Diffusion analogy and shock capturing for solving aerodynamic equations

Improving the resolution of the shock is one of the most important subjects in computational aerodynamics. In this paper the behaviour of the solutions near the shock is discussed and the reason of the oscillation production is investigated heuristically. According to the differential approximation of the difference scheme the so-called diffusion analogy equation and the diffusion analogy coefficient are defined. Four methods for improving the resolution of the shock are presented using the concept of diffusion analogy.

Numerical-Value Perturbation Method with Application of Solving Convective-Diffusion Integral Equation

The convective--diffusion equation is of primary importance in such fields as fluid dynamics and heat transfer hi the numerical methods solving the convective-diffusion equation, the finite volume method can use conveniently diversified grids (structured and unstructured grids) and is suitable for very complex geometry The disadvantage of FV methods compared to the finite difference method is that FV-methods of order higher than second are more difficult to develop in three-dimensional cases. The second-order central scheme (2cs) offers a good compromise among accuracy, simplicity and efficiency, however, it will produce oscillatory solutions when the grid Reynolds numbers are large and then very fine grids are required to obtain accurate solution. The simplest first-order upwind (IUW) scheme satisfies the convective boundedness criteria, however. Its numerical diffusion is large. The power-law scheme, QMCK and second-order upwind (2UW) schemes are also often used in some commercial codes. Their numerical accurate are roughly consistent with that of ZCS. Therefore, it is meaningful to offer higher-accurate three point FV scheme. In this paper, the numerical-value perturbational method suggested by Zhi Gao is used to develop an upwind and mixed FV scheme using any higher-order interpolation and second-order integration approximations, which is called perturbational finite volume (PFV) scheme. The PFV scheme uses the least nodes similar to the standard three-point schemes, namely, the number of the nodes needed equals to unity plus the face-number of the control volume. For instanc6, in the two-dimensional (2-D) case, only four nodes for the triangle grids and five nodes for the Cartesian grids are utilized, respectively. The PFV scheme is applied on a number of 1-D problems, 2~Dand 3-D flow model equations. Comparing with other standard three-point schemes, The PFV scheme has much smaller numerical diffusion than the first-order upwind (IUW) scheme, its numerical accuracy are also higher than the second-order central scheme (2CS), the power-law scheme (PLS), the QUICK scheme and the second-order upwind(ZUW) scheme.

Two-step digit-set-restricted modified signed-digit addition-subtraction algorithm and its optoelectronic implementation

A novel, to our knowledge, two-step digit-set-restricted modified signed-digit (MSD) addition-subtraction algorithm is proposed. With the introduction of the reference digits, the operand words are mapped into an intermediate carry word with all digits restricted to the set {(1) over bar, 0} and an intermediate sum word with all digits restricted to the set {0, 1}, which can be summed to form the final result without carry generation. The operation can be performed in parallel by use of binary logic. An optical system that utilizes an electron-trapping device is suggested for accomplishing the required binary logic operations. By programming of the illumination of data arrays, any complex logic operations of multiple variables can be realized without additional temporal latency of the intermediate results. This technique has a high space-bandwidth product and signal-to-noise ratio. The main structure can be stacked to construct a compact optoelectronic MSD adder-subtracter. (C) 1999 Optical Society of America.

Subtraction of scattering parameters for adiabatic intrinsic responses of semiconductor lasers

Thermal effects will make chip temperature change with bias current of semiconductor lasers, which results in inaccurate intrinsic response by the conventional subtraction method. In this article, an extended subtraction method of scattering parameters for characterizing adiabatic responses of laser diode is proposed. The pulsed injection operation is used to determine the chip temperature of packaged semiconductor laser, and an optimal injection condition is obtained by investigating the dependence of the lasing wavelength on the width and period of the injection pulse in a relatively wide temperature range. In this case, the scattering parameters of laser diode are measured on adiabatic condition and the adiabatic intrinsic responses of packaged laser diode are first extracted. It is found that the adiabatic intrinsic responses are evidently superior to those without thermal consideration. The analysis results indicate that inclusion of thermal. effects is necessary to acquire accurate intrinsic responses of semiconductor lasers. (C) 2008 Wiley Periodicals, Inc.

Subtraction of scattering parameters for small-signal modulation characteristics of laser diode

An extended subtraction method of scattering parameters for characterizing laser diode is proposed in this paper. The intrinsic response is extracted from the measured transmission coefficients of laser diode, and the parasitics of packaging net-work laser chip are determined from the measured reflection coefficient of laser diode simultaneously. It is shown that the theories agree well with the experimental results.

Subtraction of S-parameters for adiabatic small-signal modulation characteristics of laser diode - art. no. 60201V

An extended subtraction method of scattering parameters for characterizing laser diode is introduced in this paper. The intrinsic small-signal response can be directly extracted from the measured transmission coefficients of laser diode by the method. However the chip temperature may change with the injection bias current due to thermal effects, which causes inaccurate intrinsic response by our method. Therefore, how to determine the chip temperature and keep the laser chip adiabatic is very critical when extracting the intrinsic response. To tackle these problems, the dependence of the lasing wavelength of the laser diode on the chip temperature is investigated, and an applicable measurement setup which keeps the chip temperature stable is presented. The scattering parameters of laser diode are measured on diabatic and adiabatic conditions, and the extracted intrinsic responses for both conditions are compared. It is found that the adiabatic intrinsic responses are evidently superior to those without thermal consideration. The analysis indicates that inclusion of thermal effects is necessary to acquire accurate intrinsic response.

Solving MIN UR problem by triangle evolution algorithm with archiving and niche techniques

In this paper, as an extension of minimum unsatisfied linear relations problem (MIN ULR), the minimum unsatisfied relations (MIN UR) problem is investigated. A triangle evolution algorithm with archiving and niche techniques is proposed for MIN UR problem. Different with algorithms in literature, it solves MIN problem directly, rather than transforming it into many sub-problems. The proposed algorithm is also applicable for the special case of MIN UR, in which it involves some mandatory relations. Numerical results show that the algorithm is effective for MIN UR problem and it outperforms Sadegh's algorithm in sense of the resulted minimum inconsistency number, even though the test problems are linear.