Non-oscillatory central differencing for hyperbolic conservation laws
Journal of Computational Physics
Approximate Riemann solvers, parameter vectors, and difference schemes
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Nonoscillatory Central Schemes for Multidimensional Hyperbolic Conservation Laws
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Central finite volume methods with constrained transport divergence treatment for ideal MHD
Journal of Computational Physics
Journal of Computational Physics
Adaptive Semidiscrete Central-Upwind Schemes for Nonconvex Hyperbolic Conservation Laws
SIAM Journal on Scientific Computing
Journal of Computational Physics
FORCE schemes on unstructured meshes I: Conservative hyperbolic systems
Journal of Computational Physics
Applied Numerical Mathematics
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We propose a new central finite volume scheme on unstructured triangular grids to approximate the solution of general two-dimensional hyperbolic systems of conservation laws. The proposed method is an unstructured two-dimensional extension of the original Nessyahu and Tadmor scheme, and a generalization of the barycentric central methods of Arminjon et al. Starting with a conformal finite element triangulation, the proposed method evolves a piecewise linear numerical solution on two staggered grids, thus avoiding the resolution of the Riemann problems arising at the cell interfaces. The control cells of the original grid are the triangles of a finite element mesh, while the dual cells are the staggered quadrilaterals constructed on adjacent triangles. The resulting central scheme is second-order accurate both in space and time and is oscillations-free thanks to numerical gradients limiting. The extension of the staggered Lax-Friedrichs scheme on unstructured grids is easily obtained from the Nessyahu and Tadmor extension by simply evolving a piecewise constant solution instead of a linear one. We validate the developed schemes and solve classical two-dimensional problems arising in gas dynamics. The quality of the obtained numerical results confirms the efficiency and robustness of the proposed schemes.