A third order finite volume scheme is constructed for scalar hyperbolic conservation laws on two dimensional unstructured meshes. The scheme is based on monotone numerical flux and is particularly straightforward to implement. By applying the quadratic reconstruction based on the least square method and the maximum limiter, the numerical solution can satisfy the local maximum principle. To obtained third order accuracy in the smooth region, the proposed scheme can be used in combination with the local smooth detector. In this paper, the stability condition of the scheme is analyzed theoretically, and its accuracy and the ability of capturing singularities are verified by numerical experiments.
. A CLASS OF THIRD ORDER FINITE VOLUME SCHEME SATISFYING THE LOCAL MAXIMUM PRINCIPLE ON UNSTRUCTURED MESHES[J]. Mathematica Numerica Sinica, 2017, 39(3): 309-320.
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