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In this paper, the authors study the forward and inverse problems for a fractional boundary value problem with Dirichlet boundary conditions. The existence and uniqueness of solutions for the forward problem is first proved. Then an inverse source problem is considered. [ABSTRACT FROM AUTHOR]

In this paper, we construct a group of Saul'yev type asymmetric difference formulas for the dispersive equation. Based on these formulas we derive a new alternating 6-point group algorithm to solve dispersive equations with periodic boundary conditions. The algorithm has a high-order accuracy in space and an unconditional stability. The theoretical results are conformed to the numerical simulation. A comparison of this algorithm with the previous Alternating Group Explicit method is presented. [ABSTRACT FROM AUTHOR]

In this paper, we apply a regularized sinc method to compute the eigenvalues of a discontinuous regular Dirac system with transmission conditions at the point of discontinuity. The regularized technique allows us to insert some parameters to the well-known sinc method, strengthening the existing technique, and to avoid the aliasing error. The error analysis is established considering both the truncation and amplitude errors associated with the sampling theorem. Numerical examples together with tables and illustrative figures are given. [ABSTRACT FROM PUBLISHER]

Inclined overflow gates are widely used in open channels to meet different flow rate requirements by promptly adjusting their openings according to varied water levels. The characteristics of such gates are quite complex and need intensive study. To develop an effective and efficient numerical method for studying the hydrodynamic features of similar engineering structures with fluid structure interactions and free-surface flows, we propose a free-surface lattice Boltzmann-immersed boundary (FSLB-IB) coupling model, in which the free-surface flow is modeled by the lattice Boltzmann (LB) method and the moving boundaries are handled by the immersed boundary (IB) method. To solve the incompatibility issue arising from the coupling of the FSLB model and IB method, two treatments, namely the velocity correction in the empty cells for matching the IB speed with the local fluid velocity, and the iterative force-correction for enhancing accuracy, are introduced. The feasibility and accuracy of the proposed coupling scheme are first validated by two benchmark cases. Then the FSLB-IB scheme is applied to analyze the hydraulic characteristics of an inclined overflow gate in different working conditions. The good agreements between the simulated and empirical hydraulic parameters as well as the reasonable flow features show that the proposed coupling scheme is feasible for simulating practical hydraulic problems. [ABSTRACT FROM AUTHOR]

We present a local and point-wise scheme for imposing reflective boundary conditions to stationary internal boundaries for solving the reactive Euler equations on Cartesian grids. The scheme is presented in two and three dimensions and can run efficiently on parallel machines while still maintaining the same advantages over other methods for enforcing internal boundary conditions. Level sets are used to represent internal solid regions along with a new local node sorting algorithm that decouples internal boundary nodes by establishing their connectivity to other internal boundary nodes. This approach allows us to enforce boundary conditions via a direct procedure, removing the need to solve a coupled system of equations numerically. We examine the accuracy and fidelity of our internal boundary algorithm by simulating flows past various solid boundaries in two and three dimensions, showing good agreement between our numerical results and experimental data. [ABSTRACT FROM AUTHOR]