Similarity and Comparison of Three Finite-Volume Methods for Diffusive Fluxes Computation on Nonorthogonal Meshes

REFERENCES

• M. Shashkov and S. Steinberg , Solving Diffusion Equations with Rough Coefficients in Rough Grids , J. Comput. Phys. , vol. 129 , pp. 383 – 405 , 1996 .
   Web of Science ®Google Scholar
• F. Hermeline , A Finite Volume Method for the Approximation of Diffusion Operators on Distorted Meshes , J. Comput. Phys. , vol. 160 , pp. 481 – 499 , 2000 .
   Web of Science ®Google Scholar
• J. Breil and P.-H. Maire , A Cell-Centered Diffusion Scheme on Two-Dimensional Unstructured Meshes , J. Comput. Phys. , vol. 224 , pp. 785 – 823 , 2007 .
   Web of Science ®Google Scholar
• Z. Sheng and G. Yuan , A Finite Volume Scheme for Diffusion Equations on Distorted Quadrilateral Meshes , Transport Theory Stat. Phys. , vol. 37 , pp. 171 – 207 , 2008 .
   Web of Science ®Google Scholar
• S. Anil Lal , R. V. Reji , and K. S. Santhosh , Evaluation of Diffusive Flux across Faces of Arbitrary Shaped Finite Volume Cells , Comput. Fluids , vol. 57 , pp. 225 – 236 , 2012 .
   Web of Science ®Google Scholar
• S. R. Mathur , and J. Y. Murthy , A Pressure Based Method for Unstructured Meshes , Numer. Heat Transfer B , vol. 31 , pp. 195 – 215 , 1997 .
   Web of Science ®Google Scholar
• D. Kim , and H. Choi , A Second-Order Time-Accurate Finite Volume Method for Unsteady Incompressible Flow on Hybrid Unstructured Grids , J. Comput. Phys. , vol. 162 , pp. 411 – 428 , 2000 .
   Web of Science ®Google Scholar
• A. Dalal , V. Eswaran , and G. Biswas , A Finite-Volume Method for Navier-Stokes Equations on Unstructured Meshes , Numer. Heat Transfer B , vol. 54 , pp. 238 – 259 , 2008 .
   Web of Science ®Google Scholar
• R. Eymard , T. Gallouët , and R. Herbin. Error Estimate for Approximate Solutions of a Nonlinear Convection-Diffusion Problem , Adv. Differ. Eqs. , vol. 7 , pp. 419 – 440 , 2002 .
   Google Scholar
• S. Muzaferija , Adaptative Finite Volume Method for Flow Prediction Using Unstructured Meshes and Multigrid approach, Ph.D. thesis, Imperial College, London, UK, pp. 33–35, 1994.
   Google Scholar
• H. Jasak , Error Analysis and Estimation for the Finite Volume Method with Applications to Fluid Flows, Ph.D. thesis, Imperial College, London, UK, pp. 138–143, 1996.
   Google Scholar
• P. Traoré , Y. M. Ahipo , and C. Louste , A Robust and Efficient Finite Volume Scheme for the Discretization of Diffusive Flux on Extremely Skewed Meshes in Complex Geometries , J. Comput. Phys. , vol. 228 , pp. 5148 – 5159 , 2009 .
   Web of Science ®Google Scholar
• M. Kobayashi , A Second-Order Upwind Least-Squares Scheme for Incompressible Flows on Unstructured Hybrid Grids, Numer. Heat Transfer B , vol. 34, pp. 39–60, 1998.
   Web of Science ®Google Scholar
• J. H. Fergizer and M. Perić , Computational Methods for Fluid Dynamics, , 3rd ed. , pp. 232 – 237 , Springer-Verlag , Berlin , Heidelberg , New York , 2002 .
   Google Scholar
• W. Q. Tao , Recent Advances in Computational Heat Transfer , pp. 194 – 197 , Science Press of China , Beijing , China , 2000 . (in Chinese)
   Google Scholar
• C. D. Perez-Segarra , C. Farre , J. Cadafalch , and A. Oliva , Analysis of Different Numerical Schemes for the Resolution of Convection-Diffusion Equations Using Finite-Volume Methods on Three-Dimensional Unstructured Grids. Part I: Discretization Schemes , Numer. Heat Transfer B , vol. 49 , pp. 333 – 350 , 2006 .
   Web of Science ®Google Scholar
• Y.-Y. Tusi and T.-F. Pan , A Pressure-Correction Method for Incompressible Flows Using Unstructured Meshes , Numer. Heat Transfer B , vol. 49 , pp. 43 – 65 , 2006 .
   Web of Science ®Google Scholar
• C. D. Perez-Segarra , C. Farre , J. Cadafalch , and A. Oliva , Analysis of Different Numerical Schemes for the Resolution of Convection-Diffusion Equations Using Finite-Volume Methods on Three-Dimensional Unstructured Grids. Part II: Numerical Analysis , Numer. Heat Transfer B , vol. 49 , pp. 351 – 375 , 2006 .
   Web of Science ®Google Scholar
• W. Gao , Y.-L. Duan , and R.-X. Liu , The Finite Volume Projection Method with Hybrid Unstructured Triangular Collated Grids for Incompressible Flows , J. Hydrodynamics , vol. 21 , pp. 201 – 211 , 2009 .
   Web of Science ®Google Scholar
• Y. M. Ahipo and P. Traoré , A Robust Iterative Scheme for Finite Volume Discretization of Diffusive Flux on Highly Skewed Meshes , J. Comput. Appl. Math. , vol. 231 , pp. 478 – 491 , 2009 .
   Web of Science ®Google Scholar
• H. A. Van der Vorst , Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems , SIAM J. Sci. Stat. Comput. , vol. 13 , pp. 631 – 644 , 1992 .
   Web of Science ®Google Scholar
• I. Gustafsson , On First and Second Order Symmetric Factorization Methods for the Solution of Elliptic Difference Equations, Chalmers University of Technology, Gothenburg, Sweden 1978.
   Google Scholar
• M. M. Athavale , Y. Jiang , and A. J. Przekwas , Application of an Unstructured Grid Solution Methodology to Turbomachinery Flows, 31rd Aerospace Sciences Meeting and Exhibit, AIAA-95-0174, 1995.
   Google Scholar
• F.-B. Tian , H. X. Luo , J. L. Song , and X. Y. Lu , Force Production and Asymmetric Deformation of a Flexible Flapping Wing in Forward Flight , J. Fluid Struct. , vol. 31 , pp. 149 – 161 , 2013 .
   Web of Science ®Google Scholar
• W. J. Minkozycz , E. M. Sparrow , and J. Y. Murthy , Handbook of Numerical Heat Transfer, , 2nd ed. , pp. 22 – 25 , John Wiley , Chichester , UK , 2006 .
   Google Scholar
• D. J. Mavriplis , Revisiting the Least-Squares Procedure for Gradient Reconstruction on Unstructured Meshes, Natl. Inst. Aerospace Rep. 2003–06, NASA/CR-2003-212683, 2003.
   Google Scholar
• G. Puigt , V. Auffray , and J.-D. Müller , Discretisation of Diffusive Fluxes on Hybrid Grids , J. Comput. Phys. , vol. 229 , pp. 1425 – 1447 , 2010 .
   Web of Science ®Google Scholar
• G. W. Yuan and Z. Q. Sheng , Analysis of Accuracy of a Finite Volume Scheme for Diffusion Equations on Distorted Meshes , J. Comput. Phys. , vol. 224 , pp. 1170 – 1189 , 2007 .
   Web of Science ®Google Scholar
• L. Chang and G. W. Yuan , An Efficient and Accurate Reconstruction Algorithm for the Formulation of Cell-Centered Diffusion Schemes , J. Comput. Phys. , vol. 231 , pp. 6935 – 6952 , 2012 .
   Web of Science ®Google Scholar