Limiter-Free Third Order Logarithmic Reconstruction

A third order conservative reconstruction, in the context of finite volume schemes for hyperbolic conservation laws, is constructed based on logarithmic functions. This logarithmic method reconstructs without the use of a limiter, any preprocessing of input data, special treatments for local extrema, or shock solutions. Also the method is local in the sense that data from only the nearest neighbors are required. We test the new reconstruction method in several numerical experiments, including nonlinear systems in one and two space dimensions.

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