Abstract
A perturbation finite volume (PFV) method for the convective-diffusion integral equation is developed in this paper. The PFV scheme is an upwind and mixed scheme using any higher-order interpolation and second-order integration approximations, with the least nodes similar to the standard three-point schemes, that is, the number of the nodes needed is equal to unity plus the face-number of the control volume. For instance, in the two-dimensional (2-D) case, only four nodes for the triangle grids and five nodes for the Cartesian grids are utilized, respectively. The PFV scheme is applied on a number of 1-D linear and nonlinear problems, 2-D and 3-D flow model equations. Comparing with other standard three-point schemes, the PFV scheme has much smaller numerical diffusion than the first-order upwind scheme (UDS). Its numerical accuracies are also higher than the second-order central scheme (CDS), the power-law scheme (PLS) and QUICK scheme.
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The project supported by the National Natural Science Foundation of China (10272106, 10372106)
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Zhi, G., Guowei, Y. Perturbation finite volume method for convective-diffusion integral equation. Acta Mech Sinica 20, 580–590 (2004). https://doi.org/10.1007/BF02485861
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DOI: https://doi.org/10.1007/BF02485861