A TVD-WAF-based hybrid finite volume and finite difference scheme for nonlinearly dispersive wave equations

A total variation diminishing-weighted average flux(TVD-WAF)-based hybrid numerical scheme for the enhanced version of nonlinearly dispersive Boussinesq-type equations was developed. The one-dimensional governing equations were rewritten in the conservative form and then discretized on a uniform grid. The finite volume method was used to discretize the flux term while the remaining terms were approximated with the finite difference method. The second-order TVD-WAF method was employed in conjunction with the Harten-Lax-van Leer(HLL) Riemann solver to calculate the numerical flux, and the variables at the cell interface for the local Riemann problem were reconstructed via the fourthorder monotone upstream-centered scheme for conservation laws(MUSCL). The time marching scheme based on the third-order TVD RungeKutta method was used to obtain numerical solutions. The model was validated through a series of numerical tests, in which wave breaking and a moving shoreline were treated. The good agreement between the computed results, documented analytical solutions, and experimental data demonstrates the correct discretization of the governing equations and high accuracy of the proposed scheme, and also conforms the advantages of the proposed shock-capturing scheme for the enhanced version of the Boussinesq model, including the convenience in the treatment of wave breaking and moving shorelines and without the need for a numerical filter.     

二维浅水方程的非结构网格数值解

用Lax-W endroff格式和Lax-Friedrichs格式交替使用形成的复合型格式,对二维浅水方程在非结构网格上进行离散,利用不同格式之间数值耗散、数值色散而相互补偿和抵消的复合作用,消除数值计算中出现的非物理振荡和过度光滑现象.利用本文算法对斜水跃问题、二维矩形部分溃坝模型和二维圆形全溃模型模拟的结果表明,该算法具有较高的涌波捕捉能力,适合处理边界面复杂的浅水流动问题.     

一类椭圆型方程的快速解法—ELLIP程序包简介

本文发展了一种用FFT解一类椭圆型方程的快速程序包ELLIP。用这个程序包可以克服Hockney的POT1程序包的许多限制,拓宽了应用范围,具有推广价值。     

电磁制动对薄板坯连铸结晶器中流场的影响

本文采用不可压缩ＭＨＤ方程及零方程湍流模式，数值计算了加电磁制动器的二维薄板坯连铸结晶器中的流场。计算表明，电磁制动对于抑制涡旋、改善薄板坯连铸结晶器中的流场有明显效果。     

线性椭圆型方程的数值网格生成方法

用椭圆方程生成的数值网格是一种贴体网格；传统的网格生成方法需求解一组非线性的椭圆型偏微分方程，非线性椭圆型方程的求解非常困难且精度以影响，本文对此进行了深入的理论研究，提出了“用求解线性的椭圆型方程直接生成贴体网格”的新方法；新方法简单且易于实现，并从理论上克服了传统方法存在的不足，因此，它对计算流体力学的发展具有一定的理论意义和实用价值。     

Hydrodynamic model of vessel-generated currents

The drawdown and return currents of vessels navigating in channels have previously been described by empirical relations or by using physical models. The empirical solutions are generally limited in scope to idealized channel shapes. Physical models are unrestricted in this respect, but have limitations related to expense and scale effects. In this paper, vessel effects are modelled numerically. The vessel's displacement is represented by a moving pressure field. The movement of the pressure field is spatially varied in time, representing a vessel navigating along a channel. The hydrodynamics are described using the two-dimensional shallow water equations, which are modified to account for the effects of the imposed pressure field. A Petrov—Galerkin finite-element scheme using characteristic-based weighting is used to solve the governing equations. This Petrov—Galerkin test function is specifically designed to model flow fields containing large gradients such as those found in the vicinity of the moving vessel. The numerical results for return flows and water surface elevations are compared with flume results of vessel passages.     

用密度函数法对自由表面进行数值模拟

本文从二维非定常N-S方程出发，提出了一种处理自由表面问题的数值方法。引入密度函数法(density-function method)追踪自由表面，在密度函数的传输方程中采用TVD格式达到了二阶精度。对均匀来流中的非定常不可压方柱绕流进行了数值模拟。数值结果成功地捕捉了自由表面波动以及漩涡的生成、分离的时间发展历程。同时验证了本方法的有效性。     

河道及河口一维及二维嵌套泥沙数学模型

建立了一种河道及河口一、二维嵌套的泥沙数学模型，对基本的控制方程、方程的离散和求解方法、嵌套连接条件以及非均匀沙的处理等问题进行了研究。以非恒定非均匀不平衡输沙理论作为本文建模的基础，为方便处理，通过交界面的水位、流量和含沙量等的传递，在每一迭代内进行耦合计算。数值模拟结果与实测资料吻合较好，且计算省时，表明本文建立的嵌套模型是一种解决某些实际工程问题的可靠的和高效的工具。     

Risk based capital for guaranteed minimum withdrawal benefit

The guaranteed minimum withdrawal benefit (GMWB), which is sold as a rider to variable annuity contracts, guarantees the return of total purchase payment regardless of the performance of the underlying investment funds. The valuation of GMWB has been extensively covered in the previous literature, but a more challenging problem is the computation of the risk based capital for risk management and regulatory reasons. One needs to find the tail distribution of the profit–loss function, which differs from its expected payoff required for pricing the GMWB contract. GMWB has embedded two option-like features: Management fees are proportional to the current value of the policyholder’s account which results in an average price of the account. Thus the contract resembles an Asian option. However, the fees are charged only up to the time of the account hitting zero which resembles a barrier option payoff. Thus the GMWB is mathematically more complicated than Asian or barrier options traded on the financial markets. To the authors’ best knowledge, this is the first paper in the literature to formulate and analyse profit–loss distribution using PDE methods of such a product with intricate option-like features. Our approach is much more efficient than the current market practice of rather intensive and expensive Monte Carlo simulations due to the lack of samples for extreme cases.     

On non-ergodic asset prices

We investigate the asset prices dynamics and the long-run market shares of two competing financial mediators who are selected by consumers. We demonstrate that the social interaction among consumers constitutes an endogenous path-depending source of risk in a financial market. Depending on consumers’ evaluation of the mediator’s investment, asset prices may behave in a non-ergodic manner: the price process converges in distribution but the limiting distribution is not necessarily uniquely determined, its multiplicity being characterized by the multiplicity of possible long-run market shares. The convergence of the process is sensitive to initial conditions and depends on the history of noise-trader transactions. Long-run portfolio holdings may be in-efficient since investors holding mean-variance efficient portfolios may not be identified.