1.  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. 
2.  Eca, Luis; Hoekstra, Martin; Vaz, Guilherme: On the use of Method of Manufactured Solutions for Code Verification of RANS solvers based on Eddyviscosity Models. 02.05.2012. (Type: Presentation  Abstract  Links  BibTeX) @misc{2012ASMEV&V6140_Eca, title = {On the use of Method of Manufactured Solutions for Code Verification of RANS solvers based on Eddyviscosity Models}, author = {Luis Eca and Martin Hoekstra and Guilherme Vaz}, url = {http://www.refresco.org/download/2012asmevv6140_ecahoekstravazmmsrans/}, year = {2012}, date = {20120502}, abstract = {This presentation discusses the use of Manufactured Solutions for Code Verification of ReynoldsAveraged Navier Stokes (RANS) solvers. In this exercise we will focus on timeaveraged (statistically steady), incompressible flows. Recently, we have developed several Manufactured Solutions (MS) that mimic a nearwall turbulent flow. 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 & Allmaras and Menter oneequations models, k^(1/2) L from the one (SKL) and twoequation (KSKL) models proposed by Menter, the turbulence kinetic energy and the turbulence frequency included in twoequation kw models. The turbulence quantities are defined from “automatic wall functions” and so they are supposed to reproduce the expected behaviour of these variables. All flow fields satisfy mass conservation, i.e. mean velocity fields are divergence free. We address three types of exercises: 1. Calculation of the continuity and momentum equations with a manufactured eddyviscosity field. 2. Calculation of the turbulence quantities transport equations with the manufactured mean flow field. 3. Calculation of the complete system of equations. Two main topics are discussed: The effect of the turbulence model on the convergence properties of the RANS solver. The difficulties imposed to the Method of Manufactured Solutions by the fact that physically all turbulence quantities must remain positive.}, keywords = {}, pubstate = {published}, tppubtype = {presentation} } This presentation discusses the use of Manufactured Solutions for Code Verification of ReynoldsAveraged Navier Stokes (RANS) solvers. In this exercise we will focus on timeaveraged (statistically steady), incompressible flows. Recently, we have developed several Manufactured Solutions (MS) that mimic a nearwall turbulent flow. 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 & Allmaras and Menter oneequations models, k^(1/2) L from the one (SKL) and twoequation (KSKL) models proposed by Menter, the turbulence kinetic energy and the turbulence frequency included in twoequation kw models. The turbulence quantities are defined from “automatic wall functions” and so they are supposed to reproduce the expected behaviour of these variables. All flow fields satisfy mass conservation, i.e. mean velocity fields are divergence free. We address three types of exercises: 1. Calculation of the continuity and momentum equations with a manufactured eddyviscosity field. 2. Calculation of the turbulence quantities transport equations with the manufactured mean flow field. 3. Calculation of the complete system of equations. Two main topics are discussed: The effect of the turbulence model on the convergence properties of the RANS solver. The difficulties imposed to the Method of Manufactured Solutions by the fact that physically all turbulence quantities must remain positive. 
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.  
Eca, Luis; Hoekstra, Martin; Vaz, Guilherme On the use of Method of Manufactured Solutions for Code Verification of RANS solvers based on Eddyviscosity Models Presentation 02.05.2012. Abstract  Links  BibTeX  Tags: Code Verification, Eddyviscosity, Manufactured solutions, RANS solvers @misc{2012ASMEV&V6140_Eca, title = {On the use of Method of Manufactured Solutions for Code Verification of RANS solvers based on Eddyviscosity Models}, author = {Luis Eca and Martin Hoekstra and Guilherme Vaz}, url = {http://www.refresco.org/download/2012asmevv6140_ecahoekstravazmmsrans/}, year = {2012}, date = {20120502}, abstract = {This presentation discusses the use of Manufactured Solutions for Code Verification of ReynoldsAveraged Navier Stokes (RANS) solvers. In this exercise we will focus on timeaveraged (statistically steady), incompressible flows. Recently, we have developed several Manufactured Solutions (MS) that mimic a nearwall turbulent flow. 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 & Allmaras and Menter oneequations models, k^(1/2) L from the one (SKL) and twoequation (KSKL) models proposed by Menter, the turbulence kinetic energy and the turbulence frequency included in twoequation kw models. The turbulence quantities are defined from “automatic wall functions” and so they are supposed to reproduce the expected behaviour of these variables. All flow fields satisfy mass conservation, i.e. mean velocity fields are divergence free. We address three types of exercises: 1. Calculation of the continuity and momentum equations with a manufactured eddyviscosity field. 2. Calculation of the turbulence quantities transport equations with the manufactured mean flow field. 3. Calculation of the complete system of equations. Two main topics are discussed: The effect of the turbulence model on the convergence properties of the RANS solver. The difficulties imposed to the Method of Manufactured Solutions by the fact that physically all turbulence quantities must remain positive.}, keywords = {Code Verification, Eddyviscosity, Manufactured solutions, RANS solvers}, pubstate = {published}, tppubtype = {presentation} } This presentation discusses the use of Manufactured Solutions for Code Verification of ReynoldsAveraged Navier Stokes (RANS) solvers. In this exercise we will focus on timeaveraged (statistically steady), incompressible flows. Recently, we have developed several Manufactured Solutions (MS) that mimic a nearwall turbulent flow. 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 & Allmaras and Menter oneequations models, k^(1/2) L from the one (SKL) and twoequation (KSKL) models proposed by Menter, the turbulence kinetic energy and the turbulence frequency included in twoequation kw models. The turbulence quantities are defined from “automatic wall functions” and so they are supposed to reproduce the expected behaviour of these variables. All flow fields satisfy mass conservation, i.e. mean velocity fields are divergence free. We address three types of exercises: 1. Calculation of the continuity and momentum equations with a manufactured eddyviscosity field. 2. Calculation of the turbulence quantities transport equations with the manufactured mean flow field. 3. Calculation of the complete system of equations. Two main topics are discussed: The effect of the turbulence model on the convergence properties of the RANS solver. The difficulties imposed to the Method of Manufactured Solutions by the fact that physically all turbulence quantities must remain positive. 