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The paper is devoted to investigate the two-dimensional time-fractional Tricomi-type equation, which describes the anomalous process of nearly sonic speed gas dynamics. An efficient numerical process, based on the combination of time stepping method and meshless local weak formulation, is performed to solve the model. Firstly, an implicit finite difference scheme is used to discrete the problem in time direction. The unconditional stability of the proposed time discretization scheme is proven. Then, a meshfree method based on the combination of local Petrov-Galerkin formulation and strong form is implemented to fully discretize the underlying problem. In our implementation, the radial point interpolation basis functions and local Heaviside step functions are used as the basis and test functions, respectively. A simple collocation process is employed to impose the Dirichlet boundary conditions directly. Finally, two numerical experiments on regular and irregular domains are presented to verify the efficiency, validity and accuracy of the technique.

Transportation is one of the core components of the oil supply chain which needs rigorous optimization tools. Refined product pipelines are the preferred transportation option compared with other ones such as rail, road tankers and coastal vessels because they are reliable and economical. The problem discussed in this paper is short-term scheduling of a generic oil products transportation system characterized by a multi-product pipeline that connects a unique refinery to several distribution centers serving local markets. A novel mixed integer linear programming (MILP) formulation based on a continuous representation in both time and volume scales is presented. The problem goal is to meet product demands at minimum total cost including pumping, interface, flow restart and ON/OFF pump switching costs. To illustrate the proposed approach, three real-world examples are solved. The results show significant improvements in solution quality coupled with a reduced in computational burden compared to previous similar works.

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