Development of a flow analysis code using an unstructured grid with the cell-centered method
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A conservative finite-volume numerical method for unstructured grids with the cell-centered method has been developed for computing flow and heat transfer by combining the attractive features of the existing pressure-based procedures with the advances made in unstructured grid techniques. This method uses an integral form of governing equations for arbitrary convex polyhedra. Care is taken in the discretization and solution procedure to avoid formulations that are cell-shape-specific. A collocated variable arrangement formulation is developed, i.e. all dependent variables such as pressure and velocity are stored at cell centers. For both convective and diffusive fluxes the forms superior to both accuracy and stability are particularly adopted and formulated through a systematic study on the existing approximation ones. Gradients required for the evaluation of diffusion fluxes and for second-order-accurate convective operators are computed by using a linear reconstruction based on the divergence theorem. Momentum interpolation is used to prevent the pressure checkerboarding and a segregated solution strategy is adopted to minimize the storage requirements with the pressure-velocity coupling by the SIMPLE algorithm. An algebraic solver using iterative preconditioned conjugate gradient method is used for the solution of linearized equations. The flow analysis code (PowerCFD) developed by the present method is evaluated for its application to several 2-D structured-mesh benchmark problems using a variety of unstructured quadrilateral and triangular meshes. The present flow analysis code by using unstructured grids with the cell-centered method clearly demonstrate the same accuracy and robustness as that for a typical structured mesh.
Key WordsFlow Analysis Code Unstructured Grid System Cell-Centered Method Finite Volume Method Benchmark Solution Performance Evaluation
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- Ferziger, J. H. and Peric, M., 2002, Computational Methods for Fluid Dynamics, 3rd ed., Springer.Google Scholar
- Jiang, Y. and Przekwas, A. J., 1994, “Implicit, Pressure-Based Incompressible Navier-Stokes Equations Solver for Unstructured Meshes,” AIAA-94-0305.Google Scholar
- Miettien, A., 1997, A Study of the Pressure Correction Approach in the Collocated Grid Arrangement,Ph.D. thesis, Helsinki Univ. of Technology.Google Scholar
- Muzaferija, S., 1994, Adaptive Finite Volume Method for Flow Predictions using Unstructured Meshes and Multigrid Approach,Ph.D. Thesis, University of London.Google Scholar
- Myong, H. K., Kim, J. and Kim, J. E., 2005, “Development of 3-D Flow Analysis Code using Unstructured Grid System (II)-Code’s Performance Evaluation -,” (in Korean)Trans. KSME Part B, Vol. 29, No. 9, pp. 1057–1064.Google Scholar
- Myong, H. K., 2005, “Numerical Simulation of Lid-Driven Flow in a Square Cavity at High Reynolds Numbers” (in Korean)KSCFE J. of Computational Fluid Engineering, Vol. 10, No. 4, pp. 18–23.Google Scholar
- Myong, H. K., 2006a, “Evaluation of Numerical Approximations of Convection Flux in Unstructured Cell-Centered Method,” (in Korean)KSCFE J. of Computational Fluid Engineering, Vol. 11, No. 1, pp. 36–42.Google Scholar
- Myong, H. K., 2006b, “A New Numerical Approximation of Diffusion Flux in Unstructured Cell-Centered Method,” (in Korean)KSCFE J. of Computational Fluid Engineering, Vol. 11, No. 1, pp. 8–15.Google Scholar
- Myong, H. K., 2006c, “Numerical Study on the Characteristics of Natural Convection Flows in a Cubical Cavity,” (in Korean)Trans. KSME Part B, Vol. 30, No. 4, pp. 337–342.Google Scholar
- Myong, H. K., 2006d, “Numerical Simulation of Developing Turbulent Flow in a Circular Pipe of 180° Bend,” (in Korean) to appear in Trans. KSME Part B.Google Scholar
- Peric, M., 1985, A Finite Volume Method for the Prediction of Three-Dimensional Fluid Flow in Complex Ducts,Ph.D. Thesis, Univ. of London, UK.Google Scholar