A bounded upwinding scheme for computing convection-dominated transport problems

[1]  Long Lee,et al.  A class of high-resolution algorithms for incompressible flows , 2010 .

[2]  William F. Godoy,et al.  On the use of flux limiters in the discrete ordinates method for 3D radiation calculations in absorbing and scattering media , 2010, J. Comput. Phys..

[3]  Manuel Torrilhon,et al.  Compact third-order limiter functions for finite volume methods , 2009, J. Comput. Phys..

[4]  Rafael Alves Bonfim de Queiroz,et al.  Assessment of a high‐order finite difference upwind scheme for the simulation of convection–diffusion problems , 2009 .

[5]  Thomas L. Jackson,et al.  A high-order incompressible flow solver with WENO , 2009, J. Comput. Phys..

[6]  Silvia Bertoluzza,et al.  Numerical Solutions of Partial Differential Equations , 2008 .

[7]  V. G. Ferreira,et al.  The MAC method , 2008 .

[8]  C. Corre,et al.  High-order residual-based compact schemes for advection–diffusion problems , 2008 .

[9]  Nail K. Yamaleev,et al.  Third-order Energy Stable WENO scheme , 2008, J. Comput. Phys..

[10]  H. Deconinck,et al.  Design principles for bounded higher-order convection schemes - a unified approach , 2007, J. Comput. Phys..

[11]  Remy Baraille,et al.  The HYCOM (HYbrid Coordinate Ocean Model) data assimilative system , 2007 .

[12]  E. D. V. Bigarella,et al.  Advanced Eddy-Viscosity and Reynolds-Stress Turbulence Model Simulations of Aerospace Applications , 2006 .

[13]  C. Berthon,et al.  Stability of the MUSCL Schemes for the Euler Equations , 2005 .

[14]  Gerald Warnecke,et al.  A Runge–Kutta discontinuous Galerkin method for the Euler equations , 2005 .

[15]  Bram van Leer,et al.  Upwind and High-Resolution Methods for Compressible Flow: From Donor Cell to Residual-Distribution Schemes , 2003 .

[16]  F. Pinho,et al.  A convergent and universally bounded interpolation scheme for the treatment of advection , 2003 .

[17]  N. Phan-Thien,et al.  Upwinding with deferred correction (UPDC): an effective implementation of higher-order convection schemes for implicit finite volume methods , 2002 .

[18]  Chi-Wang Shu,et al.  Numerical Comparison of WENO Finite Volume and Runge–Kutta Discontinuous Galerkin Methods , 2001, J. Sci. Comput..

[19]  Pilar García-Navarro,et al.  Flux difference splitting and the balancing of source terms and flux gradients , 2000 .

[20]  Chi-Wang Shu,et al.  Monotonicity Preserving Weighted Essentially Non-oscillatory Schemes with Increasingly High Order of Accuracy , 2000 .

[21]  Ryoichi S. Amano,et al.  On a higher-order bounded discretization scheme , 2000 .

[22]  A. Castello F.,et al.  Freeflow: an integrated simulation system for three-dimensional free surface flows , 2000 .

[23]  H. Kamath,et al.  Accuracy Assessment of Upwind Algorithms for Steady-state Computations , 1998 .

[24]  Serge Piperno,et al.  Criteria for the design of limiters yielding efficient high resolution TVD schemes , 1998 .

[25]  George Bergeles,et al.  DEVELOPMENT AND ASSESSMENT OF A VARIABLE-ORDER NON-OSCILLATORY SCHEME FOR CONVECTION TERM DISCRETIZATION , 1998 .

[26]  A. J. Baker,et al.  Numerical simulations of laminar flow over a 3D backward‐facing step , 1997 .

[27]  Philip L. Roe,et al.  A Well-Behaved TVD Limiter for High-Resolution Calculations of Unsteady Flow , 1997 .

[28]  E. Toro.  Riemann Solvers and Numerical Methods for Fluid Dynamics , 1997 .

[29]  Ravi Samtaney,et al.  On initial‐value and self‐similar solutions of the compressible Euler equations , 1996 .

[30]  Chi-Wang Shu,et al.  Efficient Implementation of Weighted ENO Schemes , 1995 .

[31]  Marcel Zijlema,et al.  ON THE CONSTRUCTION OF A THIRD‐ORDER ACCURATE MONOTONE CONVECTION SCHEME WITH APPLICATION TO TURBULENT FLOWS IN GENERAL DOMAINS , 1996 .

[32]  Mann Cho,et al.  A comparison of higher-order bounded convection schemes , 1995 .

[33]  James P. Collins,et al.  Numerical Solution of the Riemann Problem for Two-Dimensional Gas Dynamics , 1993, SIAM J. Sci. Comput..

[34]  J. Zhu,et al.  On the higher-order bounded discretization schemes for finite volume computations of incompressible flows , 1992 .

[35]  C. Chieng,et al.  Characteristic‐based flux limiters of an essentially third‐order flux‐splitting method for hyperbolic conservation laws , 1991 .

[36]  Achi Brandt,et al.  Inadequacy of first-order upwind difference schemes for some recirculating flows , 1991 .

[37]  B. P. Leonard,et al.  A stable and accurate convective modelling procedure based on quadratic upstream interpolation , 1990 .

[38]  Hwar-Ching Ku,et al.  A pseudospectral matrix element method for solution of three-dimensional incompressible flows and its parallel implementation , 1989 .

[39]  Urmila Ghia,et al.  Analysis of incompressible massively separated viscous flows using unsteady Navier-Stokes equations , 1989 .

[40]  S. Osher,et al.  Efficient implementation of essentially non-oscillatory shock-capturing schemes,II , 1989 .

[41]  ShuChi-Wang,et al.  Efficient implementation of essentially non-oscillatory shock-capturing schemes, II , 1989 .

[42]  B. P. Leonard,et al.  Simple high-accuracy resolution program for convective modelling of discontinuities , 1988 .

[43]  B. P. Leonard.  Universal Limiter for Transient Interpolation Modeling of the Advective Transport Equations : The ULTIMATE Conservative Difference Scheme , 1988 .

[44]  Barry Koren,et al.  Upwind discretization of the steady Navier-Stokes equations , 1988 .

[45]  P. Gaskell,et al.  Curvature‐compensated convective transport: SMART, A new boundedness‐ preserving transport algorithm , 1988 .

[46]  Randall J. LeVeque,et al.  A geometric approach to high resolution TVD schemes , 1988 .

[47]  R. Pielke,et al.  The forward-in-time upstream advection scheme:extension to higher orders , 1987 .

[48]  S. Osher.  Convergence of Generalized MUSCL Schemes , 1985 .

[49]  Philip L. Roe,et al.  Efficient construction and utilisation of approximate riemann solutions , 1985 .

[50]  J. W. Boerstoel,et al.  Test Cases for Inviscid Flow Field Methods. , 1985 .

[51]  A. Jameson,et al.  Finite volume solution of the two-dimensional Euler equations on a regular triangular mesh , 1985 .

[52]  P. Sweby.  High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws , 1984 .

[53]  B. Armaly,et al.  Experimental and theoretical investigation of backward-facing step flow , 1983, Journal of Fluid Mechanics.

[54]  A. G. Hutton,et al.  THE NUMERICAL TREATMENT OF ADVECTION: A PERFORMANCE COMPARISON OF CURRENT METHODS , 1982 .

[55]  G. D. van Albada,et al.  A comparative study of computational methods in cosmic gas dynamics , 1982 .

[56]  J. Strikwerda.  Upwind Differencing, False Scaling, and Nonphysical Solutions to the Driven Cavity Problem , 1981 .

[57]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method , 1979 .

[58]  R. F. Warming,et al.  Upwind Second-Order Difference Schemes and Applications in Aerodynamic Flows , 1976 .

[59]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme. II. Monotonicity and conservation combined in a second-order scheme , 1974 .

[60]  D. Spalding.  A novel finite difference formulation for differential expressions involving both first and second derivatives , 1972 .

[61]  A. Chorin.  Numerical solution of the Navier-Stokes equations , 1968 .

[62]  R. Courant,et al.  On the solution of nonlinear hyperbolic differential equations by finite differences , 1952 .

[63]  Geo.,et al.  Compact third-order limiter functions for finite volume methods , 2009, J. Comput. Phys..

[64]  E. D. V. Bigarella,et al.  Advanced turbulence modelling for complex aerospace applications , 2007 .

[65]  R. LeVeque.  Finite Volume Methods for Hyperbolic Problems: Characteristics and Riemann Problems for Linear Hyperbolic Equations , 2002 .

[66]  Chao-An Lin,et al.  Adaptive QUICK-Based scheme to approximate convective transport , 2000 .

[67]  M. Alvesa,et al.  Effect of a high-resolution differencing scheme on finite-volume predictions of viscoelastic flows , 2000 .

[68]  G. F. Naterer,et al.  Constructing an Entropy-Stable Upwind Scheme for Compressible Fluid Flow Computations , 1999 .

[69]  Luigi Martinelli,et al.  Mesh Refinement and Modeling Errors in Flow Simulation , 1998 .

[70]  Chao-An Lin,et al.  Simple High-Order Bounded Convection Scheme to Model Discontinuities , 1997 .

[71]  Lars Davidson,et al.  Transonic inviscid/turbulent airfoil flow simulations using a pressure based method with high order schemes , 1995 .

[72]  최영돈,et al.  수치해의 정확성과 안정성이 보장되는 대류항 미분법 개선에 관한 연구 ( A Study on the Improvement of the Convective Differencing Scheme for the High - Accuracy and Stable Resolution of the Numerical Solution ) , 1992 .

[73]  Timothy J. Barth,et al.  The design and application of upwind schemes on unstructured meshes , 1989 .

[74]  T. H. Pulliam,et al.  Euler computations of AGARD Working Group 07 airfoil test cases , 1985 .

[75]  S. Osher,et al.  High resolution applications of the Osher upwind scheme for the Euler equations , 1983 .

[76]  B. Vanleer,et al.  Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection , 1977 .

[77]  F. Harlow,et al.  Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with Free Surface , 1965 .

[78]  J. Burgers.  A mathematical model illustrating the theory of turbulence , 1948 .