Development of a Compact and Accurate Discretization for Incompressible Navier-Stokes Equations Based on an Equation-Solving Solution Gradient, Part I: Kernel Scheme Fundamentals

REFERENCES

• Y.-H. Hwang , Solution of the Steady Navier-Stokes Equations by the Pressure Correction Method in the ALE Grid , Numer. Heat Transfer B , vol. 23 , pp. 237 – 255 , 1993 .
   Web of Science ®Google Scholar
• Y.-H. Hwang , Arbitrary Domain Velocity Analyses for the Incompressible Navier-Stokes Equations , J. Comput. Phys. , vol. 110 , pp. 134 – 149 , 1994 .
   Google Scholar
• Y.-H. Hwang , Calculation of Incompressible Flow on a Staggered Triangular Grid , Part I: Mathematical Formulation , Numer. Heat Transfer B , vol. 27 , pp. 323 – 336 , 1995 .
   Web of Science ®Google Scholar
• Y.-H. Hwang , Calculation of Incompressible Flow on a Staggered Triangular Grid , Part II: Applications , Numer. Heat Transfer B , vol. 27 , pp. 337 – 353 , 1995 .
   Web of Science ®Google Scholar
• Y.-H. Hwang , Stability and Accuracy Analyses for the Incompressible Navier-Stokes Equations on the Staggered Triangular Grid , Numerical Heat Transfer B , vol. 32 , pp. 321 – 349 , 1997 .
   Web of Science ®Google Scholar
• L. J. Durlofsky , B. Enguist , and S. Osher , Triangle Based Adaptive Stencils for the Solution of Hyperbolic Conservation Laws , J. Comput. Phys. , vol. 98 , pp. 64 – 73 , 1992 .
   Web of Science ®Google Scholar
• R. Abgrall , On Essentially Non-Oscillatory Schemes on Unstructured Meshes: Analysis and Implementation , J. Comput. Phys. , vol. 114 , pp. 45 – 58 , 1994 .
   Web of Science ®Google Scholar
• J. Cabello and K. Morgan , A Comparison of Higher Order Scheme used in a Finite Volume Solver for Unstructured Grid, AIAA-94–2249, 1994.
   Google Scholar
• F. Moukalled and M. Darwish , New Bounded Skew Central Difference Scheme. Part I: Formulation and Testing , Numer. Heat Transfer B , vol. 31 , pp. 91 – 110 , 1997 .
   Web of Science ®Google Scholar
• H. Jasak , H. G. Weller , and A. D. Gosman , High Resolution NVD Differencing Scheme for Arbitrarily Unstructured Meshes , Int. J. Numer. Meth. Fluids , vol. 31 , pp. 431 – 449 , 1999 .
   Web of Science ®Google Scholar
• C. Hirsch , Numerical Computation of Internal and External Flows vol. 2 , pp. 494 – 498 , John Wiley & Sons , New York , 1990 .
   Google Scholar
• T. J. Barth and P. O. Frederickson , Higher-Order Solution of the Euler Equations on Unstructured Grids using Quadratic Reconstruction, AIAA paper 90–0013, 1990.
   Google Scholar
• M. Delanaye and J. A. Essers , Quadratic-Reconstruction Finite Volume Scheme for Compressible Flows on Unstructured Adaptive Grids . AIAA J. , vol. 35 , pp. 631 – 639 , 1997 .
   Google Scholar
• C. Olivier-Gooch and M. Van Altena , A High-Order-Accurate Unstructured Mesh Finite-Volume Scheme for the Advection-Diffusion Equation , J. Comput. Phys. , vol. 181 , pp. 729 – 752 , 2002 .
   Google Scholar
• Y.-H. Hwang , Development of a Compact and Accurate Discretization for Incompressible Navier-Stokes Equations Based on an Equation-Solving Solution Gradient, Part II: Formulation on Unstructured Polygonal Mesh , Numer. Heat Transfer B , vol. 58 , pp. 170 – 192 , 2010 .
   Web of Science ®Google Scholar
• Y.-H. Hwang , Development of a Compact and Accurate Discretization for Incompressible Navier-Stokes Equations Based on an Equation-Solving Solution Gradient, Part III: Fluid Flow Simulations on Staggered Polygonal Grids , Heat Transfer B , vol. 58 , pp. 193 – 215 , 2010 .
   Web of Science ®Google Scholar
• M. Atias , M. Wolfshtein , and M. Israeli , Efficiency of Navier-Stokes Solvers , AIAA J. , vol. 15 , pp. 263 – 266 , 1977 .
   Google Scholar
• B. P. Leonard , A Stable and Accurate Convective Modelling Procedure Based on Quadratic Upstream Interpolation , Comput. Meth. Appl. Mech. Eng. , vol. 19 , pp. 59 – 98 , 1979 .
   Web of Science ®Google Scholar
• W. Shyy , A Study of Finite Difference Approximations to Steady-State, Convection-Dominated Flow Problems , J. Comput. Phys. , vol. 57 , pp. 415 – 438 , 1985 .
   Web of Science ®Google Scholar
• A. A. Kulikovsky , Simple and Accurate Scheme for Nonlinear Convection-Diffusion Equation , J. Comput. Phys. , vol. 173 , pp. 716 – 729 , 2001 .
   Google Scholar