黑体辐射逆问题方程解的唯一性与Riemann假设

黑体辐射反演是黑体辐射研究中提出的新课题.在实际应用中,许多物体的表面温度分布(a(T)),难以直接测量,但其温度辐射功率谱W(v)可以被测量,此文给出一个由功率谱W(v)获得表面温度分布a(T)的严格解并讨论其解的唯一性.     

New solitary wave solutions of (2+1)-dimensional space–time fractional Burgers equation and Korteweg–de Vries equation

In this article, via the improved fractional subequation method, the fully analytical solutions of the (2+1)-dimensional space–time fractional Burgers equation and Korteweg–de Vries equation involving Jumarie’s modified Riemann–Liouville derivative have been derived. As a result, with the aid of symbolic computation, many types of new analytical solutions are obtained, which include new solitary wave, periodic wave and rational wave solutions. The graphical representations show that these gained solutions have abundant structures.     

Interaction of a shock pulse with a contact discontinuity

Passing of a triangular moderate-intensity pulse through a constant discontinuity is considered. Decay of the shock wave that passed into the second gas is analyzed. Damping of the detonation wave after burnout of the combustible mixture is discussed. __________ Translated from Fizika Goreniya i Vzryva, Vol. 43, No. 4, pp. 102–107, July–August, 2007.     

Numerical Simulation of Fluid-Structure Interaction Using Modified Ghost Fluid Method and Naviers Equations

In this work, we deal with the 1D compressible fluid coupled with elastic solid in an Eulerian-Lagrangian system. To facilitate the analysis, the Naviers equation for elastic solid is cast into a 2×2 system similar to the Euler equation but in Lagrangian coordinate. The modified Ghost Fluid Method is employed to treat the fluid-elastic solid coupling, where an Eulerian-Lagrangian Riemann problem is defined and a nonlinear characteristic from the fluid and a Riemann invariant from the solid are used to predict and define the ghost fluid states. Theoretical analysis shows that the present approach is accurate in the sense of approximating the solution of the Riemann problem at the interface. Numerical validation of this approach is also accomplished by extensive comparison to 1D problems (both water-solid and gas-solid) with their respective analytical solutions. T.G. Liu’s current address: Department of Mathematics, Beijing University of Aeronautics and Astronautics, Beijing 100083. email: liutg@buaa.edu.cn.     

Numerical simulation of one‐dimensional flows through porous media with shock waves

This work studies an unsaturated flow of a Newtonian fluid through a rigid porous matrix, using a mixture theory approach in its modelling. The mixture consists of three overlapping continuous constituents: a solid (porous medium), a liquid (Newtonian fluid) and an inert gas (to account for the mixture compressibility). A set of two nonlinear partial differential equations describes the problem, which is approximated by means of a Glimm's scheme, combined with an operator splitting technique. Copyright © 2001 John Wiley & Sons, Ltd.     

基于有限体积法及FDS格式的感潮河段二维泥沙冲淤模型

本文以木兰溪下游裁弯河段为例，建立了有限体积法的水平二维非恒定流均匀沙不平衡输移计算模型。采用黎曼近似解通量差分裂(FDS)格式计算通过各单元边的水流、含沙量法向数值通量，并应用相关的悬移质、推移质河床变形计算公式计算冲淤变化。数值模型经相应的河工模型试验资料率定、检验后，预测了裁弯工程建成后河道可能的冲淤变化，为工程设计和施工提供依据。     

共轭解析函数的Riemann边值问题

提出了相应于Ｃａｕｃｈｙ型积分的Ｃａｕｃｈｙ型共轭积分，并用它来求Ｒｉｅｍａｎｎ边值的分片共轭解析函数的解。     

Computing the velocity of a rotating flow

To compute the time-dependent flow of a rotating incompressible fluid we consider the velocity–vorticity formulation of the Navier–Stokes equations in cylindrical coordinates. In the numerical method employed the velocity field at each time-step is found as the least squares solution of an overdetermined system of linear equations, Ax=b. We consider how to compute x using the preconditioned conjugate gradient algorithm for least squares (PCGLS) on a distributed parallel computer. The various aspects of using a parallel computer are discussed, and results for a wide range of parallel computers are presented. The parallel speed-up depends on the architecture but is typically about 80% of the number of processors used.     

The generalized Riemann problem method for the shallow water equations with bottom topography

This paper extends the generalized Riemann problem method (GRP) to the system of shallow water equations with bottom topography. The main contribution is that the generalized Riemann problem method (J. Comput. Phys. 1984; 55 (1):1–32) is used to evaluate the midpoint values of solutions at each cell interface so that the bottom topography effect is included in numerical fluxes, and at the same step the source term is discretized with an interface method in which only mid‐point values are plugged in. This scheme is well balanced between the flux gradient and bottom topography when incorporating the surface gradient method (SGM) (J. Comput. Phys. 2001; 168 (1):1–25) into data reconstruction step, and it is also suitable for both steady and unsteady flow simulations. We illustrate the accuracy of this scheme by several 1‐D and 2‐D numerical experiments. Copyright © 2005 John Wiley & Sons, Ltd.     

Boundary control of linearized Saint-Venant equations oscillating modes

The paper investigates the control of oscillating modes occurring in open-channels, due to the reflection of propagating waves on the boundaries. These modes are well represented by linearized Saint-Venant equations, a set of hyperbolic partial differential equations which describe the dynamics of one-dimensional open-channel flow around a given stationary regime. We use a distributed transfer function approach to compute a dynamic boundary controller that cancels the oscillating modes over all the canal pool. This result is recovered with a Riemann invariants approach in the case of a frictionless horizontal canal pool. The effect of a proportional boundary control on the poles of the transfer matrix is then characterized by a root locus, and we derive an asymptotic result for high frequencies closed-loop poles.