The study of hose whip phenomenon is a significant part for further researching dynamic characteristics of hose-drogue system during the aerial refueling operation. The hose whip phenomenon in hose-drogue aerial refueling is simulated based on a high-efficiency neighbor-to-neighbor algorithm. The Osher scheme and SA turbulence model are employed to solve the compressible Navier-Stokes equations, and the hose is discretized into a series of ball hinges linked by massless rigid links which form a multi-body system, the kinematical and dynamic equations are then derived for the system. The numerical model is used to simulate the hose-drogue system dynamics in multiple conditions. The results show a good correlation with previously reported flight-test data in open literature and the application of neighbor-to-neighbor algorithm saves a lot of computational cost. Results of this study may have certain guiding significance for the probe-and-drogue aerial refueling.

We present an iterative method to numerically simulate the growth and shrinkage of tumor. We transform the free boundary problem describing tumor growth into the boundary integral equations which reduce the dimensionality of the problem by one. By boundary element method, we discretize the boundary integral equations by grid points on the moving boundaries of tumor. We estimate the error of the numerical integration. We design an iterative scheme and implement successfully this scheme to visually and graphically show the evolution of the interface between the tumor and the external tissue at different moments of time. In this paper, the proliferation rate $μ$ is a function of space $x$ and time $t$. Our numerical method professor Bei Hu proposed is novel and our numerical results are in agreement with the tumor growth in vivo.

Proper positioning of collocation and source points is one of the major issues in the development of the method of fundamental solutions (MFS). In this paper, two constraints for appropriate determination of the location of collocation and source points in the MFS for two-dimensional problems are introduced. The first constraint is introduced to make sure that the solution of the problem has no oscillation between two adjacent collocation points on the boundary. Imposing the second constraint improves the condition of the generated system of equations. In other words, the second constraint reduces the condition number of the MFS system of equations. In this method, no optimization procedure is carried out. The proposed method is formulated for the Laplace problem; however, it can be developed for other problems as well. The accuracy and effectiveness of the proposed method is demonstrated by presenting several numerical examples. It is shown that boundary conditions with a sharp variation of the field variable can be well handled by the presented method. Moreover, it has been found that problems with a concave or re-entrant corner can be efficiently modelled by the proposed two-constraint method.

Because of the characteristics of carbonate reservoir, vertical well and acid fracturing have become a key technology for efficiently developing carbonate reservoir. A mathematical model for an oil-water two-phase flow fractured vertical well in triple media carbonate reservoir by conceptualizing vugs as spherical shapes is presented in this article. A semi-analytical solution is obtained in the Laplace domain by using source function theory, Laplace transformation, and superposition principle. Analysis of transient pressure responses indicates that seven characteristic flow periods of fractured vertical wells in triple media carbonate reservoir can be identified. Parametric analysis shows that water saturation of matrix, vug, fracture system and acid fracture, acid fracture half-length and acid fracture conductivity can significantly influence the transient pressure responses of fractured vertical wells in triple media carbonate reservoir. The model presented in this article can be applied to obtain important parameters pertinent to reservoir or fracture by type curve matching, and it can also provide useful information for optimizing fracture parameters.

A new high-order conservative patched grid strategy is developed with the concept of collapsed edge. Different from the traditional patched grid algorithm, where the patched interface is a line in two-dimensional space, the new strategy employs a transition region, where a collapsed edge is located within to form four point matched blocks. The introduction of the collapsed edge ensures that the grid generation of neighbouring blocks connected by the transition region is independent. The biggest advantage of this new strategy is that conservation is satisfied automatically since the numerical flux at the collapsed edge is zero. Furthermore, when applied in the framework of high-order finite difference methods based on the coordinate transformation, no essential modifications are needed. Some typical numerical examples are simulated with the new patched grid strategy combined with the fifth-order Weighted Compact Nonlinear Schemes (WCNS) to verify the capability of this new method.

In this article, we discuss a modified least–squares fictitious domain method for the solution of linear elliptic boundary value problems with the third type of boundary conditions (Robin boundary conditions). Let $\Omega$ and $\omega$ be two bounded domains of $\mathbb{R}^{d}$ such that  $\overline{\omega} \subset \Omega$.  For a linear elliptic problem in $\Omega\setminus \overline{\omega}$ with Robin boundary conditions on the boundary $\gamma$ of $\omega$, we accelerate the original least–squares fictitious domain method in Glowinski & He [1] and present a modified least–squares formulation. This method is still a virtual control type and relies on a least-squares formulation, which makes the problem solvable by a conjugate gradient algorithm operating in a well chosen control space. Numerical results show that our method costs much less iterations and the optimal order of convergence is obtained.

In this work, an adjoint-based adaptive isogeometric discontinuous Galerkin method is developed for Euler equations. Firstly, the solution space used in DG on each cell is constructed with the locally owned geometric representation by the isogeometric concept. Then the local $h$-refinement is applied directly through Bézier decomposition, without the restrictions of tensor product nature or basis function support. Furthermore, the adjoint-based error estimator is employed to enhance the estimation of practical engineering outputs. With the isogeometric concept, a novel and natural adjoint space is proposed for the associated discrete adjoint problem. Several numerical examples are selected to demonstrate its ability of handling curved geometry, capturing shocks as well as efficiency in reducing the computational cost in comparison to uniform mesh refinement.

Energy consumption is an important challenge to planning path of quadrotor and the energy-calculating of quadrotor flight trajecotry is not yet fully completed. This paper mainly researches on optimizing the convergence trajectory of the quadrotor on energy-saving. Firstly, the equivalence between the lift angular accelerated function and the flight trajectory function is proved. Then, the energy-calculating formula of quadrotor flight trajectory is obtained by using the relationship between lift and voltage. Furthermore, the quadrotor convergence trajectory model is established with the goal of minimum energy consumption. Finally, through the numerical simulation, the optimized convergence trajectories under different boundary conditions are obtained. Moreover, the specific flight position in real time can be got and implemented into the real-time flight trajectory planning.

In this paper, we present a stochastic differential game to model the three transboundary industrial pollution problems in Three Gorges Reservoir Area of Chongqing City with emission permits trading. The process of emission permits price is assumed to be stochastic and to follow a geometric Brownian motion. We make use of stochastic optimal control theory to derive the system of Hamilton-Jacobi-Bellman equations satisfied by the value functions for the cooperative games, and then propose a fitted finite volume method to solve it. The efficiency and the usefulness of this method are illustrated by an empirical study for Wanzhou District, Kaizhou District, and Yunyang County in  Chongqing City.

In this paper, we investigate the nonlinear system of Navier-Stokes and Darcy flows coupled by the Beavers-Joseph-Saffman law on the interface. The well-posedness of the weak and numerical solutions are established. Mortar elemen method is introduced to solve the coupled model. Error estimates are derived for the proposed method. We adopt an iterative algorithm to solve the nonlinear scheme generated by the coupled system. Numerical example is provided to verify the theoretical analysis.

The mechanisms of the laminar-turbulent transition and the turbulent formation are always one of the important issues in the fields of fluid mechanics, and the boundary-layer receptivity plays a key role in the laminar-turbulent transition. Although there have been plenty of achievements on the boundary-layer receptivity, it is rarely to see the study about the boundary-layer receptivity excited by the interaction of free-stream turbulence and three-dimensional localized wall roughness, which is one of the urgent problems for the prediction of the laminar-turbulent transition in engineering practice. Hence, this problem is studied in this paper by direct numerical simulation. Can the wave packet structures comprised by the two- and three-dimensional T-S waves be discovered in the boundary layer? If so, and how do the group speed and propagation direction of the excited wave packet change? Subsequently, it can prove whether the boundary-layer receptivity exists. Then, the relations between the boundary-layer receptivity and the free-stream turbulence intensity, and the length, width and height of the three-dimensional localized wall roughness are established. Above all, these researches are able to promote the theoretical foundations of the hydrodynamic stability theory and turbulence formation.

In this paper, a new method was proposed for solving two-dimensional nonlinear elliptic-parabolic interface problems with nonhomogeneous jump conditions. The method we used is a finite element method coupled with Newton's method. It is very simple and easy to implement. The grid we used here is body-fitting grids based on the idea of semi-Cartesian grid. Numerical experiments show that this method is about second order accurate in the $L^∞$ norm for different kinds of nonlinear terms and interface with complicated geometry.

In this paper, a penalty finite element method is presented for the two dimensional stationary conduction-convection problems. The existence and the convergence of the penalty stationary conduction-convection formulation are shown. An optimal error estimate of the numerical velocity, pressure and temperature is provided for the penalty finite element method when the parameters $є$ and $h$ are sufficiently small. Our numerical experiments show that our method is effective and our analysis is right.