This paper presents the critical frequency prewarping approximation to analyze the frequency character of the system model with wide frequency band, and compares the method with bilinear approximation and fourth order Runge Kutta method.

Different from the numerical simulation used by Rai , Takahashi and Dorney , we employed Euler equation and Jameson's four stage Runge Kutta scheme to study the unsteady flow in turbine stage with inlet temperature distortion.

The flow model of multiple constituents finite rate unsteady state chemical reaction was used in numerical simulation, and finite volume TVD scheme used in solving convection term of the equation group. The source term generated by chemical reaction was solved by four order Runge Kutta algorithm.

Based on the unstructured grid, Euler equations are solved using the cell-centered finite volume spatial discretization and four-stage Runge-Kutta time-stepping scheme with standard convergence acceleration techniques such as local time stepping and implicit residual smoothing.

The main numerical method of this code is coming from scheme (Jameson, Schimit and Turkel): using cell-centered finite volume method as spatial discretization tools, and a system of ordinary differential equations for time variable is obtained, which is solved by utilizing five-step Runge-Kutta scheme as time marching method , introducing artificial dissipation to damp high frequency oscillations near the shock and stagnation point.

Its dynamic behaviors are investigated by numerical Runge-Kutta method.

Second, The Runge-Kutta arithmetic is used to calculate the dynamical parameters of the micro actuator; the SIMULINK module of MATLAB is used to build the dynamical simulating model and then simulate it.

The Runge-Kutta method is used to solve the ordinary differential equations of the model.

Some neutral curves for the limiting case of a narrow gap were obtained in [2] by the Runge-Kutta method together with the intersecting line method, and the case of small Reynolds numbers and arbitrary gaps was also considered.

The results are obtained by the finite-volume solution of the Euler equations using higher-order TVD Runge-Kutta schemes.

A numerical method for calculating a fully-coupled model of one-dimensional two-phase nozzle flow is described in brief. Governing equations are derived. The Runge-Kutta-Gill method is adopted to solve the equations numerically. The solution for uniform acceleration of gas phase is utilized as an approximate solution for the dimensionless distance x*(=x/L) = 0 to 0.02,i.e.ug = ax*. The initial value of a is determined by a trial and error approach and then checked at the throat. The solution is continued to...

A numerical method for calculating a fully-coupled model of one-dimensional two-phase nozzle flow is described in brief. Governing equations are derived. The Runge-Kutta-Gill method is adopted to solve the equations numerically. The solution for uniform acceleration of gas phase is utilized as an approximate solution for the dimensionless distance x*(=x/L) = 0 to 0.02,i.e.ug = ax*. The initial value of a is determined by a trial and error approach and then checked at the throat. The solution is continued to the throat where the conditions must be satisfied. To eliminate the singularity of the equation, a superseding variable is introduced. The computations are performed for velocity-lag as well as temperature-lag of five parsticle sizes and two ratios of particle to gas flow rates.Temperature, pressure and velocity distributions of both gas and particle along the length of the nozzle are also obtained.In addition, various modes of one-dimensional two-phase nozzle flow have also been briefly reviewed.

By means of bifurcation analysis and catastrophe theory methodology,this paper explores the effects of various kinds of control systems of an aircraft in rolling maneuver on occuring jump and limit cycle phenomena,enhancing critical roll rate,extending effective region of control surface,and improving time responses.These systems involve ordinary fedback control system,aileron-roudder-interconnect(ARI)system,stability-axis yaw damper and direct force control system.The results have been verified by those time...

By means of bifurcation analysis and catastrophe theory methodology,this paper explores the effects of various kinds of control systems of an aircraft in rolling maneuver on occuring jump and limit cycle phenomena,enhancing critical roll rate,extending effective region of control surface,and improving time responses.These systems involve ordinary fedback control system,aileron-roudder-interconnect(ARI)system,stability-axis yaw damper and direct force control system.The results have been verified by those time histories which were accomplished by a fourth o-der Runge-Kutta integration routine.

This paper deals with the heat transfer of trapezoidal fin under the condit- ion of radiation and convection. By applying 4th order Runge-Kutta integration scheme and Newton-Raphson iteration technique in numerical solution, the lengthwise temperature distribution of the fin is obtainedj the influences of various parameters, including thermal conductivity, emissivity, temperature at the base of the fin, length of the fin, and distance between neighbouring fins, on the fins' heat transfer are analyzed. Furthermore,...

This paper deals with the heat transfer of trapezoidal fin under the condit- ion of radiation and convection. By applying 4th order Runge-Kutta integration scheme and Newton-Raphson iteration technique in numerical solution, the lengthwise temperature distribution of the fin is obtainedj the influences of various parameters, including thermal conductivity, emissivity, temperature at the base of the fin, length of the fin, and distance between neighbouring fins, on the fins' heat transfer are analyzed. Furthermore, a comparison is made between the effects of heat transfer of different kinds of fins: the rectangular and triangular fins which taking radiation into accountl the trapezoidal fin which neglecting radiation These results are of important significance for engineering design.