- Nicholas, S., Omidyeganeh, M. and Pinelli, A. (2022). Numerical Investigation of Regime Transition in Canopy Flows. Flow, Turbulence and Combustion. doi:10.1007/s10494-022-00363-5.
- Monti, A., Nicholas, S., Omidyeganeh, M., Pinelli, A. and Rosti, M.E. (2022). On the solidity parameter in canopy flows. Journal of Fluid Mechanics, 945. doi:10.1017/jfm.2022.551.
- Kim, J.-.H., Choi, K.-.S., Lacagnina, G., Chaitanya, P., Joseph, P., Hasheminejad, S.M. … Pinelli, A. (2022). Aerodynamic and Aeroacoustic Optimization of Leading-Edge Undulation of a NACA 65(12)-10 Airfoil. AIAA Journal, 60(4), pp. 2342–2353. doi:10.2514/1.j060716.
- Lacagnina, G., Chaitanya, P., Kim, J.-.H., Berk, T., Joseph, P., Choi, K.-.S. … Pinelli, A. (2021). Leading edge serrations for the reduction of aerofoil self-noise at low angle of attack, pre-stall and post-stall conditions. International Journal of Aeroacoustics, 20(1-2), pp. 130–156. doi:10.1177/1475472x20978379.
- Hasheminejad, S.M., Chong, T.P., Lacagnina, G., Joseph, P., Kim, J.-.H., Choi, K.-.S. … Stalnov, O. (2020). On the manipulation of flow and acoustic fields of a blunt trailing edge aerofoil by serrated leading edges. The Journal of the Acoustical Society of America, 147(6), pp. 3932–3947. doi:10.1121/10.0001377.
- Monti, A., Omidyeganeh, M., Eckhardt, B. and Pinelli, A. (2020). On the genesis of different regimes in canopy flows: a numerical investigation. Journal of Fluid Mechanics, 891. doi:10.1017/jfm.2020.155.
- Lacagnina, G., Chaitanya, P., Berk, T., Kim, J.-.H., Joseph, P., Ganapathisubramani, B. … Pinelli, A. (2019). Mechanisms of airfoil noise near stall conditions. Physical Review Fluids, 4(12). doi:10.1103/physrevfluids.4.123902.
- Monti, A., Omidyeganeh, M. and Pinelli, A. (2019). Large-eddy simulation of an open-channel flow bounded by a semi-dense rigid filamentous canopy: Scaling and flow structure. Physics of Fluids, 31(6). doi:10.1063/1.5095770.
- Rosti, M.E., Omidyeganeh, M. and Pinelli, A. (2018). Numerical Simulation of a Passive Control of the Flow Around an Aerofoil Using a Flexible, Self Adaptive Flaplet. Flow, Turbulence and Combustion, 100(4), pp. 1111–1143. doi:10.1007/s10494-018-9914-6.
- Rosti, M.E., Brandt, L. and Pinelli, A. (2018). Turbulent channel flow over an anisotropic porous wall - drag increase and reduction. JOURNAL OF FLUID MECHANICS, 842, pp. 381–394. doi:10.1017/jfm.2018.152.
- Rosti, M.E., Omidyeganeh, M. and Pinelli, A. (2018). Passive control of the flow around unsteady aerofoils using a self-activated deployable flap. Journal of Turbulence, 19(3), pp. 204–228. doi:10.1080/14685248.2017.1314486.
- Rosti, M.E., Kamps, L., Bruecker, C., Omidyeganeh, M. and Pinelli, A. (2017). The PELskin project-part V: towards the control of the flow around aerofoils at high angle of attack using a self-activated deployable flap. Meccanica, 52(8), pp. 1811–1824. doi:10.1007/s11012-016-0524-x.
- Pinelli, A., Omidyeganeh, M., Brücker, C., Revell, A., Sarkar, A. and Alinovi, E. (2017). The PELskin project: part IV—control of bluff body wakes using hairy filaments. Meccanica, 52(7), pp. 1503–1514. doi:10.1007/s11012-016-0513-0.
- Rosti, M.E., Omidyeganeh, M. and Pinelli, A. (2016). Direct numerical simulation of the flow around an aerofoil in ramp-up motion. Physics of Fluids, 28(2). doi:10.1063/1.4941529.
- Favier, J., Revell, A. and Pinelli, A. (2016). Fluid Structure Interaction of Multiple Flapping Filaments Using Lattice Boltzmann and Immersed Boundary Methods. pp. 167–178. doi:10.1007/978-3-319-27386-0_10.
- Takeishi, K., Kawahara, G., Wakabayashi, H., Uhlmann, M. and Pinelli, A. (2015). Localized turbulence structures in transitional rectangular-duct flow. Journal of Fluid Mechanics, 782, pp. 368–379. doi:10.1017/jfm.2015.546.
- Valero-Lara, P., Igual, F.D., Prieto-Matías, M., Pinelli, A. and Favier, J. (2015). Accelerating fluid–solid simulations (Lattice-Boltzmann & Immersed-Boundary) on heterogeneous architectures. Journal of Computational Science, 10, pp. 249–261. doi:10.1016/j.jocs.2015.07.002.
- Favier, J., Revell, A. and Pinelli, A. (2015). Numerical study of flapping filaments in a uniform fluid flow. Journal of Fluids and Structures. doi:10.1016/j.jfluidstructs.2014.11.010.
- Skillen, A., Revell, A., Pinelli, A., Piomelli, U. and Favier, J. (2015). Flow over a Wing with Leading-Edge Undulations. AIAA Journal, 53(2), pp. 464–472. doi:10.2514/1.j053142.
- Toja-Silva, F., Favier, J. and Pinelli, A. (2014). Radial basis function (RBF)-based interpolation and spreading for the immersed boundary method. Computers & Fluids, 105, pp. 66–75. doi:10.1016/j.compfluid.2014.09.026.
- Valero-Lara, P., Pinelli, A. and Prieto-Matias, M. (2014). Fast finite difference Poisson solvers on heterogeneous architectures. Computer Physics Communications, 185(4), pp. 1265–1272. doi:10.1016/j.cpc.2013.12.026.
- Favier, J., Revell, A. and Pinelli, A. (2014). A Lattice Boltzmann–Immersed Boundary method to simulate the fluid interaction with moving and slender flexible objects. Journal of Computational Physics, 261, pp. 145–161. doi:10.1016/j.jcp.2013.12.052.
- Valero-Lara, P., Pinelli, A. and Prieto-Matias, M. (2014). Accelerating Solid-fluid Interaction using Lattice-boltzmann and Immersed Boundary Coupled Simulations on Heterogeneous Platforms. Procedia Computer Science, 29, pp. 50–61. doi:10.1016/j.procs.2014.05.005.
- Mawson, M., Lara, P.V., Favier, J., Pinelli, A. and Revell, A. (2013). Fast Fluid-structure Interaction Using Lattice Boltzmann and Immersed Boundary Methods. .
- Revell, A., Favier, J. and Pinelli, A. (2012). Interaction of multiple flapping filaments for cylinder wake modification using the Lattice Boltzmann Method. .
- Favier, J., Pinelli, A. and Piomelli, U. (2012). Control of the separated flow around an airfoil using a wavy leading edge inspired by humpback whale flippers. Comptes Rendus Mecanique, 340(1), pp. 107–114.
- Sekimoto, A., Kawahara, G., Sekiyama, K., Uhlmann, M. and Pinelli, A. (2011). Turbulence-and buoyancy-driven secondary flow in a horizontal square duct heated from below. Physics of fluids, 23, p. 75103.
- Zerroukat, M., Bowers, A.L., Cousins, B.R., Linke, A., Rebholz, L.G., Gillman, A. … Hill, D.J. (2010). 9011 A simple mass conserving semi-Lagrangian scheme for transport problems. . doi:10.1016/j.jcp.2010.08.017.
- Pinelli, A., Naqavi, I.Z. and Piomelli, U. (2010). Immersed Boundary Method for Generalised Finite Volume and Finite Difference Navier-Stokes Solvers. .
- Pinelli, A., Uhlmann, M., Sekimoto, A. and Kawahara, G. (2010). Reynolds number dependence of mean flow structure in square duct turbulence–CORRIGENDUM. Journal of Fluid Mechanics, 653, pp. 537–537.
- Pinelli, A., Uhlmann, M., Sekimoto, A. and Kawahara, G. (2010). Reynolds number dependence of mean flow structure in square duct turbulence. Journal of Fluid Mechanics, 644, p. 107.
- Pinelli, A., Naqavi, I.Z., Piomelli, U. and Favier, J. (2010). Immersed-boundary methods for general finite-difference and finite-volume Navier-Stokes solvers. J. Comput. Physics, 229, pp. 9073–9091.
- Dejoan, A., Santiago, J.L., Martilli, A., Martin, F. and Pinelli, A. (2010). Comparison between large-eddy simulation and Reynolds-averaged Navier–Stokes computations for the MUST field experiment. Part II: effects of incident wind angle deviation on the mean flow and plume dispersion. Boundary-layer meteorology, 135(1), pp. 133–150.
- Uhlmann, M., Kawahara, G. and Pinelli, A. (2010). Traveling-waves consistent with turbulence-driven secondary flow in a square duct. Physics of fluids, 22, p. 84102.
- Santiago, J.L., Dejoan, A., Martilli, A., Martin, F. and Pinelli, A. (2010). Comparison between large-eddy simulation and Reynolds-averaged Navier–Stokes computations for the MUST field experiment. Part I: Study of the flow for an incident wind directed perpendicularly to the front array of containers. Boundary-layer meteorology, 135(1), pp. 109–132.
- Sekimoto, A., Sekiyama, K., Kawahara, G., Uhlmann, M. and Pinelli, A. (2009). Buoyancy effects on low-Reynolds-number turbulent flow in a horizontal square duct. ICHMT DIGITAL LIBRARY ONLINE.
- Santiago, J.L., Dejoan, A., Martilli, A., Martín, F. and Pinelli, A. (2007). LES and RANS simulations of the MUST experiment. Study of incident wind direction effects on the flow and plume dispersion. .
- Uhlmann, M., Pinelli, A., Kawahara, G. and Sekimoto, A. (2007). Marginally turbulent flow in a square duct. Journal of Fluid Mechanics, 588, p. 153.
- Dejoan, A., Santiago, J.L., Pinelli, A. and Martilli, A. (2007). Comparison between LES and RANS computations for the study of contaminant dispersion in the MUST field experiment. .
- Garcia-Ybarra, P.L. and Pinelli, A. (2006). Turbulent channel flow concentration profile and wall deposition of a large Schmidt number passive scalar. Comptes Rendus Mécanique, 334(8), pp. 531–538.
- Pinelli, A., Uhlmann, M. and Kawahara, G. (2005). Minimal requirements for self-sustained turbulence in a square duct: a numerical investigation. Bulletin of the American Physical Society.
- Perez, J. and Pinelli, A. (2005). Numerical investigation of meso-scale structures using a two fluid model with non-Newtonian closure. Bulletin of the American Physical Society.
- Garcı́a-Ybarra, P.L. and Pinelli, A. (2004). Distribution and deposition of low stokes number particles in turbulent channel flow. Journal of Aerosol Science, 35, pp. 411–424.
- Pinelli, A. and García Ybarra, P.L. (2003). DNS of non-isothermal turbulent flows carrying low Stokes number particles. Journal of Aerosol Science, 34(suppl. 1).
- KAWAHARA, G., JIMENEZ, J., UHLMANN, M. and PINELLI, A. (2003). Linear Instability of a Corrugated Vortex Sheet. Riron Oyo Rikigaku Koenkai Koen Ronbunshu, 52, pp. 131–132.
- Uhlmann, M. and Pinelli, A. (2003). Two-dimensional thermal convection flow with variable viscosity and embedded boundaries. .
- Uhlmann, M., Pinelli, A. and García-Ybarra, P. (2003). Toward Direct Numerical Simulation of Reacting Fluidized Beds. .
- Kawahara, G., Jimenez, J., Uhlmann, M. and Pinelli, A. (2003). Linear instability of a corrugated vortex sheet-a model for streak instability. Journal of Fluid Mechanics, 483, pp. 315–342.
- JIMÉNEZ, J., UHLMANN, M., PINELLI, A. and KAWAHARA, G. (2001). Turbulent shear flow over active and passive porous surfaces. Journal of Fluid Mechanics, 442, pp. 89–117. doi:10.1017/s0022112001004888.
- Sanz, D., Muñoz, R., Armesto, L., Hontanon, E., Pinelli, A. and Espigares, M.M. (2001). Thermophoretic sampling of combustion particles from a fluidized bed combustor. Journal of Aerosol Science, 32, pp. 589–596.
- Uhlmann, M., Pinelli, A., Jimenez, J. and Kawahara, G. (2000). The influence of wall-porosity upon the near-wall turbulence dynamics. Advances in Turbulence VIII pp. 463–466.
- KAWAHARA, G., JIMENEZ, J., UHLMANN, M. and PINELLI, A. (2000). The Instability of Streaks and the Generation Mechanism of Streamwise Vorticity in Near-Wall Turbulence. Transactions of the Japan Society of Mechanical Engineers. B, 66(642), pp. 383–391.
- Jiménez, J. and Pinelli, A. (1999). The autonomous cycle of near-wall turbulence. Journal of Fluid Mechanics, 389(1), pp. 335–359.
- Kawahara, G., JimÃĐnez, J., Uhlmann, M. and Pinelli, A. (1998). The instability of streaks in near-wall turbulence. .
- JimÃĐnez, J. and Pinelli, A. (1997). Wall turbulence: How it works and how to damp it. .
- JimÃĐnez, J. and Pinelli, A. (1997). The autonomous near-wall turbulent cycle. .
- Jimenez, J. and Pinelli, A. (1997). Wall turbulence: How it works and how to damp it. AIAA paper pp. 97–2122.
- Pinelli, A., Vacca, A. and Quarteroni, A. (1997). A spectral multidomain method for the numerical simulation of turbulent flows. Journal of Computational Physics, 136(2), pp. 546–558.
- Pinelli, A. and Vacca, A. (1996). A Parallel Spectral Multi-Domain Solver Suitable for DNS and LES Numerical Simulation of Incompressible Flows. Universidad Politecnica de Madrid, Progress and Challenges in CFD Methods and Algorithms p(SEE N 96-36048 12-34).
- Pinelli, A., Couzy, W., Deville, M.O. and Benocci, C. (1996). An efficient iterative solution method for the Chebyshev collocation of advection-dominated transport problems. SIAM journal on scientific computing, 17(3), pp. 647–657.
- Pinelli, A. and Vacca, A. (1994). Chebyshev collocation method and multidomain decomposition for the incompressible Navier‐Stokes equations. International journal for numerical methods in fluids, 18(8), pp. 781–799.
- Pinelli, A., Benocci, C. and Deville, M. (1994). Chebyshev pseudospectral solution of advection-diffusion equations with mapped finite difference preconditioning. Journal of Computational Physics, 112(1), pp. 1–11.
- Pinelli, A., Benocci, C. and Deville, M. (1994). A Chebyshev collocation algorithm for the solution of advection—diffusion equations. Computer methods in applied mechanics and engineering, 116(1), pp. 201–210.
- Pinelli, A. and Vacca, A. (1993). A two dimensional Chebyshev collocated multi-domain algorithm for the incompressible Navier-Stokes equations. Von Karman Institute for Fluid Dynamics, Technical Note, (183).
- Benocci, C., Pinelli, A. and Abba, A. (1990). Large Eddy simulation of turbulence on an alliant FX computer. Supercomputer, 7(6), pp. 77–87.
- Benocci, C. and Pinelli, A. (1990). The role of the forcing term in the large eddy simulation of equilibrium channel flow. .
- Pinelli, A. and Benocci, C. (1989). Large eddy simulation of a fully turbulent plane channel flow. NASA STI/Recon Technical Report N, 90, p. 23693.
Contact details
Address
Northampton Square
London EC1V 0HB
United Kingdom
About
Overview
Professor Pinelli holds a BSc degree in Aeronautical Engineering from the Milan Polytechnic, a postgraduate diploma course from the von Karman Institute of fluid dynamics and a PhD degree in Applied Mathematics from the École Polytechnique Fédérale de Lausanne obtained in 1994. In 1995 he moved to the laboratory of numerical fluid mechanics of the School of Aeronautics of Madrid Polytechnic (ETSIA) having been granted a Marie Curie postdoctoral fellowship. During his period at the ETSIA he has collaborated with Prof. Jiménez in the study of wall turbulence using Direct Numerical Simulation. In 1999 he became an associate professor of applied mathematics at University Carlos III in Madrid.
Since 2001 he has led the Modeling and Computational Lab at CIEMAT (Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, Madrid) widening his research interests to the simulation of environmental flows, fluid structure interaction, lattice Boltzmann methods and immersed boundary techniques. Since 2004 he was also appointed as associate professor of applied mathematics at the faculty of mathematics of the Universidad Complutense in Madrid. In June 2013, Alfredo Pinelli was appointed as professor of fluid simulation at City University. Prof. Pinelli has participated in several National and European research projects and has extensive collaborations with other researchers in EU, Canada, Japan and US.
Qualifications
- PhD, École Polytechnique Fédérale de Lausanne, Switzerland, May 1991 – Dec 1994
- Diploma Course, Master in Fluid Mechanics, Von Karman Institute for Fluid Dynamics, Belgium, 1989
- Ingeniere Aeronautico, Graduate studies in aeronautical engineering, Politecnico di Milano, Italy, 1988
Postgraduate training
- Senior Researcher (Marie Curie Fellow), Technical University of Madrid, Madrid, Spain, Feb 1995 – Jul 2000
Administrative role
- Associate Dean for Research, School of Science and Technology (City University of London), Jan 2022 – Dec 2025
Employment
- Professor of Fluid Simulation, City, University of London, 2013 – present
- Associate Professor of Applied Mathematics, Complutense University of Madrid, 2004 – 2013
- Head of the Numerical Simulation Unit, Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas, 2000 – 2013
- Associate Professor, Carlos III University of Madrid, 1999 – 2004
- Senior Researcher (Marie Curie Fellow), Technical University of Madrid, Feb 1995 – Jul 2000
Memberships of committees
- Reviewer, EPSRC Peer Review College, Apr 2016 – present
- Member, Projects Evaluation Panel of the Spanish Ministry of Science, 2005 – 2013
Research
Research interests
- Direct numerical simulations
- Computational fluid dynamics
- Solid gas transport modeling
- High performance computing
- Immersed-boundary methods
- Fluid structure interaction
- Aerodynamics
Publications
Publications by category
Book
- Pinelli, A. (1994). Preconditioned Parallel Algorithms and Spectral Solutions for the Incompressible Navier-Stokes Equations. Ecole Polytechnique Fédérale de Lausanne.
Chapters (14)
- Suardi, C.A., Pinelli, A. and Omidyeganeh, M. (2020). The Effect of the Sweep Angle to the Turbulent Flow Past an Infinite Wing. ERCOFTAC Series (pp. 321–327). Springer International Publishing. ISBN 978-3-030-42821-1.
- Monti, A., Omidyeganeh, M. and Pinelli, A. (2019). Large-Eddy Simulation of an Open Channel Flow with Submerged Rigid Vegetation. Direct and Large-Eddy Simulation XI (pp. 571–577). Springer International Publishing. ISBN 978-3-030-04914-0.
- Shahab, M.F., Omidyeganeh, M. and Pinelli, A. (2019). DNS of Separated Low-Re Flow Around a Cambered Aerofoil. Direct and Large-Eddy Simulation XI (pp. 373–380). Springer International Publishing. ISBN 978-3-030-04914-0.
- Valero-Lara, P., Paz-Gallardo, A., Foster, E.L., Prieto-Matías, M., Pinelli, A. and Jansson, J. (2016). Multicore and Manycore. Innovative Research and Applications in Next-Generation High Performance Computing (pp. 107–158). IGI Global.
- Valero-Lara, P., Pinelli, A., Favier, J. and Prieto-Matías, M. (2012). Block Tridiagonal Solvers on Heterogeneous Architectures. 10th IEEE International Symposium on Parallel and Distributed Processing with Applications, ISPA 2012, Leganes, Madrid, Spain, July 10-13, 2012 (pp. 609–616). IEEE Computer Society. ISBN 978-1-4673-1631-6.
- Uhlmann, M. and Pinelli, A. (2010). Direct numerical simulation of vertical particulate channel flow in the turbulent regime. Proceedings of the 20th International Conference on Fluidized Bed Combustion (pp. 83–96). Springer Berlin Heidelberg. ISBN 3-642-02681-8.
- Uhlmann, M., Kawahara, G. and Pinelli, A. (2009). Travelling waves in a straight square duct. Advances in Turbulence XII (pp. 585–588). Springer Berlin Heidelberg. ISBN 3-642-03084-X.
- Sekimoto, A., Pinelli, A., Uhlmann, M. and Kawahara, G. (2009). The effect of coherent structures on the secondary flow in a square duct. Advances in Turbulence XII (pp. 329–332). Springer Berlin Heidelberg. ISBN 3-642-03084-X.
- Uhlmann, M., Pinelli, A., Sekimoto, A. and Kawahara, G. (2008). Coherent Structures in Marginally Turbulent Square Duct Flow. IUTAM Symposium on Computational Physics and New Perspectives in Turbulence (pp. 137–142). Springer Netherlands. ISBN 1-4020-6471-3.
- Uhlmann, M., Pinelli, A., Sekimoto, A. and Kawahara, G. (2007). Characterisation of Marginally Turbulent Square Duct Flow. Advances in Turbulence XI (pp. 41–43). Springer Berlin Heidelberg. ISBN 3-540-72603-9.
- Uhlmann, M. and Pinelli, A. (2006). Performance of various fluid-solid coupling methods for DNS of particulate flow. IUTAM Symposium on Computational Approaches to Multiphase Flow (pp. 215–223). Springer Netherlands. ISBN 1-4020-4976-5.
- Jimenez, J. and Pinelli, A. (1999). Dynamics of the Structures of Near Wall Turbulence. IUTAM Symposium on Simulation and Identification of Organized Structures in Flows (pp. 41–49). Springer Netherlands. ISBN 94-010-5944-6.
- Jiménez, J. and Pinelli, A. (1998). The role of coherent structure interactions in the regeneration of wall turbulence. Advances in Turbulence VII (pp. 155–158). Springer Netherlands. ISBN 94-010-6151-3.
- Pinelli, A. and Vacca, A. (1994). A new multi-domain algorithm for the spectral solution of the incompressible Navier-Stokes equations. Numerical methods for the Navier-Stokes equations (pp. 199–206). Vieweg+ Teubner Verlag. ISBN 3-528-07647-X.
Conference papers and proceedings (14)
- Kim, J.H., Choi, K.S., Lacagnina, G., Joseph, P., Hasheminejad, S.M., Chong, T.P. … Pinelli, A. (2019). Optimization of leading-edge undulation of a NACA 65(12)-10 aerofoil for noise reduction and aerodynamic enhancement. doi:10.18154/RWTH-CONV-239781
- Omidyeganeh, M. and Pinelli, A. (2015). Interaction of flexible filaments with the wake of cylinder at low Reynolds numbers.
- Omidyeganeh, M. and Pinelli, A. (2015). Interaction of flexible filaments with the wake of cylinder at low Reynolds numbers.
- Skillen, A., Revell, A., Favier, J., Pinelli, A. and Piomelli, U. (2013). Investigation of wing stall delay effect due to an undulating leading edge: An les study.
- Otsuki, T., Kawahara, G., Uhlmann, M. and Pinelli, A. (2012). Turbulent puffs in a horizontal square duct under stable temperature stratification.
- Wu, M., Favier, J. and Pinelli, A. (2011). A fast Lagrangian tracking method capturing finite-size effects in particulate flows.
- Sekimoto, A., Pinelli, A., Uhlmann, M. and Kawahara, G. (2009). The effect of coherent structures on the secondary flow in a square duct. doi:10.1007/978-3-642-03085-7_80
- Uhlmann, M., Kawahara, G. and Pinelli, A. (2009). Travelling waves in a straight square duct. doi:10.1007/978-3-642-03085-7_140
- Jiménez, J., Uhlmann, M., Kawahara, G. and Pinelli, A. (1999). Turbulent flow above a porous surface.
- Jimenez, J. and Pinelli, A. (1998). Turbulence near walls.
- Jiménez, J. and Pinelli, A. (1998). The autonomous near-wall turbulent region.
- Jiménez, J. and Pinelli, A. (1997). The near-wall turbulence regeneration cycle.
- De Pietro, G., Pinelli, A. and Vacca, A. (1996). A parallel implementation of a spectral multi-domain solver for incompressibile Navier-Stokes equations. doi:10.1016/b978-044482322-9/50085-2
- Pinelli, A., Benocci, C. and Deville, M. (1992). A preconditioning technique for Chebyshev collocated advection diffusion operators.