Baur, Christine; Schäfer, Michael A fourth-order compact finite volume scheme for the convection-diffusion equation. (English) Zbl 1282.65130 Azaïez, Mejdi (ed.) et al., Spectral and high order methods for partial differential equations – ICOSAHOM 2012. Selected papers from the ICOSAHOM conference, Gammarth, Tunisia, June 25–29, 2012. Cham: Springer (ISBN 978-3-319-01600-9/hbk; 978-3-319-01601-6/ebook). Lecture Notes in Computational Science and Engineering 95, 135-144 (2014). Summary: A fourth-order compact scheme for the convection-diffusion equation is presented. To adopt this approach to non-Cartesian grids, a coordinate transformation is applied. The convection-diffusion equation is solved with a three-dimensional finite volume solver using boundary fitted, block-structured grids. The grid arrangement is collocated. The verification of the fourth-order method is done for analytical test cases. To show the influence of the boundary conditions some calculations with various conditions are performed. Furthermore, the grid dependence of solutions is studied. It is shown that the proposed approach constitutes an efficient high-order solution method for the convection-diffusion equation.For the entire collection see [Zbl 1279.65003]. MSC: 65N08 Finite volume methods for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations Keywords:fourth-order compact finite volume scheme; numerical example; convection-diffusion equation PDFBibTeX XMLCite \textit{C. Baur} and \textit{M. Schäfer}, Lect. Notes Comput. Sci. Eng. 95, 135--144 (2014; Zbl 1282.65130) Full Text: DOI