高空核电磁脉冲模拟波形的双指数函数拟合法

 许多标准和公开出版物中都用双指数函数描述高空核电磁脉冲典型波形。通过数值方法，研究了双指数函数一项重要的性质。根据该性质，详细讨论了高空核电磁脉冲模拟波形数值拟合中，双指数函数特征参数与脉冲峰值、前沿、后沿以及半宽等物理参数的关系，从而提出一种简单有效的脉冲参数计算方法。通过IEC标准中规定的高空核电磁脉冲参数的估计与一个实测高空核电磁脉冲模拟波形的数值拟合，验证了该方法的有效性和可靠性。该方法能够适应多种峰值、前沿和半宽的高宽核电磁脉冲模拟波形的数值拟合。     

Numerical investigation of the physics of rotating-detonation-engines

Rotating-detonation-engines (RDE’s) represent an alternative to the extensively studied pulse-detonation-engines (PDE’s) for obtaining propulsion from the high efficiency detonation cycle. Since it has received considerably less attention, the general flow-field and effect of parameters such as stagnation conditions and back pressure on performance are less well understood than for PDE’s. In this article we describe results from time-accurate calculations of RDE’s using algorithms that have successfully been used for PDE simulations previously. Results are obtained for stoichiometric hydrogen–air RDE’s operating at a range of stagnation pressures and back pressures. Conditions within the chamber are described as well as inlet and outlet conditions and integrated quantities such as total mass flow, force, and specific impulse. Further computations examine the role of inlet stagnation pressure and back pressure on detonation characteristics and engine performance. The pressure ratio is varied between 2.5 and 20 by varying both stagnation and back pressure to isolate controlling factors for the detonation and performance characteristics. It is found that the detonation wave height and mass flow rate are determined primarily by the stagnation pressure, whereas overall performance is closely tied to pressure ratio. Specific impulses are calculated for all cases and range from 2872 to 5511 s, and are lowest for pressure ratios below 4. The reason for performance loss is shown to be associated with the secondary shock wave structure that sets up in the expansion portion of the RDE, which strongly effects the flow at low pressure ratios. Expansion to supersonic flow behind the detonation front in RDE’s with higher pressure ratios isolate the detonation section of the RDE and thus limit the effect of back pressure on the detonation characteristics.     

A CSP and tabulation-based adaptive chemistry model

We demonstrate the feasibility of a new strategy for the construction of an adaptive chemistry model that is based on an explicit integrator stabilized by an approximation of the Computational Singular Perturbation (CSP)-slow-manifold projector. We examine the effectiveness and accuracy of this technique first using a model problem with variable stiffness. We assess the effect of using an approximation of the CSP-slow-manifold by either reusing the CSP vectors calculated in previous steps or from a pre-built tabulation. We find that while accuracy is preserved, the associated CPU cost was reduced substantially by this method. We used two ignition simulations – hydrogen–air and heptane–air mixtures – to demonstrate the feasibility of using the new method to handle realistic kinetic mechanisms. We test the effect of utilizing an approximation of the CSP-slow-manifold and find that its use preserves the order of the explicit integrator, produces no degradation in accuracy, and results in a scheme that is competitive with traditional implicit integration. Further analysis on the performance data demonstrates that the tabulation of the CSP-slow-manifold provides an increasing level of efficiency as the size of the mechanism increases. From the software engineering perspective, all the machinery developed is Common Component Architecture compliant, giving the software a distinct advantage in the ease of maintainability and flexibility in its utilization. Extension of this algorithm is underway to implement an automated tabulation of the CSP-slow-manifold for a detailed chemical kinetic system either off-line, or on-line with a reactive flow simulation code.     

Numerical study on combustion of H2—O2 in a supersonic reactive expansion in a nozzle

A study on expansion flow inside a nozzle considering full mechanism chemistry of hydrogen and oxygen was carried out. In this study, a full implicit scheme for turbulent reactive flow was obtained by combining the second order TVD scheme of Yee and Harten (1987, Implicit TVD schemes for hyperbolic conservation laws in curvilinear coordinates. American Institute of Aeronautics and Astronautics Journal, 25(2), 266–274) with the efficient implicit lower-upper scheme of Shuen and Yoon (1989, Numerical study of chemically reacting flows using a lower-upper symmetric successive overrelaxation scheme. American Institute of Aeronautics and Astronautics Journal, 27(12), 1752–1756). The species equations, Navier–Stokes equations and turbulence model were implemented in the numerical scheme and solved in conjunction with full detailed finite rate chemistry. The numerical scheme is verified by comparison with experimental results of a converging–diverging nozzle. Effects of inlet pressure, temperature and fuel-oxidant mass ratio on nozzle flow field were studied. Variation of chemical species under different conditions was investigated by considering a chemical mechanism. Results show that increasing inlet pressure increases the rate of reactions due to increasing the concentration of reactants. For lower inlet pressure the radical H increases slightly in the diverging part of the nozzle, while for higher pressures it decreases along the nozzle. Inlet fuel–oxidant mass ratio affects the variation of all species with a greater effect for a near stoichiometric ratio. It was also shown that a higher inlet temperature provides a more enhanced reaction zone in the diverging part of the nozzle.     

A least‐square weighted residual method for level set formulation

In this paper, a least‐square weighted residual method (LSWRM) for level set (LS) formulation is introduced to achieve interface capturing in two‐dimensional (2D) and three‐dimensional (3D) problems. An LSWRM was adopted for two semi‐discretized advection and reinitialization equations of the LS formulation. The present LSWRM provided good mathematical properties such as natural numerical diffusion and the symmetry of the resulting algebraic systems for the advection and reinitialization equations. The proposed method was validated by solving some 2D and 3D benchmark problems such as those involving a rotating slotted disk, the rotation of a slotted sphere, and a time‐reversed single‐vortex flow and a deformation problem of a spherical fluid. The numerical results were compared with those obtained from essentially non‐oscillatory type formulations and particle LS methods. Further, the proposed LSWRM for the LS formulation was coupled with a splitting finite element method code to solve the incompressible Navier–Stokes equations, and then, the collapse of a 3D broken dam flow was well simulated; in the simulation, the entrapping of air and the splashing of the surge front of water were reproduced. The mass conservation of the present method was found to be satisfactory during the entire simulation. Copyright © 2011 John Wiley & Sons, Ltd.     

Weighted Discrepancy and High-Dimensional Numerical Integration

The concept of weighted discrepancy of sequences was introduced by Sloan and Woniakowski when they proved a general form of a Koksma–Hlawka inequality for the numerical integration of functions. This version takes imbalances in the importance of the projections of the integrand into account.In this paper we give estimates for the weighted discrepancy of several important point sets. Further we carry out various (high-dimensional) numerical integration experiments and we compare the results with the error bounds provided by the generalized Koksma–Hlawka inequality and by the estimates for the weighted discrepancy. Finally we discuss various consequences.     

Numerical solution of the controlled Duffing oscillator by hybrid functions

A numerical method for solving the controlled Duffing oscillator is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions which consists of block-pulse functions plus Legendre polynomials are given. The method is based upon expanding various time functions in the system as their truncated hybrid functions. The operational matrix of product is introduced. This matrix together with the operational matrix of integration are utilized to reduce the solution of controlled Duffing oscillator to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.     

Spectral Analysis of Powers of the Operator (Vf)(x)=q(x)∫0 xw(t)f(t),dt

Mathematical Notes -     

The numerical approximation of center manifolds in Hamiltonian systems

In this paper we develop a numerical method for computing higher order local approximations of center manifolds near steady states in Hamiltonian systems. The underlying system is assumed to be large in the sense that a large sparse Jacobian at the equilibrium occurs, for which only a linear solver and a low-dimensional invariant subspace is available. Our method combines this restriction from linear algebra with the requirement that the center manifold is parametrized by a symplectic mapping and that the reduced equation preserves the Hamiltonian form. Our approach can be considered as a special adaptation of a general method from Numer. Math. 80 (1998) 1-38 to the Hamiltonian case such that approximations of the reduced Hamiltonian are obtained simultaneously. As an application we treat a finite difference system for an elliptic problem on an infinite strip.