# Publications

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## 2015 |

Stephens, Darrin W; Sideroff, Chris; Jemcov, Aleksandar Validation of a Fast Transient Solver based on the Projection Method Presentation 17.07.2015. Links | BibTeX | Tags: Caelus, Cavity, Junction, PISO, Plate, Pressure Matrix, SLIM, Solver @misc{Stephens2015, title = {Validation of a Fast Transient Solver based on the Projection Method}, author = {Darrin W Stephens and Chris Sideroff and Aleksandar Jemcov }, url = {http://www.appliedccm.com/wp-content/uploads/2015/08/iccm2015-presentation.pdf}, year = {2015}, date = {2015-07-17}, keywords = {Caelus, Cavity, Junction, PISO, Plate, Pressure Matrix, SLIM, Solver}, pubstate = {published}, tppubtype = {presentation} } |

Shi, Ke; Morris, Scott; Jemcov, Aleksandar A Primitive Variable Central Flux Scheme for All Mach Number Flows Conference 53rd AIAA Aerospace Sciences Meeting, 2015, At Kissimmee, FL, 2015. Abstract | Links | BibTeX | Tags: Central Flux, Convective, Elliptic, Fluxes, Solver, Validation @conference{shiprimitive, title = {A Primitive Variable Central Flux Scheme for All Mach Number Flows}, author = { Ke Shi and Scott Morris and Aleksandar Jemcov}, doi = {10.2514/6.2015-1265 }, year = {2015}, date = {2015-01-01}, booktitle = {53rd AIAA Aerospace Sciences Meeting, 2015, At Kissimmee, FL}, abstract = {A new finite volume solver for all Mach number Flows suitable for the solution on unstructured meshes with the collocated arrangement of variables is presented. The solver is based on the primitive variable equations. The newly proposed method utilizes the fractional step method that resembles the projection methods used in incompressible flow simulations. The proposed solver is suitable for the computations ranging from incompressible to supersonic flows. A notable characteristic of the newly proposed method is that the new formulation of the compressible pressure equation contains the pressure Laplacian term pre-multiplied by the time step size. Unlike the incompressible projection methods, the new pressure equation is derived from the discrete form of the continuity equation, resulting in the equation that has the potential (elliptic) and the hyperbolic (convective) parts of the pressure field separated. Central flux formulation is used for the approximation of numeric fluxes, resulting in small numerical dissipation thus making it suitable for the high fidelity computations including direct and large eddy simulations. A set of validation problems is presented in this work demonstrating the main characteristics of the newly proposed solver.}, keywords = {Central Flux, Convective, Elliptic, Fluxes, Solver, Validation}, pubstate = {published}, tppubtype = {conference} } A new finite volume solver for all Mach number Flows suitable for the solution on unstructured meshes with the collocated arrangement of variables is presented. The solver is based on the primitive variable equations. The newly proposed method utilizes the fractional step method that resembles the projection methods used in incompressible flow simulations. The proposed solver is suitable for the computations ranging from incompressible to supersonic flows. A notable characteristic of the newly proposed method is that the new formulation of the compressible pressure equation contains the pressure Laplacian term pre-multiplied by the time step size. Unlike the incompressible projection methods, the new pressure equation is derived from the discrete form of the continuity equation, resulting in the equation that has the potential (elliptic) and the hyperbolic (convective) parts of the pressure field separated. Central flux formulation is used for the approximation of numeric fluxes, resulting in small numerical dissipation thus making it suitable for the high fidelity computations including direct and large eddy simulations. A set of validation problems is presented in this work demonstrating the main characteristics of the newly proposed solver. |

## 2014 |

Jemcov, Aleksandar; Stephens, Darrin W; Sideroff, Chris Application of Time Symmetry Preserving Adjoint Solver in External Car Aerodynamics Conference SAE 2014 World Congress & Exhibition, Paper number 2014-01-0412, 2014. Abstract | Links | BibTeX | Tags: Adjoint, Aerodynamics, Automotive, Exteriors, Solver @conference{jemcov2014application, title = {Application of Time Symmetry Preserving Adjoint Solver in External Car Aerodynamics}, author = {Aleksandar Jemcov and Darrin W Stephens and Chris Sideroff}, doi = {10.4271/2014-01-0412}, year = {2014}, date = {2014-01-01}, booktitle = {SAE 2014 World Congress & Exhibition, Paper number 2014-01-0412}, institution = {SAE Technical Paper}, abstract = {Adjoint equations for the incompressible turbulent Navier-Stokes equations are presented. The main characteristic of this adjoint formulation is that it is time symmetry preserving thus kinetic energy conservative. The newly formulated equations were applied to the computation of surface shape sensitivities of an Australian V8 supercar. Three cases for the shape sensitivity were considered: sensitivity of the body, mirror, and the rear wing of the vehicle. Shape derivatives indicated that regions of large curvature, sudden changes and sharp features are responsible for the majority of the surface force sensitivity. Vector plots show the direction of change in shape required to increase the surface force. In addition, examining the rear wing shape derivatives reveal a close correlation to the flow features }, keywords = {Adjoint, Aerodynamics, Automotive, Exteriors, Solver}, pubstate = {published}, tppubtype = {conference} } Adjoint equations for the incompressible turbulent Navier-Stokes equations are presented. The main characteristic of this adjoint formulation is that it is time symmetry preserving thus kinetic energy conservative. The newly formulated equations were applied to the computation of surface shape sensitivities of an Australian V8 supercar. Three cases for the shape sensitivity were considered: sensitivity of the body, mirror, and the rear wing of the vehicle. Shape derivatives indicated that regions of large curvature, sudden changes and sharp features are responsible for the majority of the surface force sensitivity. Vector plots show the direction of change in shape required to increase the surface force. In addition, examining the rear wing shape derivatives reveal a close correlation to the flow features |

## 2013 |

Jemcov, Aleksandar; Maruszewski, Joseph P; Cokljat, Davor; Choudhury, Dipankar Pressure Correction Solver Based on Preconditioned Numeric Flux for Incompressible and Compressible Flows Inproceedings 51st Aerospace Sciences Meeting, AIAA 2013. Abstract | Links | BibTeX | Tags: Compressible, Incompressible, Solver @inproceedings{jemcov2013pressure, title = {Pressure Correction Solver Based on Preconditioned Numeric Flux for Incompressible and Compressible Flows}, author = { Aleksandar Jemcov and Joseph P Maruszewski and Davor Cokljat and Dipankar Choudhury}, doi = {10.2514/6.2013-1128 }, year = {2013}, date = {2013-01-01}, booktitle = {51st Aerospace Sciences Meeting}, organization = {AIAA}, abstract = {Pressure based solvers in collocated grid arrangement require additional dissipation term in order to prevent pressure-velocity decoupling. Typically the dissipation is added through an interpolation procedure for the face velocity. While the face velocity interpolation resolves problems related to odd-even decoupling, the resulting dissipation is somewhat larger than what is required for the solution stabilization leading to diffusive contact and shock interfaces. On the other hand, density based solvers are well known for their resolution of discontinuities. They are often used in conjunction with eigenvalue preconditioning in order to be applicable in the low Mach number and incompressible limits. Here we demonstrate how ideas from both pressure and density based solvers can be utilized to create an all speed pressure based solver with minimal dissipation. The main idea is to use density based framework to define dissipation terms while a pressure based solver is used for the overall solution algorithm and updates of primitive variables.}, keywords = {Compressible, Incompressible, Solver}, pubstate = {published}, tppubtype = {inproceedings} } Pressure based solvers in collocated grid arrangement require additional dissipation term in order to prevent pressure-velocity decoupling. Typically the dissipation is added through an interpolation procedure for the face velocity. While the face velocity interpolation resolves problems related to odd-even decoupling, the resulting dissipation is somewhat larger than what is required for the solution stabilization leading to diffusive contact and shock interfaces. On the other hand, density based solvers are well known for their resolution of discontinuities. They are often used in conjunction with eigenvalue preconditioning in order to be applicable in the low Mach number and incompressible limits. Here we demonstrate how ideas from both pressure and density based solvers can be utilized to create an all speed pressure based solver with minimal dissipation. The main idea is to use density based framework to define dissipation terms while a pressure based solver is used for the overall solution algorithm and updates of primitive variables. |

## 2012 |

Jemcov, Aleksandar; Jasak, Hrvoje Entropy Stable Multi-dimensional Dissipation Function for the Roe Scheme on Unstructured Meshes Inproceedings 50th AIAA Aerospace Sciences Meeting, AIAA 2012. Abstract | Links | BibTeX | Tags: Dissipation, Matrix, Mesh, Mesh, Meshing, Roe Scheme, Solver, Unstructured @inproceedings{jemcov2012entropy, title = {Entropy Stable Multi-dimensional Dissipation Function for the Roe Scheme on Unstructured Meshes}, author = { Aleksandar Jemcov and Hrvoje Jasak}, doi = {10.2514/6.2012-569 }, year = {2012}, date = {2012-01-01}, booktitle = {50th AIAA Aerospace Sciences Meeting}, organization = {AIAA}, abstract = {Flux difference schemes based on the Roe approximate Riemann solver provide for sharp resolution of shock waves and contact discontinuities. Despite its good properties, the Roe scheme does not possess entropy stability that is required for the scheme to provide physically correct solutions. In addition, since the approximate Riemann solver was developed using one-dimensional considerations, the carbuncle instability appears around stagnation points for mesh-aligned flows. A solution to both entropy stability and the carbuncle problem is considered here. An alternative form of the dissipation function is developed that addresses both problems. The new dissipation function is based on the multidimensional modification to dissipation function of Roe scheme. The new scheme is shown to maintain sharp resolution comparable to the Roe flux difference scheme while satisfying entropy stability and removing the carbuncle type of instability.}, keywords = {Dissipation, Matrix, Mesh, Mesh, Meshing, Roe Scheme, Solver, Unstructured}, pubstate = {published}, tppubtype = {inproceedings} } Flux difference schemes based on the Roe approximate Riemann solver provide for sharp resolution of shock waves and contact discontinuities. Despite its good properties, the Roe scheme does not possess entropy stability that is required for the scheme to provide physically correct solutions. In addition, since the approximate Riemann solver was developed using one-dimensional considerations, the carbuncle instability appears around stagnation points for mesh-aligned flows. A solution to both entropy stability and the carbuncle problem is considered here. An alternative form of the dissipation function is developed that addresses both problems. The new dissipation function is based on the multidimensional modification to dissipation function of Roe scheme. The new scheme is shown to maintain sharp resolution comparable to the Roe flux difference scheme while satisfying entropy stability and removing the carbuncle type of instability. |

## 2011 |

Borm, Oliver; Jemcov, Aleksandar; Kau, Hans-Peter Density based Navier Stokes solver for transonic flows Presentation 01.01.2011. Links | BibTeX | Tags: CHT, FSI, MRF, Riemann, Solver, SRF, Transonic @misc{borm2011density, title = {Density based Navier Stokes solver for transonic flows}, author = { Oliver Borm and Aleksandar Jemcov and Hans-Peter Kau}, url = {http://www.appliedccm.com/wp-content/uploads/2015/07/oliver_borm_slides.pdf}, year = {2011}, date = {2011-01-01}, booktitle = {6th OpenFOAM Workshop, PennState University, USA}, keywords = {CHT, FSI, MRF, Riemann, Solver, SRF, Transonic}, pubstate = {published}, tppubtype = {presentation} } |

## 2008 |

Jemcov, Aleksandar; Maruszewski, Joseph P Nonlinear Flow Solver Acceleration by Reduced Rank Extrapolation Incollection 46th AIAA Aerospace Sciences Meeting and Exhibit, pp. 609, 2008. Abstract | Links | BibTeX | Tags: Acceleration, Algorithm, Extrapolation, GMRES, Nonlinear, RRE, SIMPLE, Solver @incollection{jemcov2008nonlinear, title = {Nonlinear Flow Solver Acceleration by Reduced Rank Extrapolation}, author = { Aleksandar Jemcov and Joseph P Maruszewski}, url = {https://www.researchgate.net/profile/Aleksandar_Jemcov/publication/275275199_Nonlinear_Flow_Solver_Acceleration_by_Reduced_Rank_Extrapolation/links/5536ca190cf2058efdea9401.pdf?origin=publication_detail_rebranded&ev=pub_int_prw_xdl&msrp=mHcz4Kt3tcM0fKKvzoZAfJu5CZ7bJAZTebm7svkdI8HyTV2DqiloQBxWK3ZC9HHtc1VaKywIo53Gq4ACRkkbmQ%3D%3D_mZOVHfxww2SuKoJv0YEv1yJ19XXhbwqiKJ%2FuZ%2FsAeTe%2BZ2RdfWruA0KDkoFLyPO0ebx%2BKC9jrGwRj%2B%2F%2BKjsf7A%3D%3D}, year = {2008}, date = {2008-01-01}, booktitle = {46th AIAA Aerospace Sciences Meeting and Exhibit}, pages = {609}, abstract = {Convergence acceleration of nonlinear flow solvers through use of vector sequence ex-trapolation techniques is presented. In particular, suitability of the Reduced Rank Extrap-olation (RRE) algorithm for the use of convergence acceleration of nonlinear flow solvers is examined. In the RRE algorithm, the solution is obtained through a linear combination of Krylov vectors with weighting coefficients obtained by minimizing L2 norm of error in this space with properly chosen constraint conditions. This process effectively defines vector sequence extrapolation process in Krylov subspace that corresponds to the GMRES method applied to nonlinear problems. Moreover, when the RRE algorithm is used to solve nonlinear problems, the flow solver plays the role of the preconditioner for the non-linear GMRES method. Benefits of the application of the RRE algorithm include better convergence rates, removal of residual stalling and improved coupling between equations in numerical models. Proposed algorithm is independent of the type of flow solver and it is equally applicable to explicit, implicit, pressure and density based algorithms. Nomenclature Q Vector of conserved variables R Residual vector F c Vector of convective fluxes F v Vector of viscous fluxes S Source vector H Total enthalpy, J/m 3 p pressure, Pa τ ij viscous tensor ρ Density, Kg/m 3 u Velocity vector, m/s u X-component of velocity vector, m/s v Y-component of velocity vector, m/s w Z-component of velocity vector, m/s V Contravariant velocity, m/s f e,i Vector of external forces Φ Generic transport variable M Nonlinear preconditioning operator F Fixed-point function ∂ Q (·) Jacobian with respect to Q α ν Extrapolation coefficients c ν o t Time, s ∂Ω Boundary of computational domain Ω Computational domain}, keywords = {Acceleration, Algorithm, Extrapolation, GMRES, Nonlinear, RRE, SIMPLE, Solver}, pubstate = {published}, tppubtype = {incollection} } Convergence acceleration of nonlinear flow solvers through use of vector sequence ex-trapolation techniques is presented. In particular, suitability of the Reduced Rank Extrap-olation (RRE) algorithm for the use of convergence acceleration of nonlinear flow solvers is examined. In the RRE algorithm, the solution is obtained through a linear combination of Krylov vectors with weighting coefficients obtained by minimizing L2 norm of error in this space with properly chosen constraint conditions. This process effectively defines vector sequence extrapolation process in Krylov subspace that corresponds to the GMRES method applied to nonlinear problems. Moreover, when the RRE algorithm is used to solve nonlinear problems, the flow solver plays the role of the preconditioner for the non-linear GMRES method. Benefits of the application of the RRE algorithm include better convergence rates, removal of residual stalling and improved coupling between equations in numerical models. Proposed algorithm is independent of the type of flow solver and it is equally applicable to explicit, implicit, pressure and density based algorithms. Nomenclature Q Vector of conserved variables R Residual vector F c Vector of convective fluxes F v Vector of viscous fluxes S Source vector H Total enthalpy, J/m 3 p pressure, Pa τ ij viscous tensor ρ Density, Kg/m 3 u Velocity vector, m/s u X-component of velocity vector, m/s v Y-component of velocity vector, m/s w Z-component of velocity vector, m/s V Contravariant velocity, m/s f e,i Vector of external forces Φ Generic transport variable M Nonlinear preconditioning operator F Fixed-point function ∂ Q (·) Jacobian with respect to Q α ν Extrapolation coefficients c ν o t Time, s ∂Ω Boundary of computational domain Ω Computational domain |

## 2007 |

Jasak, Hrvoje; Jemcov, Aleksandar; Maruszewski, Joseph P Preconditioned linear solvers for large eddy simulation Conference CFD 2007 Conference, CFD Society of Canada, 2007. Abstract | BibTeX | Tags: Algebraic Multi-grid Solver, Linear Solver, Preconditioner, Simulation, Solver @conference{jasak2007preconditioned, title = {Preconditioned linear solvers for large eddy simulation}, author = { Hrvoje Jasak and Aleksandar Jemcov and Joseph P Maruszewski}, year = {2007}, date = {2007-01-01}, booktitle = {CFD 2007 Conference, CFD Society of Canada}, abstract = {Efficient solution of linear systems of equations stemming from cell centred Finite Volume Discretisation in Large Eddy Simulation is critical in large-scale simulations. This paper presents a class of sparse matrix iterative solvers combining Algebraic Multigrid (AMG) and Krylov Space techniques with the idea of combining residual reduction techniques to improve efficiency over the current solver technology. Emphasis is placed on choosing combinations of a solver, a preconditioner and a smoother and setting control parameters that yield the most efficient solution. Results show consistent superiority of AMG-preconditioned Conjugate Gradient solvers for matrices under consideration}, keywords = {Algebraic Multi-grid Solver, Linear Solver, Preconditioner, Simulation, Solver}, pubstate = {published}, tppubtype = {conference} } Efficient solution of linear systems of equations stemming from cell centred Finite Volume Discretisation in Large Eddy Simulation is critical in large-scale simulations. This paper presents a class of sparse matrix iterative solvers combining Algebraic Multigrid (AMG) and Krylov Space techniques with the idea of combining residual reduction techniques to improve efficiency over the current solver technology. Emphasis is placed on choosing combinations of a solver, a preconditioner and a smoother and setting control parameters that yield the most efficient solution. Results show consistent superiority of AMG-preconditioned Conjugate Gradient solvers for matrices under consideration |

Jemcov, Aleksandar; Maruszewski, Joseph P; Jasak, Hrvoje Acceleration and stabilization of algebraic multigrid solver applied to incompressible flow problems Conference AIAA CFD conference, 2007. Abstract | Links | BibTeX | Tags: AMG, Linear Solver, Matrix, RPM, Solver, Velocity @conference{jemcov2007acceleration, title = {Acceleration and stabilization of algebraic multigrid solver applied to incompressible flow problems}, author = { Aleksandar Jemcov and Joseph P Maruszewski and Hrvoje Jasak}, doi = {10.2514/6.2007-4330}, year = {2007}, date = {2007-01-01}, booktitle = {AIAA CFD conference}, abstract = {Acceleration and stabilization of the Algebraic Multigrid solver (AMG) through n-th order Recursive Projection Method (RPM(n)) is described. It is shown that significant acceleration can be obtained if RPM(n) is applied to AMG during the inner iteration loop in a typical implicit incompressible CFD codes. In addition to accelerating the so- lution, RPM(n) provides increased stability to the AMG Solver extending it beyond its normal range of applicability in terms of matrix conditioning and M-matrix properties. RPM(n) algorithm allows the use of agglomerative AMG solver with simple smoothers to be effectively applied to matrices that are not an M-matrix. Theoretical foundations of RPM(n)-AMG algorithm are presented with some practical aspects of the algorithm im- plementation. Numerical experiments that involve pressure correction matrices of various sizes that appear in segregated pressure based algorithms together with coupled momen- tum and pressure matrices stemming from coupled pressure based algorithms are used to illustrate the effectiveness of the method.}, keywords = {AMG, Linear Solver, Matrix, RPM, Solver, Velocity}, pubstate = {published}, tppubtype = {conference} } Acceleration and stabilization of the Algebraic Multigrid solver (AMG) through n-th order Recursive Projection Method (RPM(n)) is described. It is shown that significant acceleration can be obtained if RPM(n) is applied to AMG during the inner iteration loop in a typical implicit incompressible CFD codes. In addition to accelerating the so- lution, RPM(n) provides increased stability to the AMG Solver extending it beyond its normal range of applicability in terms of matrix conditioning and M-matrix properties. RPM(n) algorithm allows the use of agglomerative AMG solver with simple smoothers to be effectively applied to matrices that are not an M-matrix. Theoretical foundations of RPM(n)-AMG algorithm are presented with some practical aspects of the algorithm im- plementation. Numerical experiments that involve pressure correction matrices of various sizes that appear in segregated pressure based algorithms together with coupled momen- tum and pressure matrices stemming from coupled pressure based algorithms are used to illustrate the effectiveness of the method. |

Jemcov, Aleksandar; Maruszewski, Joseph P; Jasak, Hrvoje Performance improvement of algebraic multigrid solver by vector sequence extrapolation Conference CFD 2007 Conference, CFD Society of Canada, 2007. Abstract | Links | BibTeX | Tags: AMG, Extrapolation, Grid, MPE, Multigrid, PFE, RRE, Solver @conference{jemcov2007performance, title = {Performance improvement of algebraic multigrid solver by vector sequence extrapolation}, author = { Aleksandar Jemcov and Joseph P Maruszewski and Hrvoje Jasak}, url = {https://www.researchgate.net/profile/Aleksandar_Jemcov/publication/255577657_Performance_Improvement_of_Algebraic_Multigrid_Solver_by_Vector_Sequence_Extrapolation/links/0deec530e01e9a1e91000000.pdf?origin=publication_detail_rebranded&ev=pub_int_prw_xdl&msrp=l%2FRqA1L7b0MsHj%2FU443TuP1z2sy1wGnZ36isKwJidqyfbvxfh1znfzdHGghuxvDZ1UsaTbrdodbLRM48tuw%2FSQ%3D%3D_0d7vGCwXITSmkPjwIoqTdFkhnJyIFX3cZPQVfLL9zoYt2B6bVpSn9PRtuwh7yMdk54t1LUp8kE3YNFzdQE15GA%3D%3D}, year = {2007}, date = {2007-01-01}, booktitle = {CFD 2007 Conference, CFD Society of Canada}, abstract = {Algebraic Multigrid Method (AMG) performance im- provement by vector sequence extrapolation is exam- ined. Projective Forward Extrapolation (PFE), Min- imal Polynomial Extrapolation (MPE) and Reduced Rank Extrapolation (RRE) are applied to the AMG resulting in a hybrid approach, vector extrapolated AMG. The impact of vector sequence extrapolation is shown to improve performance of the AMG in number of cycles and execution time, resulting in three new methods: PFE-AMG, MPE-AMG and RRE-AMG. Computational results of the application of vector ex- trapolated AMG to sparse matrices arising from dis- cretization of fluid flow equations are presented show- ing performance improvements compared to the tradi- tional AMG.}, keywords = {AMG, Extrapolation, Grid, MPE, Multigrid, PFE, RRE, Solver}, pubstate = {published}, tppubtype = {conference} } Algebraic Multigrid Method (AMG) performance im- provement by vector sequence extrapolation is exam- ined. Projective Forward Extrapolation (PFE), Min- imal Polynomial Extrapolation (MPE) and Reduced Rank Extrapolation (RRE) are applied to the AMG resulting in a hybrid approach, vector extrapolated AMG. The impact of vector sequence extrapolation is shown to improve performance of the AMG in number of cycles and execution time, resulting in three new methods: PFE-AMG, MPE-AMG and RRE-AMG. Computational results of the application of vector ex- trapolated AMG to sparse matrices arising from dis- cretization of fluid flow equations are presented show- ing performance improvements compared to the tradi- tional AMG. |

## 2006 |

Trang, Simon CT; Stephens, Darrin W; Schwarz, Phil Modelling heat transfer in the dripper zone of a heap leaching operation Conference Fifth International Conference on CFD in the Process Industries, 2006. Abstract | Links | BibTeX | Tags: Heat Transfer, Leaching, Modelling, Solver @conference{trang2006modelling, title = {Modelling heat transfer in the dripper zone of a heap leaching operation}, author = {Simon CT Trang and Darrin W Stephens and Phil Schwarz}, doi = {10.13140/RG.2.1.1343.2167}, year = {2006}, date = {2006-01-01}, booktitle = {Fifth International Conference on CFD in the Process Industries}, journal = {a a}, abstract = {A computational fluid dynamics (CFD) solver ANSYS- CFX is used to model the heat transfer in the region near the surface of a leach heap when drippers are buried. The potential for natural convection to occur above the dripper level, thus substantially increasing heat loss from the heap, is investigated. A parameter analysis is performed which shows that the factors that may be important to the initiation of natural convection are permeability, the depth at which the drippers are buried and the space between each dripper. The current study shows that permeability is the only parameter which has a profound effect on heat loss by natural convection. }, keywords = {Heat Transfer, Leaching, Modelling, Solver}, pubstate = {published}, tppubtype = {conference} } A computational fluid dynamics (CFD) solver ANSYS- CFX is used to model the heat transfer in the region near the surface of a leach heap when drippers are buried. The potential for natural convection to occur above the dripper level, thus substantially increasing heat loss from the heap, is investigated. A parameter analysis is performed which shows that the factors that may be important to the initiation of natural convection are permeability, the depth at which the drippers are buried and the space between each dripper. The current study shows that permeability is the only parameter which has a profound effect on heat loss by natural convection. |