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A high-order finite volume method on unstructured grids using RBF reconstruction. (English) Zbl 1406.65070

The authors develop some second- and third-order finite volume methods based on an RBF (radial basis function) reconstruction method for the solutions of the Euler and Navier-Stokes equations on unstructured grids. The numerical orders are verified by the case of nonlinear equations. One of the main features of the RBF, with respect to the standard polynomial \(K\)-exact method, is that it is has stronger adaptability for different reconstruction stencils and more flexibility in choosing interpolating points. The authors first focus on the detailed process of flow-field reconstruction by using a multiquadric (MQ) basis function for the second-order and third-order schemes on unstructured triangular grids. Subsequently, they validate the accuracy order of the RBF method through the numerical test case. Furthermore, the method is used to solve several typical flow fields. Compared with the traditional \(K\)-exact high-order scheme, it is found that the BF method is more accurate and has lower numerical dissipation.

MSC:

65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
76M12 Finite volume methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
65D32 Numerical quadrature and cubature formulas
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