A harmonic scalar field has a Laplacian (i.e., both source-free and curl-free) gradient vector field and vice versa. Despite the good performance of spherical harmonic series on modeling the gravitational field generated by spheroidal bodies (e.g., the Earth), the series may diverge inside the Brillouin sphere enclosing all field-generating mass. Divergence may realistically occur when determining the gravitational fields of asteroids or comets that have complex shapes, which is known as the complex-boundary value problem (CBVP). To overcome this weakness, we propose a new spatial-domain numerical method based on the equivalence transformation which is well known in the fluid dynamics community: a potential-flow velocity field and a gravitational force vector field are equivalent in a mathematical sense, both referring to a Laplacian vector field. The new method abandons the perturbation theory based on the Laplace equation, and, instead, derives the governing equation and the boundary condition of the potential flow from the conservation laws of mass, momentum and energy. Correspondingly, computational fluid dynamics (CFD) techniques are introduced as a numerical solving scheme. We apply this novel approach to the gravitational field of the comet 67P/Churyumov–Gerasimenko which has an irregular shape. The method is validated in a closed-loop simulation by comparing the result with a direct integration of Newton’s formula. Both methods are consistent with a relative magnitude discrepancy at the percentage level and with a small directional difference root-mean-square value of $$0.78^{\circ }$$ 0 . 78 ∘ . Moreover, the Laplacian property of the potential flow’s velocity field is proved mathematically. From both theoretical and practical points of view, the new numerical method is able to overcome the divergence problem and, hence, has a good potential for solving CBVPs.

The frost resistance of low strength concrete is researched. In order to evaluate the effect of different content of silica fume on frost resistance，the quality of the cement 6%, 9%, 12% silica fume are respectively added into concrete. Freezing-thawing test results show that: the silica fume concrete has good frost resistance. Content of silica fume on concrete is not almost effect to quality loss rate. In 0-250 times of freezing-thawing cycle range, it is smaller that relative dynamic elastic modulus change rate. Relative dynamic elastic modulus of ordinary concrete decreases rapidly after 250 times of freezing-thawing cycle while dynamic elastic modulus decrease rate of the silica fume concrete tends to slow. The freezing -thawing cycles up to 350 times, silica fume concrete relative dynamic elastic modulus is 1.5 times that of ordinary concrete that show the silica fume concrete frost resistance is better than that of ordinary concrete.

The different influencing regular of fly-ash fractiontype of fibre (steel fibre and polypropylene fibre) and fibre fraction on the mechanical property and fracture behavior of Reactive Powder Concrete (PRC) are studied. Fracture mechanical properties of RPC is researched in double-K fracture model and fracture energy release rate G . Test results show that the crack propagation of RPC with steel fibers is limited. Its fracture toughness and pre-critical crack length is largely enhanced. Double-K fracture model and fracture energy release rate G are consistent with describing the fracture behavior of RPC.

The treatment of the urban sewage and the Organic industrial wastewater has been transformed from removing of the organics to the Removal of organic matter and nitrogen, phosphorus. According to the deficiency of the Traditional wastewater treatment process,the micro-pressure inner loop reactor is put forward to solve the Anaerobic, anoxic and aerobic environmental issues in this paper. Aiming at the newly development of the micro-pressure inner loop reactor, based on the methods of Computational Fluid Dynamics, using the methods of computational fluid dynamics, By analyzing the velocity distribution field, flow lines, the gas volume fraction and other factors, the result shows that the reactor Meets the actual needs of the project, and provides a theoretical basis for practical engineering equipment.

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