Please use this identifier to cite or link to this item:
|Title:||Very high-order accurate finite volume scheme for the convection-diffusion equation with general boundary conditions on arbitrary curved boundaries|
Nóbrega, J. M.
Machado, Gaspar J.
|Keywords:||arbitrary smooth curved boundaries|
general boundary conditions
reconstruction for off-site data method
very high-order accurate finite volume scheme
|Journal:||International Journal for Numerical Methods in Engineering|
|Abstract(s):||Obtaining very high-order accurate solutions in curved domains is a challenging task as the accuracy of discretization methods may dramatically reduce without an appropriate treatment of boundary conditions. The classical techniques to preserve the nominal convergence order of accuracy, proposed in the context of finite element and finite volume methods, rely on curved mesh elements, which fit curved boundaries. Such techniques often demand sophisticated meshing algorithms, cumbersome quadrature rules for integration, and complex nonlinear transformations to map the curved mesh elements onto the reference polygonal ones. In this regard, the reconstruction for off-site data method, proposed in the work of Costa et al, provides very high-order accurate polynomial reconstructions on arbitrary smooth curved boundaries, enabling integration of the governing equations on polygonal mesh elements, and therefore, avoiding the use of complex integration quadrature rules or nonlinear transformations. The method was introduced for Dirichlet boundary conditions and the present article proposes an extension for general boundary conditions, which represents an important advance for real context applications. A generic framework to compute polynomial reconstructions is also developed based on the least-squares method, which handles general constraints and further improves the algorithm. The proposed methods are applied to solve the convection-diffusion equation with a finite volume discretization in unstructured meshes. A comprehensive numerical benchmark test suite is provided to verify and assess the accuracy, convergence orders, robustness, and efficiency, which proves that boundary conditions on arbitrary smooth curved boundaries are properly fulfilled and the nominal very high-order convergence orders are effectively achieved.|
|Access:||Restricted access (UMinho)|
|Appears in Collections:||IPC - Artigos em revistas científicas internacionais com arbitragem|
Files in This Item:
|1,69 MB||Adobe PDF||View/Open|