CONTROLLED VARIATION SCHEME IN A SEQUENTIAL SOLVER FOR RECIRCULATING FLOWS, PART I: THEORY AND FORMULATION

REFERENCES

• A. Harten , High Resolution Schemes for Hyperbolic Conservation Laws , J. Comp. Phys. , vol. 49 , pp. 357 – 393 , 1983 .
   Web of Science ®Google Scholar
• A. Harten , On a Class of High Resolution Total-Variation-Stable Finite-Difference Schemes , SLAM J. Numer. Anal. , vol. 21 , no. 1 , pp. 1 – 23 , 1984 .
   Web of Science ®Google Scholar
• H. C. Yee , R. F. Warming , and A. Harten , Implicit Total Variation Diminishing (TVD) Schemes for Steady-State Calculations , J, Comp. Phys. , vol. 57 , pp. 327 – 360 , 1985 .
   Web of Science ®Google Scholar
• A. Harten and S. Osher , Uniformly High-Order Accurate Nonoscillatory Schemes , SLAM J. Numer. Anal. , vol. 24 , no. 2 , pp. 279 – 309 , 1987 .
   Web of Science ®Google Scholar
• H. C. Yee , Linearized Form of Implicit TVD Schemes for the Multidimensional Euler and Navier-Stokes Equations , Comp. Math. Appl , vol. 12A , no. 4/5 , pp. 413 – 432 , 1986 .
   Web of Science ®Google Scholar
• B. van Leer , Towards the Ultimate Conservative Difference Scheme II. Monotonicity and Conservation Combined in a Second-Order Scheme , Comp. Phys. , vol. 14 , pp. 361 – 370 , 1974 .
   Web of Science ®Google Scholar
• P. L. Roe , Characteristic-Based Schemes for the Euler Equations , Ann. Rev. Fluid Meek. , pp. 337 – 356 , 1986 .
   Google Scholar
• M. Chen , C. Hsu , and W. Shyy , Assessment of TVD Schemes for Inviscid and Turbulent Flows , Int. J. Numer. Meth. Fluids , vol. 12 , pp. 161 – 177 , 1991 .
   Web of Science ®Google Scholar
• S. V. Patankar , Numerical Heat Transfer and Fluid Flow , Hemisphere , Washington , D.C. , 1980 .
   Google Scholar
• W. Shyy , Computational Modeling for Fluid Flow and Interfacial Dynamics , Elsevier , Amsterdam , The Netherlands , 1994 .
   Google Scholar
• S. S. Thakur and W. Shyy , Development of High Accuracy Convection Schemes for Sequential Solvers , Numer. Heat Transfer, Part B , vol, 23 , pp. 175 – 199 , 1993 .
   Web of Science ®Google Scholar
• S. S. Thakur and W. Shyy , Unsteady One-Dimensional Gas Dynamics Computations Using a TVD Type Sequential Solver , AIAA Paper 92–3640, AIAA 28th Joint Propulsion Conf. , Nashville , Tenn. , 1992 .
   Google Scholar
• W. Shyy , S, S. Thakur , and H. S. Udaykumar , A High Accuracy Sequential Solver for Simulation and Active Control of a Longitudinal Combustion Instability , Comput. Systems in Eng. , vol. 4 , pp. 27 – 41 , 1993 .
   Google Scholar
• W. Shyy , S. S. Thakur , and J. Wright , Second-Order Upwind and Central Difference Schemes for Recirculating Flow Computation , AIAA J. , vol. 30 , no. 4 , pp. 923 – 932 , 1992 .
   Google Scholar
• S. S. Thakur and W. Shyy , Some Implementational Issues of Convection Schemes for Finite-Volume Formulations , Numer. Heat Transfer, Part B , vol. 24 , pp. 31 – 55 , 1993 .
   Web of Science ®Google Scholar
• H. C. Yee , Construction of Explicit and Implicit Symmetric TVD Schemes and Their Applications , J. Comp. Phys. , vol. 68 , pp. 151 – 179 , 1987 .
   Web of Science ®Google Scholar
• W. Shyy , A Study of Finite Difference Approximations to Steady-State, Convection-Dominated Flow Problems , J. Comp. Phys. , vol, 57 , pp. 415 – 438 , 1985 .
   Web of Science ®Google Scholar
• P. J. Roache , Computational Fluid Dynamics , Hermosa , Albuquerque , N.M. , 1972 .
   Google Scholar
• B. P. Leonard , A Stable and Accurate Convective Modelling Procedure Based on Quadratic Upstream Interpolation , Comp. Meth. Appi Mech. Eng. , vol. 19 , pp. 59 – 98 , 1979 .
   Web of Science ®Google Scholar
• W. Shyy and S. S. Thakur , Controlled Variation Scheme in a Sequential Solver for Recirculating Flows, Part II. Applications , Numer. Heat Transfer, Part B , vol. 25 , no. 3 , pp. 273 – 286 , 1994 .
   Web of Science ®Google Scholar