Schemes by Leonard - structured grids
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SHARP - Simple High Accuracy Resolution Program
B. P. Leonard. Simple high-accuracy resolution program for convective modelling of discontinuities.
International Journal for Numerical Methods in Fluids, 8:1291–1318, 1988.
ULTIMATE - Universal Limiter for Transport Interpolation Modelling of the Advective Transport Equation
B. P. Leonard. Universal limiter for transient interpolation modelling of the advective transport equations. Technical Memorandum TM-100916 ICOMP-88-11, NASA, 1988.
ULTIMATE-QUICKEST
B. P. Leonard. The ULTIMATE conservative difference scheme applied to unsteady one–dimensional advection. Computer Methods in Applied Mechanics and Engineering, 88:17–74, June 1991.
ULTRA-SHARP : Universal Limiter for Thight Resolution and Accuracy in combination with the Simple High-Accuracy Resolution Program (also ULTRA-QUICK)
B. P. Leonard and S. Mokhtari. Beyond first-order upwinding: the ULTRA-SHARP alternative for non-oscillatory steady state simulation of convection. International Journal of Numerical Methods in Engineering, 30:729–766, 1990.
B. P. Leonard and S. Mokhtari. ULTRA-SHARP nonoscillatory convection schemes for highspeed steady multidimensional flow. Technical Memorandum TM-102568 ICOMP-90-12, NASA, April 1990.
UTOPIA - Uniformly Third Order Polynomial Interpolation Algorithm
B. P. Leonard, M. K. MacVean, and A. P. Lock.
Positivity-preserving numerical schemes for multidimensional advection. Technical Memorandum TM-106055 ICOMP-93-05, NASA, March 1993.
NIRVANA - Non-oscilatory Integrally Reconstructed Volume-Avaraged Numerical Advection scheme
B. P. Leonard, A. P. Lock, and M. K. MacVean. The NIRVANA scheme applied to one–dimensional advection. International Journal of Numerical Methods in Heat and Fluid Flow, 5:341–377, 1995.
ENIGMATIC - Extended Numerical Integration for Genuinely Multidimensional Advective Transport Insuring Conservation
B. P. Leonard, A. P. Lock, and M. K. MacVean.
Extended numerical integration for genuinely multidimensional advective transport insuring conservation.
In C. Taylor and P. Durbetaki, editors, Numerical Methods in Laminar and Turbulent Flow, volume 9, pages 1–12. Pineridge Press, 1995.
MACHO : Multidimensional Advective - Conservative Hybrid Operator
B. P. Leonard, A. P. Lock, and M. K. MacVean.
Conservative explicit unrestricted-timestep multidimensional constancy-preserving advection schemes. Monthly Weather Review, 124:2588–2606, November 1996.
COSMIC : Conservative Operator Splitting for Multidimensions with Internal Constancy
B. P. Leonard, A. P. Lock, and M. K. MacVean. Conservative explicit unrestricted-timestep multidimensional constancy-preserving advection schemes. Monthly Weather Review, 124:2588–2606, November 1996.
QUICKEST - Quadratic Upstream Interpolation for Convective Kinematics with Estimated Streaming Terms
B. P. Leonard. Elliptic systems: Finite-difference method IV. In W. J. Minkowycz, E. M. Sparrow, G. E. Schneider, and R. H. Pletcher, editors, Handbook of Numerical Heat Transfer, pages 347–378. Wiley, New York, 1988.
AQUATIC - Adjusted Quadratic Upstream Algorithm for Transient Incompressible Convection
B. P. Leonard A survey of finite differences with upwinding for numerical modelling of the incompressible convective diffusion equation.
In C. Taylor and K. Morgan, editors, Computational Methods in Transient and Turbulent Flow, pages 1–35. Pineridge Press, Swansea, 1981.
EXQUISITE - Exponential or Quadratic Upstream Interpolation for Solution of the Incompressible Transport Equation
B. P. Leonard.
A survey of finite differences with upwinding for numerical modelling of the incompressible convective diffusion equation.
In C. Taylor and K. Morgan, editors, Computational Methods in Transient and Turbulent Flow, pages 1–35. Pineridge Press, Swansea, 1981.
EULER-QUICK
B.P.Leonard
Locally modified QUICK scheme for highly convective 2D and 3D flows,
in: Proc. 5th International Conf. on Numerical Methods in Laminar and Turbulent Flow, Montreal (1987) 35-47.
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