tended to a step function with the increase of the ow complexity; the tests performed over the nonorthogonality correctors showed that these methods maintained the secondorder of the code while discarding the correctors originated a constant numerical error in the solution; in grids where the excentricity factor was independent from grid renement, compared to the noncorrected case (constant numerical error), the excentricity correctors (correctly implemented) decreased significantly the magnitude of the numerical error. However, these correctors only guaranteed rstorder accuracy.}, keywords = {Code Verification, Convection schemes, Excentricity, MMS, Nonorthogonality, RANS, SST, Validation, Verification}, pubstate = {published}, tppubtype = {mastersthesis} } The purpose of this Thesis was to Verify the RANS solver ReFRESCO. This analysis was executed over three distinct parts of the code: convection schemes, nonorthogonality and excentricity correctors. Moreover, it was performed the implementation and evaluation of the numerical properties of two nonorthogonality and three excentricity new correction methods. In order to execute the Verification of ReFRESCO, grid refinement studies were performed to check if the numerical error tend to zero with the correct order of grid convergence (theoretical order). The calculation of the numerical error required the use of the Method of Manufactured Solutions to create exact solutions of the RANS equations. Thus, three manufactured solutions were used, each one resembling a different flow. The main conclusions of the present Thesis were: the convection schemes are correctly coded; the Hybrid scheme order of grid convergence did not vary linearly with the blending factor and it tended to a step function with the increase of the ow complexity; the tests performed over the nonorthogonality correctors showed that these methods maintained the secondorder of the code while discarding the correctors originated a constant numerical error in the solution; in grids where the excentricity factor was independent from grid renement, compared to the noncorrected case (constant numerical error), the excentricity correctors (correctly implemented) decreased significantly the magnitude of the numerical error. However, these correctors only guaranteed rstorder accuracy.  
Eca, Luis; Hoekstra, Martin; Vaz, Guilherme Manufactured solutions for steady flow Reynoldsaveraged Navier–Stokes solvers Journal Article International Journal of Computational Fluid Dynamics, 26 (5), pp. 313332, 2012. Abstract  Links  BibTeX  Tags: KSKL, MMS, RANS, SKL, SpalartAllmaras, SST, Verification @article{2012IJCFD_Eca_et_al_MMS, title = {Manufactured solutions for steady flow Reynoldsaveraged Navier–Stokes solvers}, author = {Luis Eca and Martin Hoekstra and Guilherme Vaz}, editor = {Taylor & Francis}, url = {http://www.refresco.org/?post_type=wpdmpro&p=844 }, doi = {DOI: 10.1080/10618562.2012.717617}, year = {2012}, date = {20120911}, journal = {International Journal of Computational Fluid Dynamics}, volume = {26}, number = {5}, pages = {313332}, abstract = {This paper presents manufactured solutions (MS’s) for code verification of incompressible flow solvers based on the Reynoldsaveraged Navier–Stokes (RANS) equations. The proposed solutions mimic statistically steady, twodimensional or threedimensional nearwall turbulent flows in a simple domain (rectangle or rectangular box) at a given Reynolds number. The proposed analytical functions cover the mean flow quantities and the dependent variables of several eddyviscosity turbulence models. Namely, the undamped eddyviscosity of the Spalart and Allmaras and Menter oneequations models, the one (SKL) and twoequation (KSKL) models proposed by Menter, the turbulence kinetic energy and the turbulence frequency included in twoequation KOmega models. A basic flow field resembling a turbulent flat plate flow is constructed with the turbulence quantities defined from ‘automatic wall functions’ that are supposed to reproduce more or less the normal behaviour of these variables. Alternative flow fields are constructed superposing a perturbation flow field that creates a ‘recirculation zone’. However, the nearwall solution of the basic flow is kept to avoid zero friction at the wall. Threedimensional MS’s are obtained from the blending of the basic twodimensional MS’s in the transverse direction. All flow fields satisfy mass conservation, i.e. mean velocity fields are divergencefree. The source functions required for the balancing of momentum and turbulence quantities transport equations and all the dependent variables and their derivatives are available in Fortran 90 modules.}, keywords = {KSKL, MMS, RANS, SKL, SpalartAllmaras, SST, Verification}, pubstate = {published}, tppubtype = {article} } This paper presents manufactured solutions (MS’s) for code verification of incompressible flow solvers based on the Reynoldsaveraged Navier–Stokes (RANS) equations. The proposed solutions mimic statistically steady, twodimensional or threedimensional nearwall turbulent flows in a simple domain (rectangle or rectangular box) at a given Reynolds number. The proposed analytical functions cover the mean flow quantities and the dependent variables of several eddyviscosity turbulence models. Namely, the undamped eddyviscosity of the Spalart and Allmaras and Menter oneequations models, the one (SKL) and twoequation (KSKL) models proposed by Menter, the turbulence kinetic energy and the turbulence frequency included in twoequation KOmega models. A basic flow field resembling a turbulent flat plate flow is constructed with the turbulence quantities defined from ‘automatic wall functions’ that are supposed to reproduce more or less the normal behaviour of these variables. Alternative flow fields are constructed superposing a perturbation flow field that creates a ‘recirculation zone’. However, the nearwall solution of the basic flow is kept to avoid zero friction at the wall. Threedimensional MS’s are obtained from the blending of the basic twodimensional MS’s in the transverse direction. All flow fields satisfy mass conservation, i.e. mean velocity fields are divergencefree. The source functions required for the balancing of momentum and turbulence quantities transport equations and all the dependent variables and their derivatives are available in Fortran 90 modules. 