Adaptive positive nodal method for transport equation

An analysis of the Weighted Linear Moments-Weighted Linear Discontinuous scheme (WLM-WLD scheme) for the transport equation is presented for the plane geometry case. The WLM-WLD scheme is an analogy of the WDD scheme in the class of schemes that use the zeroth and first spatial flux moments. It combines the high accuracy of nodal schemes with the main advantages of the WDD scheme such as arithmetic simplicity of algorithm and applicability to general multidimensional curvilinear geometry. The WLM-WLD scheme with the adaptive fix-up algorithm that is needed to ensure the positivity of solution gives an essential computational gain both in accuracy and speed for deep penetration transport problems compared with the WDD scheme.