#### Boris Diskin

NIA Senior Research Fellow

Director of NIA Center for High Performance Aerospace Computing (HiPAC)

Tel: (757) 325-6700

Email: bdiskin@nianet.org

**Education**

- Ph.D., The Weizmann Institute of Science, Israel, 1998
- M.Sc. The Weizmann Institute of Science, Rehovot, Israel, 1993
- B. Sc./M.Sc Institute of Nuclear Power Engineering, Obninsk, Russia,1988

**Work Experience**

- Director of NIA Center for High Performance Aerospace Computing (HiPAC), 2014-present
- Research Fellow, NIA,2013-present
- Associate Research Fellow, NIA, 2008 — 2012:
- Senior Research Scientist, NIA, 2003-2008
- Research Associate Professor, UVA, Charlottesville, VA, 2008-2016
- Research Associate Professor, UCLA, Los Angeles, CA, 2005-2008
- Senior Staff Scientist, ICASE, NASA LaRC, Hampton, VA, 2002
- Staff Scientist, ICASE, NASA LaRC, Hampton, VA, 2000-2002
- Visiting Scientist, ICASE, NASA LaRC, Hampton, VA, 1998-2000
- Visiting Scientist, summer program, ICASE, NASA LaRC, 1996, 1997
- Research and Teaching Associate, Institute of Nuclear Power Engineering, Obninsk, Russia, 1988-1991

**Research Areas/Expertise**

- Adjoint-based sensitivity analysis, design optimization, and grid adaptation for unsteady aerodynamics and multidisciplinary applications
- Structured/unstructured grid discretizations and solvers
- Multigrid, convergence acceleration
- Multiscale simulations of turbulent flows and advanced materials

**Current Research**

**High-Fidelity Multidisciplinary Design Optimization of Rotorcraft (supported by NASA’s Revolutionary Vertical Lift Technology project, E. M. Lee-Rausch, Technical Monitor)**

A rotorcraft analysis involves many disciplines such as aerodynamics, acoustics, structural dynamics, flight mechanics, and others to account for complex interactions of unsteady fluids with highly flexible rotor blades. Computationally-intensive, high-fidelity discipline models are needed to accurately represent complex physics associated with rotorcraft aeromechanics. Multidisciplinary analysis and optimization (MDAO) become especially challenging in the presence of many design variables. Adjoint-based discretely consistent methodologies provide rigorous and efficient means to evaluate sensitivity of a desired objective functions and constraints computed using high-fidelity physics-based methods to many design variables. This project aims at developing a high-fidelity, adjoint-based, MDAO tool to aid in the design of efficient, low-noise rotorcraft configurations.

**Efficient Iterative Solutions for Turbulent Flows (supported by NASA’s Transformative Tools and Technologies project, W.K. Anderson, Technical Monitor)**

Advance solver technologies are used to accelerate convergence of current Reynolds averaged Navier–Stokes solvers and adjoints for steady and unsteady flow solutions. While significant efficiency gains in turbulent-flow solutions on unstructured grids have been recently obtained with agglomeration multigrid and methods based on Newton-Krylov approach, the computational efficiency is still insufficient, especially for unsteady turbulent flows on high density meshes with grid stretching. Current multi-year collaboration between NIA and the FUN3D group has already led to development and FUN3D implementation of several cutting-edge capabilities, which provide significant convergence acceleration on practical anisotropic grids. To further reduce computational time required for simulation of complex turbulent flows, improved relaxation schemes are needed to accelerate convergence and to provide an effective preconditioner for Krylov projection methods. Improved solver technologies are required to enable efficient solutions of multi-disciplinary problems including the adjoint-based multidisciplinary design and optimization. Additional technology is required to enable efficient solution of coupled systems on the modern computer architecture.

**Extending Capabilities and Improving Solutions of Cell-Center Unstructured-Grid Flow Solvers (supported by NASA’s Transformative Tools and Technologies project, Airspace Technology Demonstrations project, and CST Integrated Supersonic Airframe Technology project; N.T. Frink and M.J. Pandya, Technical Monitors)**

The cell-center unstructured-grid Navier-Stokes solver, USM3D, is used extensively to analyze aircraft configurations across a wide range of applications within NASA, other government agencies, industry, and academia. Recently, the USM3D framework has been extended to include mixed-element meshes that can handle a broader range of problems more efficiently. Accuracy of mixed-element solutions has been verified extensively. Various enhancements have been implemented in the mixed-element USM3D, including a scalable hierarchical adaptive nonlinear iteration method, and led to significant improvements in efficiency and robustness of USM3D solutions for turbulent flow simulations. Enabling steady and time-dependent applications with a variety of turbulence models at high Reynolds numbers to be simulated efficiently on massively parallel computers requires a long-term fundamental research activity. The principle purpose of this research is the determination and implementation of practical approaches that expand USM3D capabilities and improve accuracy, efficiency, scalability, and automation of turbulent-flow simulations of increased fidelity used for aerospace applications.

**Publications**

**Referred Journal Articles and Book Chapters**

- Wang L., Diskin B., Biedron R. T., Nielsen E. J., Sonneville V., and Bauchau O. A., “High-Fidelity Multidisciplinary Design Optimization Methodology with Application to Rotor Blades,”
*Journal of the American Helicopter Society*, accepted - Wang L., Diskin B., Biedron R. T., Nielsen E. J., and Bauchau O. A., “High-Fidelity Multidisciplinary Sensitivity Analysis and Design Optimization for Rotorcraft Applications,”
*AIAA Journal,*published online 12/27/2018,DOI:10.2514/1.J056587 - Callejo A., Bauchau O., and Diskin B., “Adjoint method for the sensitivity analysis of composite beam cross-sections,”
*Computers & Structures (2019*), 213:100-111; DOI: 10.1016/j.compstruc.2018.12.004 - Blonigan P. J., Wang Q., Nielsen E. J., and Diskin B., “Least Squares Shadowing Sensitivity Analysis ofChaotic Flow around a Two-Dimensional Airfoil,”
*AIAA Journal(2018),*56:658-672; DOI:10.2514/1.J055389 - Pandya, M. J., Diskin B., Thomas, J. L., and Frink N. T., “Assessment of USM3D Hierarchical Adaptive Nonlinear Method Preconditioners for Three-Dimensional Cases,”
*AIAA Journal*(2017) 55(10), pp. 3409-3424; DOI:2514/1.J055823 - Nielsen E.J. and Diskin B. “High-Performance Aerodynamic Computations for Aerospace Applications,”
*Parallel Computing*(2017), vol. 64, May 2017, pp. 20-32; DOI: 10.1016/j.parco.2017.02.004 - Diskin B. and Thomas J. L. “Introduction: Evaluation of RANS Solvers on Benchmark Aerodynamic Flows,”
*AIAA Journal*(2016), 54(9), pp. 2561-2562; DOI: 10.2514/1.J054642 - Diskin B., Thomas J. L., Rumsey C. L., and Schwöppe A. “Grid Convergence Study of RANS Solutions for Benchmark Flows in Two Dimensions,”
*AIAA Journal*(2016), 54(9),, pp. 2563-2588; DOI: 10.2514/1.J054555 - Pandya, M. J., Diskin B., Thomas, J. L., and Frink N. T., “Improved Convergence and Robustness of USM3D Solutions on Mixed Element Grids,”
*AIAA Journal*(2016), 54(9), pp. 2589-2610; DOI: 10.2514/1.J054545 - Rallabhandi S. K., Nielsen E. J., and Diskin B., “Sonic Boom Mitigation through Aircraft Design and Adjoint Methodology,”
*AIAA Journal of Aircraft*(2014), 51, pp. 502-510 - Nielsen E. J. and Diskin B., “Discrete Adjoint-Based Design Optimization of Unsteady Turbulent Flows on Dynamic Overset Unstructured Grids,”
*AIAA Journal*(2013), 51(6), pp. 1355-1373 - Schwöppe A. and Diskin B., “Accuracy of the Cell-Centered Grid Metric in the TAU-Code,” in “New Results in Numerical and Experimental Fluid Mechanics, in
*Notes on Numerical Fluid Mechanics and Multidisciplinary Design*(2013), 121, pp. 429-437, Springer, NY - Diskin B. and Thomas J. L., “Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations: Inviscid Fluxes,”
*AIAA Journal*(2011), 49(4), pp. 836-854 - Yamaleev N. K., Diskin B., and Pathak K., “Adjoint-Based Methodology for Anisotropic Mesh Adaptation,” in
*Computational Fluid Dynamics 2010*, pp. 571-576, 2011, Springer, NY. - Thomas J. L., Diskin B., and Nishikawa H., “A Critical Study of Agglomerated Multigrid Methods for Diffusion on Highly Stretched Grids,”
*Computers & Fluids*(2011),41(1), pp. 82-93 - Diskin B., Thomas J. L., Nielsen E. J., Nishikawa H., and White J. A., “Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations: Viscous Fluxes,”
*AIAA Journal*(2010), 48(7), pp. 1326-1338. - Nielsen E. J., Diskin B., and Yamaleev N. K., “Discrete adjoint-based design optimization of unsteady turbulent flows on dynamic unstructured grids,”
*AIAA Journal*(2010), 48(6), pp. 1195-1206 - Nishikawa H., Diskin B., and Thomas J. L., “A critical study of agglomerated multigrid methods for diffusion,”
*AIAA Journal*(2010), 48(4), pp. 839-847 - Yamaleev N. K., Diskin B., and Nielsen E. J.,“Local-in-time adjoint-based methods for design optimization of unsteady flows,”
*Journal of Computational Physics*(2010), 229(14), pp. 5394-5407 - Diskin B. and Thomas J. L. “Notes on accuracy of finite-volume discretization schemes on irregular grids,”
*Applied Numerical Mathematics*(2010),60(3), pp. 224-226 - Thomas J. L., Diskin B., and Ramsey C. L., “Towards Verification of Unstructured-Grid Solvers,”
*AIAA Journal*(2008), 46(12), pp. 3070-3079 - Liao W., Diskin B., Peng Y., Luo L.-S. , “Textbook-efficiency multigrid solver for three-dimensional unsteady compressible Navier–Stokes equations,”
*Journal of Computational Physics*(2008), 227(15), pp. 7160-7177 - Diskin B., Thomas J. L., and Mineck R. E., “On quantitative analysis methods for multigrid solutions,”
*SIAM Journal on Scientific Computing*(2005), 27(1), pp. 108-129 - Diskin B., and Harik V. M., “On Efficient Multigrid Methods for Materials Processing Flows with Small Particles,” in “Micromechanics and Nanoscale Effects, MEMS, Multi-Scale Materials and Micro-Flows” (V. M. Harik and L. S. Luo, eds.) pp. 119–144, Kluwer Academic Publishers, 2004
- Diskin B. and Thomas J. L., “New factorizable discretizations for the Euler equations,”
*SIAM Journal on Scientific Computing*(2003), 25(2), pp. 657-681 - Thomas J. L., Diskin B., and Brandt A., “Textbook Multigrid Efficiency for Fluid Simulations,”
*Annual Review of Fluid Mechanics*(2003), 35, pp. 317–340 - Thomas J. L., Diskin B., Brandt A., and South J. C., “General Framework for Achieving Textbook Multigrid Efficiency: Quasi-1-D Euler Example,” in “Frontiers of Computational Fluid Dynamics — 2002,” (D. A. Caughey and M. M. Hafez, eds.), World Scientific, Singapore, 2002
- Thomas J. L., Diskin B., and Brandt A., “Textbook Multigrid Efficiency for the Incompressible Navier-Stokes Equations: High Reynolds Number Wakes and Boundary Layers,”
*Computers & Fluids*(2001), 30(7-8), pp. 853-874 - Llorente I. M., Prieto M., and Diskin B., “A Parallel Multigrid Solver for 3D Convection and Convection-Diffusion Problems,”
*Parallel Computing*(2001), 27, pp. 1715-1741 - Diskin B., “Efficient Multigrid Methods for Solving Upwind-Biased Discretizations of the Convection Equation,”
*Applied Mathematics and Computation*(2001), 123(3), pp. 343-379 - Diskin B. and Thomas J. L., “Half-Space Analysis of the Defect-Correction Method for Fromm Discretization of Convection,”
*SIAM Journal on Scientific Computing*(2000), 22(2), pp. 633-655 - Llorente I. M., Diskin B., and Melson N. D., “Alternating Plan Smoothers for Multiblock Grids,”
*SIAM Journal on Scientific Computing*(2000), 22(1), pp. 218-242 - Brandt A. and Diskin B., “Multigrid Solvers for Nonaligned Sonic Flows,”
*SIAM Journal on Scientific Computing*(2000), 21(2), pp. 473-501 - Brandt A. and Diskin B., “Multigrid Solvers for Nonaligned Sonic Flows: the Constant Coefficient Case,”
*Computers & Fluids*(1999), 28(4-5), pp. 511-549 - Diskin B., “Multigrid Algorithm with Conditional Coarsening for the Nonaligned Sonic Flow,”
*Electronic Trans. Num. An*., v. 6, pp. 106-119, 1997 - Brandt A. and Diskin B., “Multigrid Solvers on Decomposed Domains,” Domain Decomposition Methods in Science and Engineering, (A. Quarteroni, J. Periaux, Yu. A. Kuznetsov, and O.Widlund, eds.), in
*Math*., v. 157, pp. 135-155., Amer. Math. Soc., Providence, RI, 1994

*Referred Conference Articles*

- Zhou Y., Diskin B., Gauger N.R., Pardue J., Chernikov A., Tsolakis C., Drakopoulos F., and Chrisochoides N., “Hybrid RANS/LES Simulation of Vortex Breakdown Over a Delta Wing,” CFD conference, Aviation-2019, June 17-21, Dallas TX
- Callejo A., Bauchau O., Diskin B., and Wang L., “High-performance sensitivity analysis of rotor blade cross-sections,” AHS Forum 75, Philadelphia, PA, May 13-16, 2019
- Wang L., Diskin B., Lopes L.V., Nielsen E.J., Lee-Rausch E.J., and Biedron R.T., “High-Fidelity Multidisciplinary Design Optimization of Low-Noise Rotorcraft,” AHS Forum 75, Philadelphia, PA, May 13-16, 2019
- Pandya M. J., Jespersen D. C., Diskin B., Thomas J. L., and Frink N. T., “Accuracy, Scalability, and Efficiency of Mixed-Element USM3D for Benchmark Three-Dimensional Flows,” AIAA-2019-2333, SciTech-2019, San Diego, CA, Jan. 2019
- Wang L., Diskin B., Biedron R. T., Nielsen E. J., Sonneville V., and Bauchau O. , “High-Fidelity Multidisciplinary Sensitivity Analysis Framework for Rotorcraft Optimization,” AIAA-2019-1699, SciTech-2019, San Diego, CA, Jan. 2019
- Wang L., Diskin B., Biedron R. T., Nielsen E. J., Sonneville V., and Bauchau O. A., “High-Fidelity Multidisciplinary Design Optimization Methodology with Application to Rotor Blades,” AHS International Technical Meeting, Aeromechanics Design for Transformative Vertical Flight, San Francisco, CA, January 16-19, 2018
- Diskin B., Anderson W. K., Pandya M. J., Rumsey C. L., Lui Y., and Nishikawa H., “Grid Convergence of Three-Dimensional Benchmark Turbulent Flows,”AIAA-2018-1102, invited paper, SciTech-2018, Kissimmee, FL, Jan. 2018
- Nishikawa H. and Diskin B., “Customized Grid Generation and Processing for Benchmark Three-Dimensional Flows,”invited paper,”AIAA-2018-1101, SciTech-2018, Kissimmee, FL, Jan. 2018
- Callejo A., Bauchau O., Diskin B., and Wang L., “Sensitivity analysis of beam cross-section stiffness using adjoint method” , IDETC-67846, ASME 2017, International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Cleveland, OH, August 2017
- Ordaz I.,Nielsen E. J., Rallabhandi S. K., and Diskin B., “Mitigation of Engine Inlet Distortion through Adjoint-Based Design,” AIAA-2017-3410, Aviation-2017, Denver, CO, June 2017
- Blonigan J.,Wang Q.,Nielsen E. J., and DiskinB., “A non-intrusive algorithm for sensitivity analysis of chaotic flow simulations,” AIAA-2017-0532, SciTech-2017, Grapevine, TX, Jan. 2017
- Wang L., Diskin B., Biedron R. T., Nielsen E. J., and Bauchau O. A. “Sensitivity Analysis of Multidisciplinary Rotorcraft Simulations,” AIAA-2017-1670, Invited paper SciTech-2017, Grapevine, TX, Jan. 2017
- Diskin B., Thomas J. L., Rumsey C. L., and Pandya M. J., “Reference Solutions for Benchmark Three Dimensional Turbulent Flows,” AIAA-2016-0858, Invited paper SciTech-2016, San Diego, CA, Jan. 2016
- Pandya M. J., Diskin B., Thomas J. L., and Frink N. T., “Assessment of Preconditioner for a USM3D Hierarchical Adaptive Nonlinear Iteration Method (HANIM),” AIAA-2016-0860, Invited paper SciTech-2016, San Diego, CA, Jan. 2016
- Blonigan P. J., Wang Q., Nielsen E. J., and Diskin B., “Least Squares Shadowing Sensitivity Analysis of Chaotic Flow around a Two-Dimensional Airfoil,” AIAA-2016-0296, SciTech-2016, San Diego, CA, Jan. 2016
- Blonigan P. J., Wang Q., Nielsen E. J., and Diskin B., “Sensitivity Analysis of Chaotic Flow around Two-Dimensional Airfoil,” 68th Annual Meeting of the APS Division of Fluid Dynamics, Nov. 22-24, 2015Boston, MA
- Diskin B., Thomas J. L., Rumsey C. L., and Schwöppe A. “Grid Convergence for Turbulent Flows,” AIAA-2015-1746, Invited paper; SciTech-2015, Kissimmee, Florida, FL, Jan 2015
- Pandya M. J., Diskin B., Thomas, J. L., and Frink N. T., “Improved Convergence and Robustness of USM3D Solutions on Mixed Element Grids,” AIAA-2015-1747, Invited paper; SciTech-2015, Kissimmee, Florida, FL, Jan 2015
- Diskin B. and Nishikawa H., “Evaluation of Multigrid Solutions for Turbulent Flows,” AIAA-2014-0082, Invited paper; SciTech-2014, National Harbor, MD, Jan 2014
- Nishikawa H., Diskin B., Thomas J. L., and Hammond D. H., “Recent Advances in Agglomerated Multigrid,” AIAA-2013-0863; 51
^{st}AIAA Aerospace Sciences Meeting, Grapevine, TX, Jan 2013 - Rallabhandi S. K., Nielsen E. J. and Diskin B., “Sonic Boom Mitigation through Aircraft Design and Adjoint Methodology,” AIAA-2012-3220, 42nd AIAA Fluid Dynamics Conference and Exhibit, New Orleans, LA, June 2012
- Nielsen E. J. and Diskin B., “Discrete Adjoint-Based Design Optimization of Unsteady Turbulent Flows on Dynamic Overset Unstructured Grids,” AIAA-2012-0554; 50th AIAA Aerospace Sciences Meeting, Nashville, TN, Jan 2012
- Diskin B. and Thomas J. L., “Effects of mesh irregularity on accuracy of finite-volume schemes,” invited paper, AIAA-2012-0609; 50
^{th}AIAA Aerospace Sciences Meeting, Nashville, TN, Jan 2012 - Diskin B. and Thomas J. L., “Convergence of defect-correction and multigrid iterations for inviscid flows,” AIAA-2011-3235; 20
^{th}AIAA Computational Fluid Dynamics Conference, Honolulu, Hawaii, June 2011 - Diskin B. and Yamaleev N. K., “Grid Adaptation Using Adjoint-Based Error Minimization,” AIAA-2011-3986; 20
^{th}AIAA Computational Fluid Dynamics Conference, Honolulu, Hawaii, June 2011 - Nishikawa H., Diskin B., and Thomas J. L., “Development and Application of Parallel Agglomerated Multigrid Method for Complex Geometries,” AIAA-2011-3232; 20
^{th}AIAA Computational Fluid Dynamics Conference, Honolulu, Hawaii, June 2011 - Schwöppe A. and Diskin B. “Genauigkeit der zell-zentrierten Netz-Metrik im TAU-Code” (in German), DLR STAB-Symposium, Berlin, Germany, Nov. 2010.
- Nishikawa H., Diskin B., and Thomas J. L., “Development and Application of Agglomerated Multigrid Methods for Complex Geometries,” AIAA-2010-4731; 40
^{th}AIAA Fluid Dynamics Conference and Exhibit, Chicago, IL, June 2010 - Yamaleev N. K., Diskin B., and Pathak K., “Error Minimization via Adjoint-Based Anisotropic Grid Adaptation” AIAA-2010-4436; 40
^{th }AIAA Fluid Dynamics Conference and Exhibit, Chicago, IL, June 2010 - Yamaleev N. K., Diskin B., and Pathak K., “Adjoint-Based Methodology for Anisotropic Mesh Adaptation,” 6th International Conference on Computational Fluid Dynamics, St. Petersburg, Russia, July 2010
- Diskin B. and Thomas J. L., “Comparison of Cell-Centered and Node-Centered Unstructured Finite-Volume Discretizations: Inviscid Fluxes,” AIAA-2010-1079; 48
^{th}AIAA Aerospace Sciences Meeting, Orlando, FL, Jan 2010 - Nielsen E. J., Diskin B., and Yamaleev N. K., “Discrete Adjoint-Based Design Optimization of Unsteady Turbulent Flows on Dynamic Unstructured Grids,” AIAA-2009-3802; 19
^{th}AIAA Computational Fluid Dynamics Conference, San Antonio, TX, June 2009 - Nishikawa H., Diskin B., and Thomas J. L., “A Critical Study of Agglomerated Multigrid Methods for Diffusion,” AIAA-2009-4138; 19
^{th}AIAA Computational Fluid Dynamics Conference, San Antonio, TX, June 2009 - Diskin B., Thomas J. L., Nielsen E. J., Nishikawa H., and White J. A., “Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations. Part I: Viscous Fluxes,” AIAA-2009-597; 47
^{th}AIAA Aerospace Sciences Meeting Orlando, Florida, Jan 2009 - Yamaleev N. K., Diskin B., and Nielsen E. J., “Locally Optimal Control/Design Strategies for Unsteady Compressible Flows,” AIAA-2009-1169; 47
^{th}AIAA Aerospace Sciences Meeting, Orlando, Florida, Jan 2009 - Yamaleev N. K., Diskin B., and Nielsen E. J., “Adjoint-based Methodology for Time-Dependent Optimization,” AIAA-2008-5857, 12
^{th}AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Victoria, BC, Canada, Sept 2008 - Thomas J. L., Diskin B., and Rumsey C. L., “Towards Verification of Unstructured-Grid Solvers,” AIAA-2008-666, 46
^{th}AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, Jan 2008. - Diskin B., Liao W., and Luo Li-Shi., “Textbook Efficient Multigrid Solvers for Three-Dimensional Unsteady Compressible Navier-Stokes Equations,” AIAA-2007-4328, 18
^{th}AIAA Computational Fluid Dynamics Conference, Miami, FL, June 2007. - Diskin B. and Thomas J. L., “Accuracy of Mixed-Element Finite Volume Discretization Schemes,” SIAM Conference on Computational Science and Engineering, Costa Mesa, CA, Feb 2007.
- Diskin B., Harik V. M., Ounaies Z., and Brandt A., “Systematic Upscaling Models for Multiphysics Simulations of In-Field Processing of Polymer Nanocomposites,” American Society for Composites 20th Annual Technical Conference, Philadelphia, PA, Sept, 2005.
- Mineck R. E., Thomas J. L., and Diskin B., “Analysis Tools for CFD Multigrid Solvers,” AIAA Paper 2004-2532, 34
^{th}AIAA Fluid Dynamics Conference, Portland, OR, June 2004. - Brandt A., Diskin B. and Thomas J. L., “Textbook Multigrid Efficiency for Computational Fluid Dynamics Simulations,” AIAA Paper 2001-2570, invited paper for 15
^{th}AIAA CFD Conference, Anaheim, CA, June, 2001. - Diskin B. and Thomas J. L., “Distributed Relaxation for Conservative Discretizations,” AIAA Paper 2001-2571, 15
^{th}AIAA CFD Conference, Anaheim, CA, June, 2001. - Diskin B., Llorente I. M., and Santiago R., “An Efficient Highly Parallel Multigrid Method for the Advection Operator,” The International Parallel CFD 2000 Conference, Trondheim, Norway, May 2000
- Thomas J. L., Diskin B., and Brandt A., “Distributed Relaxation Multigrid and Defect Correction Applied to the Compressible Navier-Stokes Equations,” AIAA Paper 99-3334, 14
^{th}AIAA CFD Conference, Norfolk, VA, July, 1999. - Llorente I. M., Diskin B., and Melson N. D., “Parallel Multigrid with Blockwise Smoothers for Multiblock Grids,” Parallel CFD’99, Williamsburg, Virginia, 1999.

*Technical Reports*

- Liu Y., Anusonti-Inthra P., and Diskin B., “Development and Validation of a Multidisciplinary Tool for Accurate and Efficient Rotorcraft Noise Prediction (MUTE),” NASA/CR-2011-217057, February 2011.
- Diskin B. and Thomas J. L., “Accuracy of Gradient Reconstruction on Grids with High Aspect Ratio,” NIA Report 2008-12.
- Diskin B. and Thomas J. L., “Accuracy Analysis for Mixed-Element Finite-Volume Discretization Schemes,” NIA Report 2007-08.
- Diskin B., Thomas J. L., and Mineck R. E., “Textbook multigrid efficiency for leading edge stagnation,” NASA/TM-2004-213037, May 2004
- Diskin B., and Harik V. M., “On Efficient Multigrid Methods for Materials Processing Flows with Small Particles,” NIA Report 2004-01.
- Brandt, A., Diskin B., and Thomas J. L., “Recent Advances in Achieving Textbook Multigrid Efficiency for Computational Fluid Dynamics Simulations,” ICASE Report 2002-16, May 2002.
- Diskin B. and Thomas J. L., “Analysis of boundary conditions for factorizable discretizations of the Euler equations,” ICASE Report 2002-13, May 2002.
- Diskin B. and Thomas J. L., “New factorizable discretizations for the Euler equations,” ICASE Report 2002-6, April 2002.
- Llorente I. M., Prieto M., and Diskin B., “An Efficient Parallel Multigrid Solver for 3-D Convection-Dominated Problems,” ICASE Report 2000-29, August 2000.
- Thomas J. L., Diskin B., Brandt A., and South J. C., “General Framework for Achieving Textbook Multigrid Efficiency: 1-D Euler Example,” ICASE Report 2000-30, August 2000.
- Thomas J. L., Diskin B., and Brandt A., “Textbook Multigrid Efficiency for the Incompressible Navier-Stokes Equations: High Reynolds Number Wakes and Boundary Layers,” ICASE Report 99-51, December 1999.
- Diskin B., “Solving Upwind-Biased Discretizations II: Multigrid Solver Using Semicoarsening,” ICASE Report 99-25, July 1999.
- Llorente I. M., Diskin B., and Melson N. D., “Plane Smoothers for Multiblock Grids: Computational Aspects,” ICASE Report 99-17, May 1999.
- Diskin B. and Thomas J. L., “Solving Upwind-Biased Discretizations: Defect-Correction Iterations,” ICASE Report 99-14, March 1999.