Inverse mixed problems of a discrete system for a rod are studied, i.e., stiffness and mass matrices of discrete system of a rod are reconstructed from some frequency data and part of mode data. Three inverse mixed problems are formulated. Solving methods for these problems are given. And conditions of existing solutions for these inverse problems are discussed. Numerical examples are also shown. Potential worth for this type of inverse problems is analysed.

Conditions and method for constructing stiffness distribution function of various parameters symmetric simple supported beams with a symmetric or anti-symmetric mode and specified polynomial density distributing function are discussed. It is shown that the constructed stiffness distribution functions are positive functions in case with different density distributing. Two numeral examples are given. And two problems correlated are explained.

A PML model based on fixed surface roughness is used in simulation of surface roughness effect on flow in mini-channels. Compared with 3-D simulation, results of pressure drop agree well. With PML model and 3-D model we simulate different flow rates and roughness, it shows that surface roughness results in speed linear flow substrate. Pressure drop and relative roughness follow a secondary power relation as Re number is fixed. Pressure drop increased linearly with Re number as roughness elements is equal.

A non-Newtonian shear-thinning model is shown and applied to multiphase flow simulation in 3-D micro-tubes.The model is validated by comparing simulation and experimental results.Velocity simulated agrees well with experimental data and shows F-L effect in microscale hemodynamics.To investigate non-membrane hemodialysis,we simulate hemodialysis in a T-shape mixer.Simulation indicates that components with larger mass diffusion coefficient pervade sufficiently and they can be separated from other components.

A joint-scalar probability density function (PDF) model is used to simulate bluff-body stabilized turbulent non-premixed Sydney flames HM1. In Situ Adaptive Tabulation (ISAT) algorithm is used to accelerate chemistry calculations. A modified LRR-IP Reynolds stress model is applied to obtain mean flow and turbulent mixing fields. We consider three chemical kinetical schemes for methane chemistry. Simulation results are compared with experimental data. It shows that the model and mechanisms predict flow field, scalar field and local extinction well. C2 chemistry has minor effect on flame HM1.

Two-dimensional and three-dimensional simulations are performed to investigate supersonic cold gas flows in micro-nozzles using continuum-based no-slip and slip models,respectively.The validity of continuum-based models is examined by DSMC method.The study focuses on low Reynolds number effects,three-dimensional effect and propulsive performance of the micro-nozzle flow.It shows that compared to the prediction of propulsive performance,the simulation of local flow fields needs a more stringent model.The no slip N-S equations are able to predict propulsive performance of micro-nozzles with Kn < 0.03.Reynolds number is a key parameter in governing low Reynolds number effect and propulsive performance.The strong viscous losses can be mitigated and better propulsive performance can be achieved at higher chamber pressures.The micro-nozzle with the ratio of etch depth to throat width more than 13 has a good 2D characteristic as Re > 1000.

We design a controller for uncertain Lorenz systemes with multiple inputs containing sector nonlinearity and deadzones,and demonstrate its effectiveness theoretically.With this controller the controlled Lorenz system drives system orbits asymptotically to arbitrarily objective trajectories evenif there exist uncertainties,deadzones and sector nonlinearities in the inputs.Finally,by emulation studies of controlled Lorenz systems,effectiveness of the controller is demonstrated.

In a perturbation analysis,a two-dimensional theoretical solution based on Navier-Stokes equations is constructed for gaseous slip flows in a micro-channel with different slip conditions.The micro-channel flow is investigated theoretically and numerically at various inlet pressure ratios,aspect ratios and fluid cases with several slip models.The influence of the rarefaction effect,thermal creep effect and slip conditions is emphasized.Simulations show that Kn is a key parameter in determining the magnitude of rarefaction effects while Re is a key parameter indicating the thermal creep.Excellent agreements with experimental results are observed in both theoretical and numerical results of low-velocity micro-channel flows at very large aspect ratios.

Gas filtration combustion in porous media differs substantially from the combustion with free flame. A one-dimensional model is proposed, and a perturbation theory is used for the combustion front velocity analysis of the methane-air premixed combustion in an inert packed bed, The temperature distribution is predicted for either fully-developed or transient combustion state, based on direct solution and Green's function method. Finally, computational experiments are given and the results are satisfactory.

The instantaneous response of a laminar diffusion flamelet is investigated numerically. A detailed mechanism GRI-Mech 3.0(53-species and 325-reaction) is empolyed to describe the CH₄ oxidation and NO_x formation. A predication of steady flamelct structures is compared with the experimental data to validate the method. A step variation of strain rate is used to simulate the influence of a instantaneous flow field on the flamelet local structure. The response of flamelet structures(temperature and species concentration) to the strain rate variation is given and analyzed. We focus on the influence of the step size of the strain rate. It is found that the flamelet response to the strain rate variation is not symmetric,and the response time is inverse proportional to the strain rate variation as it is small. In addition, the mean response time of temperature is much longer than the flow time scale of a typical turbulent combustion field, which demonstrates the importance of unsteadiness in the numerical simulation of turbulent combustions.

The various order explicit schemes based on exponential fitting and Newton interpolants are constructed for partial differential equations.The various precision can be achieved by employing the various order explicit schemes.When the schemes are applied to heat transport equations at the microscale and strong transient heat transport in thin film,the effects are admirable.Numerical calculations show the present method is high accurate and computationally efficient.

Common formulae for the free-order explicit multistep method of precise time integration are proposed. When the higher order explicit algorithms of precise time integration are applied for calculating the ray equation and the classical trajectories of diatomic system, the effect is admirable. The numerical results reveal that the pressent method is higher accurated and efficient, capable of keeping computational stability for long time simulation, and suitable for higher order numerical computation.

An algorithm is proposed to combine Kirchhoff integral and an unsteady flow computation. Axisymmetric jet flows are given by DNS using 5-order accurate upwind compact scheme and 3-order accurate Runge-Kutta scheme. Kirchhoff integral is used to predict the far-field sound. Numerical results show that far-field sound pressure has the directivity and reaches maximal value at 20° diverged from the flow direction. The directivity is attenuating while the propagation distance is increasing.

The flow fields of 2-D compressible axisymmetric jet are simulated by solving N-S equations. The discretization method has high order accuracy. The information and development of the large vortical structure and it's role in the jet development are studied. The Kelvin-Helmholtz wave appears firstly when jet losts it's stability, and then the single vortex rolls up. After that, with the development of jet, the vortex structures begin to pair and merge because of the increasement of non-linear effects. It is also shown that the pressure distribution is directly relative to the large vortical structures.