Narrow Results

In this paper, a kind of Godunov-type Lagrangian scheme is developed in the one space dimension. The Riemann problems are constructed at the interface and the velocity and pressure are evaluated using an implicit characteristic method. Two different methods are used to solve for the equation of energy conservation. Four one-dimensional numerical examples are first presented to obtain the parameter through comparison of the L₁ errors with the changing parameter values. The method having the minimal error is then extended to two dimensions and a cell-centered conservative Lagrangian scheme is proposed for the compressible multi-medium flow. The numerical results for some classical two dimensional hydrodynamic test cases show that the proposed numerical methods are effective and feasible.

This paper establishes a simplified model of a flexible beam with multiple nonlinear supports that present cubic stiffness to study the potential application of cubic nonlinearities in the vibration control of beams. The Lagrangian method (LM) is used to predict transverse dynamic responses of the flexible beam with multiple nonlinear supports that present cubic stiffness, whereas the harmonic balance method (HBM) and Galerkin truncation method (GTM) are utilized to study the accuracy of the LM. Against the background, the effect of nonlinear supports that present cubic stiffness on the nonlinear transverse dynamic responses of the beam is studied. For this study, the accuracy of the LM is guaranteed under the 4-term truncation number. Nonlinear transverse dynamic responses of the flexibly constrained beam with multiple nonlinear supports that present cubic stiffness are sensitively influenced by their initial calculation values. For different boundary conditions or working statuses, the maximum restoring forces at both ends of the flexible beam can be suppressed effectively by optimizing the parameters of nonlinear supports that present cubic stiffness. Appropriate parameters of nonlinear supports that present cubic stiffness are good at vibration control of the flexibly constrained beam. In addition, complicated dynamic responses of the flexible beam with multiple nonlinear supports that present cubic stiffness are motivated under some inappropriate parameters of nonlinear supports.

Prediction of particle transport in enclosed environment is crucial to the welfare of its occupants. The prediction requires not only a reliable particle model but also an accurate flow model. This paper introduces two categories of flow models — Reynolds Averaged Navier-Stokes equation modeling (RANS modeling) and Large Eddy Simulation (LES); as well as two popular particle models — Lagrangian and Eulerian methods. The computed distributions of air velocity, air temperature, and tracer-gas concentration in a ventilated room by the RANS modeling and LES agreed reasonably with the experimental data from the literature. The two flow models gave similar prediction accuracy. Both the Lagrangian and Eulerian methods were applied to predict particle transport in a room. Again, the computed results were in reasonable agreement with the experimental data obtained in an environmental chamber. The performance of the two methods was nearly identical. Finally the flow and particle models were applied to study particle dispersion in a Boeing 767 cabin and in a small building with six rooms. The computed results look plausible.

Mathematical models and computer simulations are useful experimental tools for building and testing theories. Many mathematical models in biology can be formulated by a nonlinear system of ordinary differential equations. This work deals with the numerical solution of the hantavirus infection model, the human immunodeficiency virus (HIV) infection model of CD4${}^{+}$T cells and the susceptible–infected–removed (SIR) epidemic model using a new reliable algorithm based on shifted Boubaker Lagrangian (SBL) method. This method reduces the solution of such system to a system of linear or nonlinear algebraic equations which are solved using the Newton iteration method. The obtained results of the proposed method show highly accurate and valid for an arbitrary finite interval. Also, those are compared with fourth-order Runge–Kutta (RK4) method and with the solutions obtained by some other methods in the literature.

In this paper, two wire routing algorithms called LMR and LMR-FSC are proposed. Both of the algorithms are based on the Lagrangian method for the continuous valued constrained optimization problem. In LMR (Lagrangian method for routing) all the nets are routed simultaneously. The problem of deciding the net-ordering and rip-up reroute scoring metrics doesn't exist, rather nets are routed by a natural continuous valued shove aside resulting from the mutual competition of the nets. The characteristics of massive parallelism of LMR makes it suitable for neurocomputing. LMR-FSC (Lagrangian method for routing with forced satisfaction of consistency) is a cost-based iterative algorithm. Initially illegal condition of overlapping of different nets is allowed. The overlapping of different nets is accounted as cost. The wires placed on the higher cost parts are gradually moved to the lower cost parts. Each net is routed for a minimum cost. Effectiveness of both the approaches is shown by some experimental results.